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标题: Portfolio Management【Reading 60】Sample [打印本页]

作者: tango_gs 时间: 2012-4-2 17:56 标题: [2012 L2] Portfolio Management【Session 18- Reading 60】Sample

Mean-variance analysis assumes that investor preferences depend on all of the following EXCEPT:

A)	correlations among asset returns.

B)	skewness of the distribution of asset returns.

C)	expected asset returns.

Mean-variance analysis assumes that investors only need to know expected returns, variances, and covariances in order create optimal portfolios. The skewness of the distribution of expected returns can be ignored.

作者: tango_gs 时间: 2012-4-2 17:56

One of the assumptions of mean-variance analysis is that all investors are risk-averse, which means they:

A)	are not willing to make risky investments.

B)	prefer less risk to more for any given level of volatility.

C)	prefer less risk to more for any given level of expected return.

In mean-variance analysis we assume that all investors are risk averse, which means they prefer less risk to more for any given level of expected return (NOT for any given level of volatility.) It does NOT mean that they are unwilling to take on any risk.

作者: tango_gs 时间: 2012-4-2 17:57

What are the expected return and expected standard deviation for the two-asset portfolio described as:

Expected Return/Correlation
Variance
Weight

E(R1) = 10%
Var(1) = 9%
w1 = 30%

E(R2) = 15%
Var(2) = 25%
w2 = 70%

r1,2 = 0.4

E(Rport)

σport

10.5%

15.58%

13.5%

39.47%

11.5%

3.95%

E(Rport) = w1E(R1) + w2E(R2) = (0.3)(10.0) + (0.7)(15.0) = 13.5%
σport = [(w1)2(σ1)2 + (w2)2(σ2)2 + 2w1w2σ1σ2ρ1,2]1/2
= [(0.3)2(0.09) + (0.7)2(0.25) + 2(0.3)(0.7)(0.3)(0.5)(0.4)]1/2 = 39.47%

作者: tango_gs 时间: 2012-4-2 17:58

Allen Marko, CFA, is analyzing the diversification benefits available from investing in three equity funds. He is basing his analysis on monthly returns for the three funds and an appropriate market index over the past twenty years. He feels that there is no reason that the past performance should not carry forward into the future. Treasury bills currently pay 5%.

Table 1: Expected Returns, Variances, and Covariance for Funds A, B, & C

Equity Fund A
Equity Fund B
Equity Fund C

Average Return
12%
9%
8%

Variance
0.0256
0.0196
0.0172

Correlation of A & B is 0.50
Correlation of A & C is 0.38
Correlation of B & C is 0.85

Marko has also obtained information about a fourth fund, Fund D. He does not have any information regarding the covariance of Fund D with Funds A, B, and C. The average return and variance for fund D are 10% and 0.018, respectively. The beta of Fund D is 0.714. Based on this data, what is the expected return of a portfolio that is made up of 60% of Fund A, 30% of Fund B, and 10% of Fund C?

10.2%.

10.7%.

11.4%.

Expected return for the portfolio = (0.6)(0.12) + (0.3)(0.09) +(0.1)(0.08)= 0.107 or 10.7%. (Study Session 18, LOS 60.a)

Which of the following is closest to the standard deviation of a portfolio that is made up of 60% of Fund A, 30% of Fund B, and 10% of Fund C?

14.840%.

2.205%.

13.062%.

Standard deviation of a three asset portfolio:

σportfolio = [(0.6)2(0.0256) + (0.3)2(0.0196) + (0.1)2(0.0172) + 2(0.60)(0.30)(0.50)(0.16)(0.14) + 2(0.60)(0.10)(0.38)(0.16)(0.13)+ 2(0.3)(0.1)(0.85)(0.14)(0.13)]0.5

= [0.017062]1/2 = 0.13062 or 13.062%.

(Study Session 18, LOS 60.a)

With respect to the relative efficiencies of the Funds, which of the following is most accurate?

A)	Fund B is inefficient relative to Fund D.

B)	No determination is possible.

C)	Fund B and D are both inefficient.

To be inefficient, the return must be lower while the variance is higher. The only case where that relationship exists is with respect to Fund B and D. (Study Session 18, LOS 60.b)

If Marko had to choose to form a portfolio using only T-bills and one of the four funds, which should he choose?

Fund A.

Fund B.

Fund D.

The easiest way to approach this question is to calculate the Sharpe ratio for each fund and choose the one with the highest ratio. The highest Sharpe ratio reflects the highest excess return for a given level of risk.
The Sharpe ratios are as follows:

Fund A = (12 − 5) / 16.00 = 0.44

Fund B = (9 − 5) / 14.00 = 0.29

Fund D = (10 − 5) / 13.42 = 0.37

Fund A has the highest Sharpe ratio and therefore would be the best one to combine with T-bills.
An alternative way to answer the question can be seen by combining Fund A with T-bills in a portfolio to get an average/expected return equal to each of the other portfolios and computing the variance for each of those portfolios. Then compare the variance of the portfolio composed of A and the T-bills to the corresponding variance of the other asset.
To find the appropriate weights for the portfolio to earn the return of Fund B, solve for W in the following equation: 9% = W × 12% + (1 − W) × 5%. The solution is W = 0.5714.
0.5714 in Fund A and 0.429 in T-bills has a variance equal to (0.5714)(0.5714)(0.0256) = 0.00836.
Applying the same procedure to Fund D gives W = 0.80
0.80 in Fund D and 0.20 in T-bills has a variance equal to (0.80)(0.80)(0.018) = 0.01152.
Thus, a CAL formed with Fund A can dominate the CAL of each of the other three portfolios. (Study Session 18, LOS 60.d)

Which of the following statements regarding the graph of return vs. risk for all possible portfolio combinations consisting of Funds A, B, and C is least accurate?

A)	Combinations of Fund A, B, and C will dominate all other combinations of portfolios that have a lower return for the same level of risk.

B)	If the objective of the portfolio manager is to minimize risk the optimal portfolio must lie on the curved line below the minimum-variance portfolio.

C)	If the objective of the portfolio manager is to maximize return the optimal portfolio must lie on the curved line above the minimum-variance portfolio.

The curved line below the minimum-variance portfolio represents all portfolio combinations that are dominated by other portfolio combinations. Based on the efficient frontier created by these two funds higher returns at the same level of risk can be achieved above the minimum-variance portfolio. (Study Session 18, LOS 60.b)

The beta of Fund A is 1.2, the expected return of T-bills is 5% and the standard deviation for the market is 13%. What is the covariance between the market portfolio and Fund A?

0.020.

0.081.

0.156.

The beta for fund A is equal to the covariance of fund A and the market divided by the variance of the market. Therefore, 1.2 = COV(A,Market) / (0.13)2
Solving for COV(A,Market) = (1.2)(0.13)2 = 0.0203. (Study Session 18, LOS 60.a)

作者: tango_gs 时间: 2012-4-2 18:00

Sandy Wilson is a research analyst for WWW Equities Investments. She has just finished collecting the information on Table 1 to answer questions posed by her supervisor, Jackie Lewis. For example, using the Capital Market Line (CML), Lewis wants to know the market price of risk. Also, given all the attention paid to index funds in recent years, Lewis asked Wilson to see if any one of the securities would prove a better investment than the S&P 500. If not, can she compose a portfolio from stocks A, B, and C that is more efficient than the S&P 500?
Lewis wants Wilson to explore whether the results on Table 1 are congruent with the Capital Asset Pricing Model (CAPM). Using a regression analysis where the S&P 500 represents the market portfolio, she computes the beta of Stock A, and finds that it equals one. Using this, she will derive the betas of the other stocks and compare them to betas estimated with other techniques. As she performs her calculations, she reviews reasons why her results might not be congruent with the CAPM. Lewis asserts that the S&P 500 may not be a good proxy for “the market portfolio” needed for CAPM calculations.

Table 1

Expected Return and Risk for Selected Investments
Investment
Expected Return
Standard Deviation

Stock A
12%
30%

Stock B
15%
35%

Stock C
11%
40%

S&P 500
12%
22%

Treasury Bills
3%
0%

Correlation Coefficient for Stocks A and B equals 0.4.
Correlation Coefficient for Stocks A and C equals -0.5.
Correlation Coefficient for Stocks B and C equals 0.1.

Assuming that the S&P 500 is the market portfolio and her estimates are accurate, what is the price of risk based on the slope of the Capital Market Line (CML)?

0.409.

0.545.

0.250.

The market price of risk, or return per unit of standard deviation risk, is determined as follows: (0.12 − 0.03) / 0.22 = (0.09 / 0.22) = 0.409. (Study Session 18, LOS 60.d)

What is the expected return and standard deviation of a portfolio that consists of 40% of stock A and 60% of stock B?

A)	Expected Return: 13.8%, Standard Deviation: 29.5%.

B)	Expected Return: 13.8%, Standard Deviation: 28.0%.

C)	Expected Return: 13.8%, Standard Deviation: 33.0%.

E(RP) = 0.4(0.12) + 0.6(0.15) = 0.048 + 0.09 = 0.138 or 13.8%The portfolio standard deviation is:
[(0.4)2(0.3)2 + (0.6)2(0.35)2 + 2(0.4)(0.6)(0.3)(0.35)(0.4)]0.5 = [0.0144 + 0.0441 + 0.02016]0.5 = 0.2805
(Study Session 18, LOS 60.a)

Wilson uses the computed beta of stock A, the covariance of stock A and B, and their standard deviations to compute stock B’s beta. Given stock B’s expected return, the results are:

A)	not congruent with the CAPM, which does not support Lewis’ assertion concerning the S&P 500 as a proxy for the market.

B)	congruent with the CAPM, which does not support Lewis’ assertion concerning the S&P 500 as a proxy for the market.

C)	not congruent with the CAPM, which supports Lewis’ assertion concerning the S&P 500 as a proxy for the market.

The provided standard deviations and covariance and the beta of stock A can be entered into the following relationship:
covariance(A,B)=(beta of A) × (beta of B) × (Variance of market) gives us
(0.3 × 0.35 × 0.40) = 0.042 = 1 × (beta of B) × (0.22 × 0.22)
beta of B = 0.042 / 0.0484 = 0.868.
expected return of B = risk free rate + (beta of B) × (Market risk premium),
expected return of B = 0.03 + (0.868) × (0.12 − 0.03) = 0.108 < 0.15, which is the expected return she computed from her analysis. One explanation for this is that the S&P 500 is not a good proxy for the market portfolio. (Study Session 18, LOS 60.a,g)

Based upon the given information, can Wilson compose a portfolio with any one of the three stocks and Treasury bills that is more efficient than the S&P 500?

A)	No, the S&P 500 is more efficient than any of the individual stocks.

B)	Yes, stock B.

C)	Yes, stock A.

To investigate this, Wilson can first rule out stocks A and C. Both of them have an expected return that is less than or equal to the S&P 500, but their standard deviations are higher. Wilson must perform some calculations to see if stock B is more efficient than the S&P 500. Wilson would first determine the portfolio weights that can make the expected return of the stock B and T-bill portfolio equal to the S&P 500 portfolio. By setting up 0.12 = w × 0.15 + (1 − w) × 0.03 and solving for w, Wilson finds that a (0.75 / 0.25) stock B/T-bill portfolio has the same expected return of 0.12. The standard deviation of that portfolio is (0.75 × 35%) = 26.25% > 24% which is the standard deviation of the S&P 500. Thus, the portfolio using Stock B and Treasury bills is not more efficient than the S&P 500. (Study Session 18, LOS 60.b)

With regard to the capital allocation line (CAL), moving along the CAL above the point of the tangency portfolio represents:

A)	borrowing at the risk-free rate to be invested in more than 100% of the tangency portfolio.

B)	buying T-bills to reduce risk yet still maximize efficiency by being on the CAL.

C)	increasing risk exposure by being above the efficient frontier.

Moving along the CAL above the tangency portfolio represents borrowing at the risk free rate (shorting T-bills) to invest in more than your original capital in the tangency portfolio. The CAL becomes the efficient frontier when the risk free asset is available to invest in. (Study Session 18, LOS 60.d)

Which of the following is least likely an assumption of the Capital Asset Pricing Model (CAPM)?

A)	Capital markets are perfectly competitive and all assets are marketable.

B)	The distribution of investors' forecasts of a given asset’s return is normal.

C)	Investors can borrow and lend at the risk-free rate.

The CAPM assumes that investors have the same forecast of a given asset’s return. Thus, according to the required assumption, the distribution will not be normal because the variance of the forecasts is zero. (Study Session 18, LOS 60.e)

作者: luckygiftvn 时间: 2012-4-2 18:22

Given the following information, what is the expected return on the portfolio of the two funds?

The Washington Fund
The Jefferson Fund

Expected Return
30%
36%

Variance
0.0576
0.1024

Investment
$2,000,000
$6,000,000

Correlation
0.40

33.0%.

34.5%.

31.5%.

First calculate the portfolio weights on each fund:

WWash = $2 million/$8 million = 0.25
WJeff = $6 million/$8 million = 0.75

The expected portfolio return is the weighted average of the funds' expected returns:

E(RP) = (0.25)(30%) + (0.75)(36%) = 34.5%.

作者: luckygiftvn 时间: 2012-4-2 18:22

Which of the following statements is least accurate regarding modern portfolio theory?

A)	The capital market line is developed under the assumption that investors can borrow or lend at the risk-free rate.

B)	All portfolios on the capital allocation line are perfectly negatively correlated.

C)	For a portfolio made up of the risk-free asset and a risky asset, the standard deviation is the weighted proportion of the standard deviation of the risky asset.

All portfolios on the capital allocation line are perfectly positively correlated. Both remaining statements are each true.

作者: luckygiftvn 时间: 2012-4-2 18:22

Joe Janikowski owns a portfolio consisting of 2 stocks. Janikowski has compiled the following information:

Stock	Topper Manufacturing		Base Construction
Expected Return (percent	12		11
Standard Deviation (percent)	10		15
Portfolio Weighting (percent)	75		25
Correlation		0.22

The expected return for the portfolio is:

11.50%.

12.00%.

11.75%.

Expected return is computed by weighting each stock as a percentage of the entire portfolio, and then multiplying each stock by the expected return. The expected return is: ((0.75 × 12) + (0.25 × 11)) = 11.75.

The standard deviation of the portfolio is closest to:

0.0909.

0.0839.

0.0070.

The formula for the standard deviation of a two-stock portfolio is: the square root of [((0.75)² × (0.10)²) + ((0.25)² × (0.15)²) + (2 × (0.75) × (0.25) × (0.22) × (0.15) × (0.10))] = 0.0909.

作者: luckygiftvn 时间: 2012-4-2 18:23

Andy Green, CFA, and Sue Hutchinson, CFA, are considering adding alternative investments to the portfolio they manage for a private client. They have found that it is recommended that a large, well-diversified portfolio like the one that they manage should include a 5 to 10% allocation in alternative investments such as commodities, distressed companies, emerging markets, etc.. After much discussion, Green and Hutchinson have decided that they will not choose individual assets themselves. Instead of choosing individual alternative investments, they will add a hedge fund to the portfolio. They decide to divide up their research by having each of them take a different focus. In their research of hedge funds, Green focuses on hedge funds that have the highest returns. Hutchinson focuses on finding hedge funds that can allow the client’s portfolio to lower risk while, with the use of leverage, maintain the same level of return.
After completing their research into finding appropriate hedge funds, Green proposes two hedge funds: the New Horizon Emerging Market Fund, which takes long-term positions in emerging markets, and the Hi Rise Real Estate Fund, which holds a highly leveraged real estate portfolio. Hutchinson proposes two hedge funds: the Quality Commodity Fund, which takes conservative long-term positions in commodities, and the Beta Naught Fund, which manages an equity long/short portfolio that has the goal of targeting the portfolio’s market risk to zero. The Beta Naught Fund engages in short-term pair trading to capture additional returns while keeping the beta of the fund equal to zero. The table below lists the statistics for the client’s portfolio without any alternative investments and for the four hedge funds based upon recent data. The expected return, standard deviation and beta of the client portfolio and the hedge funds are expected to have the same values in the near future. Green uses the market model to estimate covariances between portfolios with their respective betas and the variance of the market return. The variance of the market return is 324(%2).

Current Client Portfolio
New Horizon
Hi Rise Real Estate
Quality Commodity
Beta Naught

Average
10%
20%
10%
6%
4%

Std. Dev.
16%
50%
16%
16%
25%

Beta
0.8
0.9
0.4
-0.2
0

Green and Hutchinson have decided to sell off 10% of the current client portfolio and replace it with one of the four hedge funds. They have agreed to select the hedge fund that will provide the highest Sharpe Ratio when 10% of the client’s portfolio is allocated to that hedge fund.
As an alternative to investing 10% in one hedge fund, Green and Hutchinson have discussed investing 5% in the Beta Naught Fund and 5% in one of the other three hedge funds. This new 50/50 hedge fund portfolio would then serve as the 10% allocation in alternative investments for the client’s portfolio. Green and Hutchinson divided up their research into return enhancement and diversification benefits. Based upon the stated goals of their research, which of the two approaches is more likely to lead to an appropriate choice? The focus of:

A)	neither manager is appropriate and will not achieve a meaningful result.

B)	Green’s research.

C)	Hutchinson’s research.

Simply increasing return may not be appropriate if the risk level increases more than the return increases. Focusing on assets that help diversify the existing portfolio is more appropriate because any reduction in return can be offset by an increase in leverage. (Study Session 18, LOS 60.a, b)

Of the proposed hedge funds, which is most likely to introduce active risk into the client’s portfolio?

A)	Hi Rise Real Estate Fund.

B)	New Horizon Emerging Market Fund.

C)	The Beta Naught Fund.

The Beta Naught Fund is the only one that takes short-term positions. (Study Session 18, LOS 60.a)

Which of the following is closest to the expected return of the client’s portfolio if 10% of the portfolio is invested in the New Horizon Emerging Market Fund?

10.2%.

11.0%.

11.8%.

11% = (0.9 × 10%) + (0.1 × 20%) (Study Session 18, LOS 60.a)

Which of the following is closest to the expected standard deviation of the client’s portfolio if 10% of the portfolio is invested in the Quality Commodity Fund?

9.6%.

14.2%.

16.0%.

The market model offers a simple way to estimate the covariance between two assets, using the beta of each asset and the variance of the market return. Here, covariance is -51.84 = 0.8 × (-0.2) × 324. The variance of the new client portfolio is 200.59 = (0.9 × 0.9 × 16 × 16) + (0.1 × 0.1 × 16 × 16) + (2 × 0.9 × 0.1 × (-51.84)). The square root of the variance of the new client portfolio is approximately 14.2%. (Study Session 18, LOS 60.a,g)

Which of the following is closest to the expected return of a portfolio that consists of 90% of the original client’s portfolio, 5% of the Hi Rise Real Estate Fund and 5% in the Beta Naught Fund?

9.0%.

9.7%.

10.4%.

9.7% = (0.9 × 10%) + (0.05 × 10%) + (0.05 × 4%) (Study Session 18, LOS 60.a)

There was a discussion of allocating 5% each in Beta Naught and one of the other funds. When combined with Beta Naught in a 50/50 portfolio, which of the other three funds will produce a portfolio that has the lowest standard deviation?

A)	Either Hi Rise or Quality Commodity.

B)	New Horizon only.

C)	Quality Commodity only.

Since the beta of Beta Naught is zero, its covariance with any of the other funds is zero. Thus, the lowest standard deviation will be achieved with the fund with the lowest standard deviation. Since Hi Rise and Quality Commodity have the same standard deviation, which is less than New Horizon, either of them would produce the same result. (Study Session 18, LOS 60.a)

作者: luckygiftvn 时间: 2012-4-2 18:23

Which of the portfolios represented in the table below are NOT efficient?

Portfolio
A
B
C
D
E
F
G
H
(Rp)
10%
12.5%
15%
16%
17%
18%
18%
20%
sp
23%
21%
25%
29%
29%
32%
35%
45%

A)	B, D, and F.

B)	A, D, and G.

C)	B, E, and F.

Relative to any other portfolio, an inefficient portfolio has greater risk at the same return (portfolio G), less return at the same level of risk (portfolio D), or less return and more risk (portfolio A).

作者: luckygiftvn 时间: 2012-4-2 18:24

The efficient frontier enables managers to reduce that number of possible portfolios considered because the portfolios on the efficient frontier:

A)	have lower risk levels for every level of expected return than all other possible portfolios.

B)	have higher risk levels for every level of expected return than all other possible portfolios.

C)	have higher expected returns for every level of risk than all other possible portfolios.

If we are selecting portfolios from a large number of stocks, say the S&P 500, rather than just two stocks, the number of possible combinations is extremely large. We can restrict our search for possible portfolio combinations by focusing on those portfolios on the efficient frontier. We know they dominate all the other possible choices because they offer higher return for the same level of risk.
The minimum-variance frontier consists of portfolios that have lower risk levels for every level of expected return than all other possible portfolios.

作者: luckygiftvn 时间: 2012-4-2 18:24

An analyst has gathered the following data:

Portfolio
Weight S&P(%)
Weight EAFE(%)
PORT σ (%)
E(Rp)(%)
A

100
0
10
10
B

70
30
6
C

30
70
11
D

0
100
15
20

Which portfolio represents the minimum variance portfolio?

A)	Portfolio C.

B)	Portfolio B.

C)	Portfolio A.

Minimum variance portfolio among the choices presented is portfolio B (70% S&P, 30% EAFE).

For a U.S. investor with extreme risk aversion, is there a benefit to international diversification?

A)	Yes, since a 100% weighting in international stocks results in a doubling of the expected return with only a 50% increase in risk.

B)	Yes, since a 30% weighting in the EAFE index results in an increased return and decreased standard deviation than 100% investment in the S&P index.

C)	Yes, since a 70% weighting in the EAFE index results in a much higher expected return with a minimal increase in portfolio standard deviation than 100% investment in the S&P index.

To answer this question, it is necessary to complete the table.
ERportB = (0.70)(10) + (0.30)(20) = 13
ERportC = (0.30)(10) + (0.70)(20) = 17

Portfolio	Weight S&P(%)	Weight EAFE(%)	PORTσ(%)	E(Rp)(%)
A	100	0	10	10
B	70	30	6	13
C	30	70	11	17
D	0	100	15	20

For portfolio B, the addition of EAFE is return enhancing and risk reducing, so even in the presence of extreme risk aversion there is a benefit. By choosing portfolio B, E(r) increases to 13% and portfolio risk decreases to 6%. For portfolios C and D, returns are increasing but so is the risk level. Both of these risk-return trade-offs may have some merit, but we cannot be sure in the presence of extreme risk aversion.

Assume the annual Treasury bill (T-bill) yields 4%. Which portfolio is the most desirable (i.e., highest Sharpe ratio)?

A)	Portfolio B.

B)	Portfolio A.

C)	Portfolio C.

Sharpe (Portfolio A) = (10 – 4) / 10 = 0.60

Sharpe (Portfolio B) = (13 – 4) / 6 = 1.5

Sharpe (Portfolio C) = (17 – 4) / 11 = 1.18

作者: luckygiftvn 时间: 2012-4-2 18:25

The efficient frontier consists of portfolios that have:

A)	the minimum standard deviation for any given level of expected return.

B)	the maximum expected return for any given standard deviation.

C)	capital allocation lines with slopes greater than 1.0.

The efficient frontier consists of (efficient) portfolios that have the maximum expected return for any given standard deviation. The efficient frontier starts at the global minimum-variance portfolio and continues above it on the minimum variance frontier. The minimum-variance frontier is the expected return-standard deviation combinations of the set of portfolios that have the minimum variance for every given level of expected return. Efficient portfolios can have capital allocation line (CAL) slopes less than 1.0. These slopes, however, will all be less than that of the CAL of the market portfolio (the capital market line).

作者: luckygiftvn 时间: 2012-4-2 18:25

The portfolio on the minimum-variance frontier that has the smallest standard deviation is the:

A)	market portfolio.

B)	global minimum-variance portfolio.

C)	optimal efficient portfolio.

The global minimum-variance portfolio is the portfolio on the minimum-variance frontier that has the smallest standard deviation (or variance). It is the portfolio at the tip of the bullet. The market portfolio, in which each asset is held in proportion to its market value, cannot have the smallest standard deviation of the portfolios on the minimum variance frontier.

作者: luckygiftvn 时间: 2012-4-2 18:25

When solving for the minimum-variance frontier for many assets, the constraint is:

A)	portfolio weights must sum to one.

B)	weighted-average covariances must sum to zero.

C)	weighted-average expected asset returns must sum to expected portfolio return.

This is the second step in determining the minimum-variance frontier. For every expected return between the smallest and largest expected return, determine the single portfolio with the smallest variance. We assume that the portfolio weights add up to one (this is the constraint on the portfolio weights). This step requires expected returns, variances, and covariances to calculate expected return and variance of the portfolios.

作者: luckygiftvn 时间: 2012-4-2 18:25

The efficient frontier is useful for portfolio management because:

A)	portfolios on the efficient frontier are useful as factor portfolios.

B)	portfolios on the efficient frontier are optimal: the correlation between each efficient portfolio, and the market portfolio is negative.

C)	it significantly reduces the number of portfolios a manager must consider.

作者: luckygiftvn 时间: 2012-4-2 18:26

Chris McDonald, CFA, is a portfolio manager for InvesTrack, a firm that seeks to closely track a selected index or indexes with each of its funds. McDonald is analyzing the returns of several of InvesTrack’s managed funds. The primary fund, Marketrack, or the MT portfolio, tracks a combination of a major stock index, bond index, real estate index, and a precious metals index. The stock index in the MT portfolio closely follows the S&P 500. The weights on each of the indexes in the MT target portfolio are approximately the same as the weights that the analysts at InvesTrack have estimated for these assets in the overall economy. McDonald believes that the MT portfolio is more likely to lie on the efficient frontier than a portfolio of only stocks. In a recent discussion with his assistants, Joseph Kreager and Maria Ito, McDonald said the low correlations between classes such as precious metals and real estate in the portfolio will improve the diversification of the portfolio. Kreager proposes that the ultimate goal should be to combine assets to achieve the minimum variance portfolio on the efficient frontier.
McDonald proposes that the returns of the MT portfolio can serve as a better representation of a market portfolio than an index like the Dow Jones Industrial Average or the S&P 500, which many analysts and portfolio managers use as a market proxy. For example, he asserts that betas estimated using the MT portfolio will be a more realistic representation of systematic risk, and this will make the betas more reliable in decisions concerning the effects of diversification. Furthermore, he suggests that the capital asset line (CAL) based upon the MT portfolio should be steeper than that based upon the S&P 500 alone. Kreager claims that that the MT portfolio will only have steeper CAL if the average returns of the indexes other than the stock index in the MT tracking portfolio are higher than the S&P 500. Ito responds that MT portfolio CAL will be higher than the S&P 500 CAL only if the standard deviation of the returns of the other indexes in the MT tracking portfolio are lower than the S&P 500.
Recently a customer holding a position in TTX stock wanted to explore the purchase of shares in a real estate investment trust (REIT). McDonald ran a regression of the return of the stock on the return of the MT portfolio, and he also ran a regression of the REIT’s return on the return of MT portfolio. Using monthly returns over three years, the results of the market model regressions are:

(Return of the TTX stock)t = −0.006 + 1.28 × (Return of MT portfolio)t + εt

(Return of the REIT) t = 0.014 + 0.60 × (Return of MT portfolio) t + ηt

The annualized standard deviations of the monthly returns for each of these investments are σTTXstock = 38, σREIT = 24, and σMT = 16. McDonald asks Kreager to compute the variance covariance matrix based upon these results. He also asks Kreager to compute the standard deviation of the unexplained risk for each of the assets.
After performing the regressions, Kreager investigates the property of beta drift. Using a monthly time-series, he finds that the betas of both the TTX stock and the REIT both follow an AR(1) process:

βt+1 = 0.1 + 0.9 × βt-1

Using this AR(1) process, Kreager tries to determine if the covariance between the two assets will increase or decrease in the next time period. He assumes the variance of the MT portfolio will remain the same.
After viewing the statistics, Ito gathers information on the S&P 500 and finds that its average return is 12%, and the standard deviation is 20%. The current risk-free rate is 5%. She wants to investigate whether McDonald’s assertion that the MT portfolio CAL is steeper than the S&P 500 CAL is true. In Kreager and Ito's responses to McDonald’s proposition that the CAL of the MT portfolio should be steeper than that of the S&P 500:

A)	only one is correct.

B)	both are correct.

C)	both are incorrect.

Kreager asserts that the CAL will be steeper if the average returns on the non-stock indexes are greater than the S&P 500. The fact is that the slope, which is also called the Sharpe Ratio, also depends upon the standard deviation of the MT portfolio. Without further information, it is impossible to know if Kreager is correct, but his statement is clearly not correct taken in isolation.
Ito asserts that the CAL will be steeper if the standard deviations of the non-stock indexes are less than the S&P 500. The fact is that the slope, which is also called the Sharpe Ratio, also depends upon the return of the MT portfolio. Without further information, it is impossible to know if Ito is correct, but her statement is clearly not correct taken in isolation.

In response to Kreager’s assertion that the goal is to try to achieve the minimum variance portfolio on the efficient frontier, McDonald should:

A)	disagree under any circumstances.

agree.

C)	agree only if it can be achieved with long positions in assets.

Any portfolio on the efficient frontier with a return greater than the minimum variance portfolio can be combined with the risk-free asset to create a portfolio that has a superior risk-return tradeoff when compared with the minimum variance portfolio. Thus, achieving the minimum variance portfolio would not be a worthwhile goal.

With the given information, Ito finds that the CAL of the S&P 500 is equal to the CAL of the MT portfolio if the return of the MT portfolio equals:

8.6%.

10.6%.

11.4%.

The CAL of the S&P 500 is 0.35 = (12 − 5) / 20. To find the return that gives this slope for the CAL, Ito would solve for R in the expression 0.35 = (R − 5) / 16. This gives 5.6 = R − 5, R = 10.6.

作者: luckygiftvn 时间: 2012-4-2 18:27

An investor holds a single stock, Amgen, in her portfolio. She would like to add one additional stock to her portfolio. Which stock should she add to achieve the most diversification benefits?

Correlation Matrix

Fund
Amgen
WW
XX
ZZ

Amgen
1.0

WW
0.5
1.0

XX
0.1
-0.2
1.0

YY
0.3
0.4
0.8

ZZ
0.0
0.8
0.9
1.0

Stock WW.

Stock XX.

Stock ZZ.

As the correlation between assets decreases, the benefits of diversification increase. Of the three stocks, ZZ has the lowest correlation with Amgen.

作者: luckygiftvn 时间: 2012-4-2 18:27

It can be determined from the figure below that ρ2 is:

A)	between 0.2 and 1.0.

B)	between 0.0 and 0.2.

C)	between -1.0 and 0.2.

The diversification benefits are greater if the correlation between the returns of the assets in the portfolio is lower. If the correlation equals +1, the minimum variance frontier is a straight line and there is no benefit to diversification (ρ3). If the correlation equals = -1, the minimum variance frontier is two line segments (ρ1). Therefore ρ2 must be less than 0.2 and greater than –1.0. It could be equal to zero, but we can’t tell for sure given the information in the problem.

作者: luckygiftvn 时间: 2012-4-2 18:28

Matton, CFA, has been asked to invest $100,000, choosing one or more of the following three stocks. All stocks have the same expected return and standard deviation. The correlation matrix for the three stocks is given below:

Stock Correlations
X
Y
Z

X
1.00
0.15
0.70

Y
0.15
1.00
0.51

Z
0.70
0.51
1.00

Which of the three stocks, X, Y, and Z, should be included in the portfolio?

A)	X, Y, and Z.

B)	Any investment in the three stocks will result in the exact same expected return and risk.

C)	X and Y only.

Diversification benefits occur whenever a stock is added that is not perfectly positively correlated with other stocks in the portfolio. Since none of the stocks are perfectly positively correlated with the other stocks, it would be beneficial to purchase all three rather than just one or two stocks

作者: luckygiftvn 时间: 2012-4-2 18:28

Consider an equally-weighted portfolio comprised of seven assets in which the average asset variance equals 0.31 and the average covariance equals 0.27. What is the variance of the portfolio?

24.16%.

27.5%.

27.00%.

Portfolio variance = σ2p = (1 / n) σ 21 + [(n − 1) / n]cov = [(1 / 7) × 0.31] + [(6 / 7) × 0.27] = 0.044 + 0.231 = 0.275 = 27.5%

作者: luckygiftvn 时间: 2012-4-2 18:28

Consider an equally-weighted portfolio comprised of five assets in which the average asset standard deviation equals 0.57 and the average correlation between all asset pairs is −0.21. The variance of the portfolio is closest to:

1.82%.

1.00%.

10.00%.

Portfolio variance = σ2p = (1 / n) σ 21 + [(n - 1) / n]cov
ρ1,2 = (cov1,2) / (σ1 σ2) therefore cov1,2 = (ρ1,2)(σ1 σ2) = (−0.21)(0.57)(0.57) = −0.068
σ2 = (0.57)2 = 0.32
σ2p = (1 / 5)(0.32) + (4 / 5)(−0.068) = 0.064 + (−0.0544) = 0.0096 or 1.00%

作者: luckygiftvn 时间: 2012-4-2 18:28

Consider an equally-weighted portfolio comprised of 17 assets in which the average asset standard deviation equals 0.69 and the average covariance equals 0.36. What is the variance of the portfolio?

32.1%.

36.7%.

37.5%.

Portfolio variance = σ2p = (1 / n) σ 21 + [(n − 1) / n]cov = [(1 / 17) × 0.48] + [(16 / 17) × 0.36] = 0.028 + 0.339 = 0.367 = 36.7%

作者: luckygiftvn 时间: 2012-4-2 18:29

Which of the following statements regarding the capital market line (CML) is least accurate? The CML:

A)	implies that all portfolios on the CML are perfectly positively correlated.

B)	slope is equal to the expected return of the market portfolio minus the risk-free rate.

C)	dominates everything below the line on the original efficient frontier.

The slope of the CML = (the expected return of the market − the risk-free rate) / (the standard deviation of returns on the market portfolio)
Because the CML is a straight line, it implies that all the portfolios on the CML are perfectly positively correlated.

作者: luckygiftvn 时间: 2012-4-2 18:29

Which of the following statements regarding the capital market line (CML) is least accurate? The CML:

A)	implies that all portfolios on the CML are perfectly positively correlated.

B)	slope is equal to the expected return of the market portfolio minus the risk-free rate.

C)	dominates everything below the line on the original efficient frontier.

作者: luckygiftvn 时间: 2012-4-2 18:29

The capital market line (CML) is the capital allocation line with the:

A)	global minimum-variance portfolio as the tangency portfolio.

B)	market portfolio as the tangency portfolio.

C)	market portfolio as the global minimum-variance portfolio.

The CML is the capital allocation line (CAL) with the market portfolio as the tangency portfolio.

作者: luckygiftvn 时间: 2012-4-2 18:30

The equation of the capital market line (CML) says that the expected return on any portfolio equals the:

A)	risk-free rate plus the product of the market risk premium and the market's portfolio standard deviation.

B)	risk-free rate plus the product of the market price of risk and the portfolio's standard deviation.

C)	risk-free rate plus the product of the market price of risk and the market's portfolio standard deviation.

The CML is the capital allocation line with the market portfolio as the tangency portfolio. The equation of the CML is:

E(RP) = RF + [(E(RM) – RF)/sM] sp
where:
E(RM) = the expected return on the market portfolio, M
sM = the standard deviation of the market portfolio, M
RF = the risk-free return

The intercept is the risk-free rate, RF. The slope is equal to [(E(RT) – RF) / sT], where [E(RT) – RF] is the expected risk premium on the tangency portfolio.

作者: luckygiftvn 时间: 2012-4-2 18:30

Which of the following does NOT describe the capital allocation line (CAL)?

A)	The CAL is tangent to the minimum-variance frontier.

B)	It is the efficient frontier when a risk-free asset is available.

C)	It runs through the global minimum-variance portfolio.

If a risk-free investment is part of the investment opportunity set, then the efficient frontier is a straight line called the capital allocation line (CAL). The CAL is tangent to the minimum-variance frontier of risky assets; therefore, it cannot run through the global minimum-variance portfolio.

作者: luckygiftvn 时间: 2012-4-2 18:30

If a risk-free asset is part of the investment opportunity set, then the efficient frontier is a:

A)	curve called the minimum-variance frontier.

B)	curve called the efficient portfolio set.

C)	straight line called the capital allocation line (CAL).

If a risk-free investment is part of the investment opportunity set, then the efficient frontier is a straight line called the capital allocation line (CAL), whether or not risky asset correlations are equal to one. The y-intercept of the CAL is the risk-free rate. The CAL is tangent to the minimum-variance frontier of risky assets.

作者: luckygiftvn 时间: 2012-4-2 18:31

The capital allocation line (CAL) with the market portfolio as the tangency portfolio is the:

A)	minimum variance line.

B)	capital market line.

C)	security market line.

The capital market line is the capital allocation line with the market portfolio as the tangency portfolio.

作者: luckygiftvn 时间: 2012-4-2 18:31

Adrian Jones is the portfolio manager for Asset Allocators, Inc., (AAI). Jones has decided to alter her framework of analysis. Previously, Jones made recommendations among efficient portfolios of risky assets only. Now, Jones has decided to make recommendations that include the risk-free asset. The efficient frontier for Jones has changed shape from a:

A)	curve to the thick curve.

B)	line to a curve.

C)	curve to a line.

Initially, Jones selected only efficient portfolios comprising risky assets. Formally, Jones selected portfolios along the Markowitz efficient frontier (a curve). When Jones decided to add the risk-free asset, her efficient frontier changed from a curve (the Markowitz efficient frontier) to a line (the capital market line). The capital market line starts at the risk-free rate and extends along (tangent to) the Markowitz curve.

作者: luckygiftvn 时间: 2012-4-2 18:31

If an investors’ portfolio lies on the capital market line (CML) at the point where the CML touches the efficient frontier then this implies the investor has:

A)	less than 100% of their money invested in the market portfolio.

B)	100% of their funds invested in the market portfolio.

C)	a larger percentage of their money invested in the market portfolio and have loaned the remaining amount at the risk-free rate.

Portfolios that are on the CML where the CML touches the efficient frontier implies that 100% of investors funds should be invested in the market portfolio to achieve greatest utility.

作者: luckygiftvn 时间: 2012-4-2 18:32

Investment Management Inc. (IMI) uses the capital market line to make asset allocation recommendations. IMI derives the following forecasts:

Expected return on the market portfolio: 12%
Standard deviation on the market portfolio: 20%
Risk-free rate: 5%

Samuel Johnson seeks IMI’s advice for a portfolio asset allocation. Johnson informs IMI that he wants the standard deviation of the portfolio to equal one half of the standard deviation for the market portfolio. Using the capital market line, the expected return that IMI can provide subject to Johnson’s risk constraint is closest to:

6.0%.

8.5%.

7.5%.

The equation for the capital market line is:

Johnson requests the portfolio standard deviation to equal one half of the market portfolio standard deviation. The market portfolio standard deviation equals 20%. Therefore, Johnson’s portfolio should have a standard deviation equal to 10%. The intercept of the capital market line equals the risk free rate (5%), and the slope of the capital market line equals the Sharpe ratio for the market portfolio (35%). Therefore, using the capital market line, the expected return on Johnson’s portfolio will equal:

作者: luckygiftvn 时间: 2012-4-2 18:32

Portfolio Management Associates (PMA) provides asset allocation advice for pensions. PMA recommends that all their pension clients select an appropriate weighting of the risk-free asset and the market portfolio. PMA should explain to its clients that the market portfolio is selected because the market portfolio:

A)	maximizes return and minimizes risk.

B)	maximizes the Sharpe ratio.

C)	maximizes return.

The risk and return coordinate for the market portfolio is the tangency point for the capital market line (CML). The CML has the steepest slope of any possible portfolio combination. The slope of the CML is the Sharpe ratio. Therefore, the Sharpe ratio is highest for the market portfolio

作者: luckygiftvn 时间: 2012-4-2 18:33

The best possible risk-return trade-off attainable, given the investor’s expectations of expected returns, variances, and covariances, is represented by the:

A)	the slope of the minimum-variance frontier at the global minimum-variance portfolio.

B)	slope of the capital allocation line (CAL).

C)	standard deviation of the market portfolio.

We can interpret the slope coefficient [(E(RT) − RF) / sT] of the CAL the same way we do the slope of any straight line (it’s the change in E(RT) for a one unit change in sT). Thus, it represents the risk-return trade from moving along the CAL and how much additional expected return do we get for a one-unit increase in risk. Because the tangency portfolio T is the best portfolio, the slope of the CAL line represents the best possible risk-return trade-off attainable, given the investor’s expectations of expected returns, variances, and covariances.

作者: AndyNZ 时间: 2012-4-2 18:34

Which of the following is NOT an assumption necessary to derive the capital asset pricing model (CAPM)?

A)	Investors only need to know expected returns, variances, and covariances in order create optimal portfolios.

B)	Transactions costs are small for large investors.

C)	Investors are price takers whose buy and sell decisions don't affect asset prices.

The derivation of the CAPM requires the assumption that transactions costs, and taxes are zero for all investors. Both remaining choices are necessary assumptions.

作者: AndyNZ 时间: 2012-4-2 18:35

Which of the following is NOT a prediction of the capital asset pricing model (CAPM)?

A)	All investors hold an equally weighted market portfolio of all assets.

B)	All investors identify the same risky tangency portfolio and combine it with the risk-free asset to create their own optimal portfolios.

C)	The market price of risk is the slope of the capital market line.

The CAPM predicts that all investors hold the market portfolio - a portfolio in which each asset is held in proportion to its market value. This portfolio is value-weighted, not equally weighted. The capital allocation line is then the capital market line (CML) and the market price of risk is the slope of the CML. The security market line (SML) describes the relationship between asset risk and expected return, where risk is measured by beta.

作者: AndyNZ 时间: 2012-4-2 18:36

An investor is considering an investment. After a great deal of careful research he determines that the forecasted return on the investment is 15% and estimates the beta to be 2.0. The risk-free rate of interest is 3%, and the return on the market is 13%. Should the project be undertaken?

A)	No, the forecasted return is less than the expected return of 23%.

B)	Yes, the forecasted return is less than the expected return of 18%.

C)	Yes, the forecasted return is more than the expected return of 13%.

Per the Capital Asset Pricing Model (CAPM), the expected rate of return
= Rf + b[E(Rm) – Rf]
= 3 + 2(13.0 − 3.0) = 23%.

Since the forecated return of 15% is less than expected rate of return of 23%, the investment should not be undertaken.

作者: AndyNZ 时间: 2012-4-2 18:36

The market is expected to return 12% next year and the risk free rate is 6%. What is the expected rate of return on a stock with a beta of 0.9?

11.4.

13.0.

10.8.

ERstock = Rf + ( ERM − Rf ) Betastock.

作者: AndyNZ 时间: 2012-4-2 18:36

Figment, Inc., stock has a beta of 1.0 and a forecast return of 14%. The expected return on the market portfolio is 14%, and the long-run inflationary expectation is 3%. Which of the following statements is most accurate? Figment, Inc.’s stock:

A)	is properly valued.

B)	valuation relative to the market cannot be determined.

C)	is overvalued.

Since Figment, Inc.’s, stock has a beta equal to 1.0, then the expected return of this stock is equal to the expected return on the market portfolio, which also has a beta of 1.0. Since Figment’s expected return is equal to its required return, the stock is properly valued.

作者: AndyNZ 时间: 2012-4-2 18:36

Callard Corp. stock has a beta of 1.5. If the current risk-free interest rate is 6%, and the expected return on the market is 14%, what is the expected rate of return for Callard Corp.’s stock?

20%.

18%.

14%.

ERcc = 0.06 + 1.5(0.14 − 0.06) = 18%

作者: AndyNZ 时间: 2012-4-2 18:37

Howard Michaels, CFA, is an analyst for Donaldson Associates. Michaels is considering recommending a position in the retail sector for Donaldson’s institutional clients. Michaels has gathered the following information to help his guide his decision. Based on previous research, Michaels expects the market and Treasury bills to return 10% and 4%, respectively.

Company [td] $1 Discount Store	Everything $5 [/td]
Forecasted Return	12%	11%
Standard Deviation of Returns	8%	10%
Beta	1.5	1.0

What would be the expected return for each investment, assuming the capital asset pricing model (CAPM) holds?

Discount

Everything

13%

10%

19%

10%

19%

14%

The expected return is the return predicted by the CAPM for a given level of systematic risk (β). To calculate the expected return for each investment, use the following formula:

E(Ri) = RF + βi (E(RM – RF))

Therefore, the required for $1 Discount = 4% + 1.5(10% – 4%) = 13%. Similarly, the expected return for Everything $5 = 4% + 1.0(10% – 4%) = 10%.

According to the CAPM which investment is either underpriced, overpriced, or properly priced?

Discount

Everything

Underpriced

Properly priced

Underpriced

Overpriced

Underpriced

According to the CAPM, $1 Discount Stores requires a return of 13% based on its systematic risk level of β = 1.5. However, the forecasted return is only 12%. Therefore, the security is current overvalued.
According to the CAPM Everything $5 requires a return of 10% based on its systematic risk level of β = 1.0. However, the forecasted return is 11%. Therefore, the security is current undervalued.
To illustrate this result graphically, we plot both securities in relation to the security market line (SML). Note that β is in the independent variable on the X-axis, not σ (total risk). Since $1 Discount is overvalued, it plots below the line while Everything $5 is undervalued and plots above the SML.

Harry Jordan, an associate of Michaels, recommends the $1 Discount Store investment because it has a higher forecasted return and lower risk. Is Jordan’s assertion correct?

A)	Yes, because from the table, we can confirm Jordan's statement that Discount has a higher return and lower risk than everything.

B)	No, since capital market theory states that the return on investment is based on the amount of total risk in the investment.

C)	No, because according to the CAPM model it has been determined that Discount is overvalued.

Jordan is incorrect by basing his claim on the use of standard deviation (total risk) as the measure of risk. Capital market theory asserts that the return on an investment is based on the amount of systematic risk in the investment (β). Because the unsystematic, or security specific portion of total risk can be diversified away, an investor is only compensated for assuming systematic risk.

Which of the following is least likely an assumption that is necessary to derive the CAPM?

A)	Investors expectations are homogeneous.

B)	Markets are perfectly competitive.

C)	Limited risk-free borrowing.

The CAPM assumes that unlimited risk-free borrowing and lending is permitted.

作者: AndyNZ 时间: 2012-4-2 18:38

According to the capital asset pricing model (CAPM), if the expected return on an asset is too low given its beta, investors will:

A)	sell the stock until the price falls to the point where the expected return is again equal to that predicted by the security market line.

B)	sell the stock until the price rises to the point where the expected return is again equal to that predicted by the security market line.

C)	buy the stock until the price rises to the point where the expected return is again equal to that predicted by the security market line.

The CAPM is an equilibrium model: its predictions result from market forces acting to return the market to equilibrium. If the expected return on an asset is temporarily too low given its beta according to the SML (which means the market price is too high), investors will sell the stock until the price falls to the point where the expected return is again equal to that predicted by the SML

作者: AndyNZ 时间: 2012-4-2 18:38

Leslie Vista has never been satisfied with the capital asset pricing model (CAPM) because of its restrictive assumptions. While the model seems to work fairly well in her own stock-valuation systems, she does not trust results that depend on assumptions that are unrealistic in the real world. Vista is a literal thinker and prefers tangible solutions. She does not hold with theory and rarely draws intuitive conclusions. As an alternative to the CAPM, Vista decides to try out the arbitrage pricing model (APT). She likes the APT because it does not rely on the several assumptions that underlie the CAPM. Vista does some research comparing the CAPM to the APT and lists some of the assumptions of the CAPM:

Markets are perfectly competitive.
Investors use the Markowitz mean-variance framework.
Represented by a multi-factor model.
Unlimited risk-free lending and borrowing is permitted.

When Vista tells her boss, Mark Mazur, about her desire to use the APT, Mazur warns her of weaknesses in both models. Mazur also explains that the company has established the capital asset pricing model as its in-house valuation method and advises that Vista familiarize herself with how to derive the capital market line (CML) and the security market line (SML).After reviewing studies on the CAPM and the APT, Vista decides to develop her own microeconomic multifactor model. She establishes a proxy for the market portfolio, then considers the importance of various factors in determining stock returns. She decides to use the following factors in her model:

Changes in payout ratios.
Credit rating changes.
Companies’ position in the business cycle.
Management tenure and qualifications.

In order to derive the CML, Vista needs the:

A)	expected market return, portfolio beta, and risk-free rate.

B)	risk-free rate, market variance, portfolio variance, and expected market return.

C)	market variance, portfolio beta, risk-free rate, and expected portfolio return.

The CML is derived by using the risk-free rate, portfolio variance (standard deviation), market variance (standard deviation), and expected market return to calculate expected portfolio returns.

Vista’s analysis of CAPM assumptions is flawed. Which of the following assumptions that Vista noted is not part of the CAPM?

A)	Investors use the Markowitz mean-variance framework.

B)	Markets are perfectly competitive.

C)	Represented by a multi-factor model.

The CAPM is represented by a single factor model with the factor being market risk. The APT is a multifactor model where several factors could be used to explain the model's returns.

Which of the following factors is least appropriate for Vista’s factor model?

A)	Management tenure and qualifications.

B)	Companies’ position in the business cycle.

C)	Changes in payout ratios.

Microeconomic factors are factors measured by characteristics of the companies themselves, like price-to-earnings (P/E) ratios or growth rates. Macroeconomic factors are economic influences on security returns. A company’s position in the business cycle is dependent on the cycle itself, and cannot be accurately measured by looking at a company’s fundamentals. Payout ratios and management tenure are pieces of company-specific data suitable for use in a microeconomic factor model.

After further research on valuation models, Vista is most likely to use:

A)	the zero-beta CAPM because it does not require the assumption that investors can borrow at the risk-free rate.

B)	discounted cash flows, despite the need to estimate future cash flows and terminal values.

C)	APT because it allows the use of a variety of factors.

APT, the zero-beta CAPM, and the security market line (part of the CAPM) are all theoretical models in that they require the use of assumptions that are impossible to justify rationally. Discounted cash flows (DCF) require some estimation, but the calculations are based on real, tangible data. In addition, DCF models are not difficult to test, and studies have shown that valuation strategies based on discounted cash flows can be successful at picking winning stocks. Since Vista is a literal thinker and prefers tangible solutions, she is most likely to use the discounted cash flow approach to valuation rather than a theoretical model.

作者: AndyNZ 时间: 2012-4-2 18:39

What is the beta of Franklin stock if the current risk-free rate is 6%, the expected risk premium on the market portfolio is 9%, and the expected rate of return on Franklin is 17.7%?

1.3.

2.5.

3.9.

Using the Capital Asset Pricing Model:

6% + beta (9%) = 17.7%
beta = 1.3

作者: AndyNZ 时间: 2012-4-2 18:39

The market is expected to return 15% next year and the risk-free rate is 7%. What is the expected rate of return on a stock with a beta of 1.3?

17.4.

17.1.

10.4.

ERstock = Rf + ( ERM − Rf ) Betastock

作者: AndyNZ 时间: 2012-4-2 18:40

What is the expected rate of return for a stock that has a beta of 0.8 if the risk-free rate is 5%, and the market risk premium is 7%?

10.6%.

6.6%.

8.0%.

ERstock = 0.05 + 0.8(0.07) = 10.6%

作者: AndyNZ 时间: 2012-4-2 18:40

What is the expected rate of return for a stock that has a beta of 1.2 if the risk-free rate is 6% and the expected return on the market is 12%?

7.2%.

13.2%.

12.0%.

ERstock = 0.06 + 1.2(0.12 − 0.06) = 13.2%

作者: AndyNZ 时间: 2012-4-2 18:40

Answer the following three questions based on the information in the table shown below for the risk-free security, market portfolio, and stocks A, B, and C. Their respective betas and forecasted returns based on fundamental analysis of the economy, industry, and specific company analysis are also provided.

Stock
Beta
F(R)

A
0.5
0.065

B
1.0
0.095

C
1.5
0.115

Risk-free
0.0
0.030

Market
1.0
0.090

Based on the information in the above table, the expected returns for stocks A, B, and C for a risk-averse investor are:

4.5%

9.0%

13.5%

6.0%

9.0%

12.0%

6.5%

9.5%

11.5%

>
The expected rate of return for any individual security or portfolio can be calculated using the capital asset pricing model (CAPM):

E(R) = rf + Bi(RM – rf)

Expected rate of return for A = 0.03 + 0.5(0.09 – 0.03) = 0.03 + 0.03 = 0.06 or 6.0%.
Expected rate of return for B = 0.03 + 1.0(0.09 – 0.03) = 0.03 + 0.06 = 0.09 or 9.0%.
Expected rate of return for C = 0.03 + 1.5(0.09 – 0.03) = 0.03 + 0.09 = 0.12 or 12.0%.

Based on the information in the above table, which of the stocks should be held long in a well-diversified portfolio?

A)	A, B, and C.

B)	Both A and B.

A only.

The first step is to calculate the expected rate of return for each security using the capital asset pricing model (CAPM):

E(R) = rf + Bi(RM – rf).

If the forecasted return is greater than the expected return, then the stock is under-priced and should be included in the portfolio.
If the FR is less than the expected return, then the security is over-priced and should not be included in the portfolio.

The forecasted returns for stocks A and B are greater than their expected returns. Therefore, both A and B should be included in the portfolio and not stock C.

Based on the information in the above table, which stocks are currently in equilibrium?

A)	Stocks A and B are in equilibrium.

B)	None of the stocks are in equilibrium.

C)	All of the stocks are in equilibrium.

Stocks in equilibrium are properly priced and will lie on the security market line. The forecasted return for the individual security will equal the expected return based on the CAPM. The first step is to calculate the expected rate of return for each security using the CAPM:

E(R) = rf + Bi(RM − rf).

Expected rate of return for A = 0.03 + 0.5(0.09 − 0.03) = 0.03 + 0.03 = 0.06 or 6.0%.
Expected rate of return for B = 0.03 + 1.0(0.09 − 0.03) = 0.03 + 0.06 = 0.09 or 9.0%.
Expected rate of return for C = 0.03 + 1.5(0.09 − 0.03) = 0.03 + 0.09 = 0.12 or 12.0%.
Based on the expected returns given in Table 1 and the calculated required returns for stocks A, B, and C, none of the stocks are in equilibrium.

作者: AndyNZ 时间: 2012-4-2 18:42

The covariance between stock A and the market portfolio is 0.05634. The variance of the market is 0.04632. The beta of stock A is:

1.2163.

0.8222.

0.0026.

Beta = Cov(RA,RM) / Var(RM) = 0.05634/0.04632 = 1.2163.

作者: AndyNZ 时间: 2012-4-2 18:43

The covariance of the market returns with the stock's returns is 0.005 and the standard deviation of the market’s returns is 0.05. What is the stock's beta?

1.0.

0.1.

2.0.

Betastock = Cov(stock,market) ÷ (σMKT)2 = 0.005 ÷ (0.05)2 = 2.0

作者: AndyNZ 时间: 2012-4-2 18:43

Which of the following statements regarding beta is least accurate?

A)	The market portfolio has a beta of 1.

B)	A stock with a beta of zero will tend to move with the market.

C)	Beta is a measure of systematic risk.

A stock with a beta of 1 will tend to move with the market. A stock with a beta of 0 will tend to move independently of the market.

作者: AndyNZ 时间: 2012-4-2 18:43

What is the beta of Hamburg Corp.’s stock if the covariance of the stock with the market portfolio is 0.23, and the standard deviation of the market returns is 32%?

2.25.

1.65.

0.72.

BetaH = 0.23 / (0.32)2 = 2.25
Hamburg stock is, on average, more than twice as volatile as the market.

作者: AndyNZ 时间: 2012-4-2 18:44

Jung Wu, CFA, uses the security market line to determine if stocks are undervalued or overvalued. Wu recently completed an analysis of Sang Tractor Supplies (STS) and derived the following forecasts for STS and for the broad market:

Forecasted return for STS: 10%
Standard deviation forecasted for STS: 15%
Expected return on the stock market index: 12%
Standard deviation on the stock market index: 20%
Correlation between STS and stock market index: 0.60
Risk-free rate: 6%

To determine the fair value of STS, Wu should use the following risk value and should make the following valuation decision:

Risk value

Valuation

0.45	Undervalued

0.15	Overvalued

0.45	Overvalued

Wu uses the security market line as his framework of analysis. The appropriate risk measure for the security market line is the stock’s beta. The formula for beta equals:

where covim is the covariance between any asset i and the market index m, σi is the standard deviation of returns for asset i, σm is the standard deviation of returns for the market index, ρim is the correlation between asset i and the market index.
To determine the fair valuation for STS, Wu must compare his forecasted return against the equilibrium expected return using his security market line framework of analysis. The equation for the security market line is the capital asset pricing model:

E(R) = RF + β[E(Rm) – RF] = 0.06 + 0.45[0.12 – 0.06] = 0.087 = 8.7%.

Wu’s forecasted (10%) exceeds the equilibrium expected (or required) return for STS. Therefore, Wu should determine that STS is undervalued (should make a buy recommendation).

作者: AndyNZ 时间: 2012-4-2 18:45

Janet Bellows, a portfolio manager, is attempting to explain asset valuation to a junior colleague, Bill Clay. Bellows explanation focuses on the capital asset pricing model (CAPM). Of particular interest is her discussion of the security market line (SML), and its use in security selection.
Bellows begins with a short review of the capital asset pricing model, including a discussion about its assumptions regarding transaction costs, taxes, holding periods, return requirements, and borrowing and lending at the risk-free rate.
Bellows then illustrates the SML, and explains how changes in the expected market return and the risk-free rate affect the line. In an effort to learn whether Clay understands the concepts she has explained to him, Bellows decides to test Clay’s knowledge of valuation using the CAPM.
Bellows provides the following information for Clay:

The risk-free rate is 7%.
The market risk premium during the previous year was 5.5%.
The standard deviation of market returns is 35%.
This year, the market risk premium is estimated to be 7%.
Stock A has a beta of 1.30 and is expected to generate a 15.5% return.
The covariance of Stock B with the market is 0.18.
The standard deviation of Stock B’s returns is 41%.

Using this information, Clay must calculate expected stock returns and betas. Bellows especially wants to know Stock A’s required return, and whether or not the stock is a good buy.
Bellows then proposes a hypothetical situation to Clay: The stock market is expected to return 12.5% next year. Clay questions that return estimate in the context of the data listed above, and Bellows responds with four possible explanations for the estimate:

The estimated risk premium is incorrect.
Interest rates are likely to fall 1.5% over the next year.
Given the data above, the return estimate is correct.
The market beta is expected to rise over the next year.

Then Bellows provides Clay with the following information about Ohio Manufacturing, Texas Energy, and Montana Mining:

Stock
Ohio Texas Montana
Beta 0.50 XX% 1.50
Required Return 10.5% 11.0% XX%
Expected Return 12.0% 10.0% 15.0%
Expected S&P 500 return 14.0%

Clay has been tasked with providing an investment recommendation on the three stocks.
Based on the stock and market data provided above, which of the following data regarding Stock A is most accurate?

Required
12-month return

Investment advice

16.1%

Buy

14.15%

Buy

16.1%

Sell

ERstock = Rf + βstock (ERM − Rf). = 7% + 1.3 (14% − 7%) = 16.1%.The market risk premium for the upcoming year should be used in the calculation. Stock A’s required return is higher than its expected return, and as such the stock plots below the security market line. Stock A should be sold, not bought. (Study Session 18, LOS 60.f)

The beta of Stock B is closest to:

1.07.

0.51.

1.47.

Beta = (covariance of stock B with the market) / (variance of the market portfolio)
= 0.18 / (0.35)2 = 1.47.
(Study Session 18, LOS 60.f)

Which of the following represents the best investment advice?

A)	Buy Montana and Texas because their required return is lower than their expected return.

B)	Avoid Texas because its expected return is lower than its required return.

C)	Buy Montana because it is expected to return more than Texas, Ohio, and the market portfolio.

We can use the security market line (SML) to estimate the required return or beta on the various securities, and compare this with the expected returns.
The SML looks like this: E(r) = Rrf + β (RPM).
Since Montana’s beta is 1.50: 7.0 + 1.50(7.0) = 17.5% = the required return. Because Montana’s expected return is 15%, and the required return is 17.5%, Montana should not be purchased. Note that this is true even though Montana’s expected return is more than the other stocks and the market: it is not enough to compensate for the level of market risk assumed by holding the stock.
Texas’ required return = 11.0 = 7.0 + β(7.0), so β = (4/7) = 0.57. However, its expected return is less than the required return, so regardless of the beta value, Texas should not be purchased.
Ohio’s required return is given as 10.5, and the expected return is 12.0. Hence, Ohio is a buy. (Study Session 18, LOS 60.f)

Assuming the market return estimate of 12.5% is accurate, which of the following statements is the best explanation for the estimate?

A)	The estimated risk premium is incorrect.

B)	Interest rates are likely to fall 1.5% over the next year.

C)	Given the data above, the return estimate is correct.

The expected return on the market during the upcoming year is 14% (7% risk-free rate plus the expected 7% market risk premium). As such, the 12.5% estimate does not match the data. The most rational justification for a lower expected return is an error in the estimated risk premium. Falling interest rates may boost expected stock returns, but the current rate is the most relevant to the projected market return for the upcoming year. (Study Session 18, LOS 60.f)

With regard to the capital asset pricing model, relaxing assumptions about:

A)	risk free borrowing and lending rates results in a lower intercept and steeper slope.

B)	taxes will reduce differences between the capital market lines of different investors.

C)	homogeneous expectations will result in the SML appearing more as a band instead of a line.

Taxes change investors’ return expectations. Considering different marginal tax rates will result in a vast array of different after-tax requirements, leading to a vast array of CMLs and SMLs for different investors. The assumption of no transaction costs allows investors to make a profit even if a stock is just slightly off the SML. If risk-free borrowing and lending does not exist, then a portfolio of risky securities must be created such that the portfolio beta equals zero. The zero-beta portfolio is similar to the risk-free asset in that both have zero betas, but they differ in that the zero-beta portfolio has a non-zero standard deviation. The expected return on the zero-beta portfolio exceeds the risk-free rate therefore the SML will now have a higher intercept and a flatter slope. (Study Session 18, LOS 60.f)

If the market risk premium decreases by 1%, while the risk-free rate remains the same, the security market line:

A)	becomes steeper.

B)	parallel-shifts downward.

C)	becomes flatter.

Since the security market line runs from the risk-free rate (RFR) through the market return, holding the RFR constant and decreasing the market risk premium will cause the SML to become flatter. (Study Session 18, LOS 60.f)

作者: bapswarrior 时间: 2012-4-2 18:47

How are the capital market line (CML) and the security market line (SML) similar?

A)	The CML and SML use the standard deviation as a risk measure.

B)	The CML and SML can be used to find the expected return of a portfolio.

C)	The market portfolio will plot directly on the CML and the SML.

All portfolios will plot on the SML. The only portfolio that will plot on the CML is the market portfolio, because it is perfectly diversified.

作者: bapswarrior 时间: 2012-4-2 18:47

The security market line (SML) is a graphical representation of the relationship between return and:

A)	systematic risk.

B)	unsystematic risk.

C)	total risk.

The SML graphically represents the relationship between return and systematic risk as measured by beta.

作者: bapswarrior 时间: 2012-4-2 18:47

Rachel Stephens, CFA, examines data for two computer stocks, AAA and BBB, and derives the following results:

Standard deviation for AAA is 0.50.
Standard deviation for BBB is 0.50.
Standard deviation for the S&P500 is 0.20.
Correlation between AAA and the S&P500 is 0.60.
Beta for BBB is 1.00.

Stephens is asked to identify the stock that has the highest systematic risk and the stock that has the highest unsystematic risk. Stephens should draw the following conclusions:

Highest Systematic Risk

Highest Unsystematic Risk

Stock AAA

Stock BBB

Stock AAA

Stock BBB

First, compare the betas for the two stocks. The beta for AAA can be derived with the formula:

Therefore, AAA has larger beta and greater systematic risk than stock BBB which has a beta equal to 1. To assess the unsystematic risk, note that total risk is measured by the standard deviation. Note that the standard deviations for AAA and BBB are identical. Therefore, AAA and BBB have identical total risk. Moreover, note that:total risk = systematic risk + unsystematic risk.
We have already concluded that both stocks have identical total risk and that AAA has greater systematic risk. Therefore, BBB must have higher unsystematic risk.

作者: bapswarrior 时间: 2012-4-2 18:48

Kaskin, Inc., stock has a beta of 1.2 and Quinn, Inc., stock has a beta of 0.6. Which of the following statements is most accurate?

A)	The expected rate of return will be higher for the stock of Kaskin, Inc., than that of Quinn, Inc.

B)	The stock of Kaskin, Inc., has more total risk than Quinn, Inc.

C)	The stock of Quinn, Inc., has more systematic risk than that of Kaskin, Inc.

Beta is a measure of systematic risk. Since only systematic risk is rewarded, it is safe to conclude that the expected return will be higher for Kaskin’s stock than for Quinn’s stock.

作者: bapswarrior 时间: 2012-4-2 18:48

Glimmer Glass has a correlation of 0.67 with the market portfolio, a variance of 23%, and an expected return of 14%. The market portfolio has an expected return of 11% and a variance of 13%. Glimmer stock is approximately:

A)	11% less volatile than the average stock.

B)	4% more volatile than the average stock.

C)	19% more volatile than the average stock.

Beta is equal to the covariance divided by the market portfolio variance, or the product of the correlation and the ratio of the stock standard deviation to the market standard deviation. To derive the standard deviation, we take the square root of the variance. So beta = 0.67 × 0.479583 / 0.360555 = 0.891183. Glimmer shares are about 11% less volatile than the average stock.

作者: bapswarrior 时间: 2012-4-2 18:48

Which of the following statements about using the capital asset pricing model (CAPM) to value stocks is least accurate?

A)	The CAPM reflects unsystematic risk using standard deviation.

B)	If the CAPM expected return is too low, then the asset’s price is too high.

C)	The model reflects how market forces restore investment prices to equilibrium levels.

The capital asset pricing model assumes all investors hold the market portfolio, and as such unsystematic risk, or risk not related to the market, does not matter. Thus, the CAPM does not reflect unsystematic risk and does not rely on standard deviation as the measure of risk but instead uses beta as the measure of risk. The remaining statements are accurate.

作者: bapswarrior 时间: 2012-4-2 18:49

The capital market line:

A)	helps determine asset allocation.

B)	uses nondiversifiable risk.

C)	has a slope equal to the market risk premium.

The purpose of the CML is to determine the percentages allocated to the market portfolio and the risk-free asset. Both remaining answers reflect characteristics of the security market line.

作者: bapswarrior 时间: 2012-4-2 18:49

Jim Williams, CFA, manages individual investors' portfolios for Clarence Farlow Associates. Clarence Farlow Jr., CEO of Clarence Farlow Associates, is looking for some new investment ideas. Farlow is obsessive about value, however, and never buys stocks that look expensive. He has assigned Williams to assess the investment merits of several securities. Specifically, Williams has collected the following data for three possible investments.

Stock
Price Today Forecasted Price* Dividend Beta
Alpha 25 31 2 1.6
Omega 105 110 1 1.2
Lambda 10 10.80 0 0.5
*Forecast Price = expected price one year from today.

Williams plans to value the three securities using the security market line, and has assembled the following information for use in his valuation:

Securities markets are in equilibrium.
The prime interest rate is expected to rise by about 2% in the year ahead.
Inflation is expected to be 1% over the upcoming year.
The expected return on the market is 12% and the risk-free rate is 4%.
The market portfolio's standard deviation is 40%.

Williams eventually decides to construct a portfolio consisting of 10 shares of Alpha, 2 shares of Omega, and 20 shares of Lambda.Based on valuation via the SML, which of the following statements is most accurate?

A)	Williams should buy Alpha but not Omega.

B)	Both Alpha and Omega are overpriced.

C)	Neither Alpha nor Lambda is correctly priced.

SML valuation hinges on the relationship between the forecasted return (FR) and expected return (ER).

FR = (ending price − beginning price + dividends) / beginning price.
ER = RFR + β (RMkt − RFR).

For Alpha: FR = (31 − 25 + 2) / 25 = 32%, ER = 4 + 1.6(12 − 4) = 16.8%.
Since FR > ER, stock is underpriced.
For Omega: FR = (110 − 105 + 1) / 105 = 5.7%, ER = 4 + 1.2(12 − 4) = 13.6%.
Since FR < ER, stock is overpriced.
For Lambda: FR = (10.8 − 10 + 0) / 10 = 8%, ER = 4 + 0.5(12 − 4) = 8%.
Since FR = ER, stock is correctly priced.

The covariance of Omega with the market portfolio is closest to:

0.576.

0.480.

0.192.

Beta = covi,M / market portfolio variance, so covi,M = 1.2 × (0.4)2 = 0.192.

Williams calculates the required return for Omega. According to the capital asset pricing model (CAPM) the required return is closest to:

12.0%.

13.6%.

5.7%.

The required return (RR) uses the equation of the SML: risk-free rate + Beta × (expected market rate − risk-free rate). For Omega, RR = 4 + 1.2(12 − 4) = 13.6%. The expected return of 5.7% need not be the same as the required return under CAPM.

作者: bapswarrior 时间: 2012-4-2 18:50

The single-factor market model predicts that the covariance between two assets (asset i and asset j) is equal to:

A)	the beta of i times the beta of j.

B)	the beta of i times the beta of j divided by the standard deviation of the market portfolio.

C)	the beta of i times the beta of j times the variance of the market portfolio.

One of the predictions of the single-factor market model is that Cov(Ri,Rj) = bibjsM2. In other words, the covariance between two assets is related to the betas of the two assets and the variance of the market portfolio.

作者: bapswarrior 时间: 2012-4-2 18:50

Joseph Capital Management is considering implementing a mean-variance optimization model as part of their portfolio management process, however, the firm’s investment committee is unsure whether the model should use historical estimates or market model estimates for the inputs to the model. Joseph’s Senior Portfolio Manager, Travis Palmer, puts together a memo to the committee contrasting the two methods of calculating inputs. The memo includes the following points:

Point 1:
Using the historical estimate is far simpler and involves fewer computations than the market model method.

Point 2:
The use of market model estimates implicitly assumes that the market itself is mean-variance efficient.

Point 3:
Both the use of market model estimates and historical estimates rely on historical data to some degree.

Point 4:
One of the problems with using market model estimates for estimating returns is that the market model implicitly assumes the market index is representative of the entire market.

After reviewing Palmer’s memo, Joseph’s investment committee would be CORRECT to:

A)	agree with Point 3, but disagree with Points 2 and 4.

B)	agree with Points 2 and 3, but disagree with Point 1.

C)	agree with Points 1 and 4, but disagree with Point 3.

The committee should disagree with Point 1. The use of historical estimates involves computing the covariance of between each stock in a portfolio with every other stock in the portfolio, while the use of the market model only relies on computing the covariance of each stock with the market index, resulting in fewer computations.
The committee should agree with Points 2, 3, and 4. The market model regresses historical returns of a stock/portfolio with the corresponding returns of a market index and implicitly assumes that historical relationships are reflective of future relationships. The market model also implicitly assumes that the market itself is mean-variance efficient and that the index used for market returns is representative of the entire market.

作者: bapswarrior 时间: 2012-4-2 18:50

Which of the following is NOT an assumption necessary to derive the single-factor market model? The:

A)	firm-specific surprises are uncorrelated across assets.

B)	market portfolio is the tangency portfolio.

C)	expected value of firm-specific surprises is zero.

The result that the market portfolio is the tangency portfolio is a prediction of the CAPM model, not the market model. The market model assumes that there are two sources of risk, unanticipated macroeconomic events and firm-specific events. We use the return on the market portfolio as a proxy for the macroeconomic factor and assume all stocks have varying degrees of sensitivity to this macro factor. In addition, each stock’s returns are uniquely affected by firm-specific events uncorrelated across stocks and with the macro events. The remaining choices are the assumptions necessary to derive the single-factor market model.

作者: bapswarrior 时间: 2012-4-2 18:51

Carl Dursham recently earned the CFA designation and has just been hired by Quad Cities Consultants, which is a money management firm for private, high net worth clients. Quad Cities Consultants has just assigned Dursham his first client. The client’s name is Sally Litner. Litner has just received a multi-million dollar inheritance consisting of certificates of deposit that are about to mature. She is only 30 years old and recognizes that she should probably invest in assets like stocks that have a higher risk and return. Litner is a high school mathematics teacher and has an aptitude for formulas and equations, but she has never applied it to investments. Litner feels that Dursham will probably do a good job for her, but she wants him to explain to her how he will approach creating her portfolio.
When Dursham and Litner first meet, Litner says that she has heard of a stock that has done very well and is expected to continue to experience dramatic increases in the future. The name of the stock is IntMarket Corporation, which is a company that facilitates commerce on the Internet, and its recent return and standard deviation are 24% and 60% respectively. She asks Dursham if he thinks she should invest 100% of her portfolio in IntMarket Corporation. Dursham looks up the beta of IntMarket and finds that it is 1.6. He says that IntMarket Corporation might be a good first position, and he says that a good second position might be Granite Bank. The return and standard deviation of the bank stock is 12% and 30% respectively. Its beta is 0.9. The covariance of the bank stock with IntMarket Corporation is 576.
Dursham explains how diversification can lower risk and computes the statistics for portfolios that have various weights in IntMarket and Granite Bank. Litner is intrigued by Dursham’s demonstration concerning the effects of diversification. She asks about the effect of adding a third asset to the portfolio. To help illustrate the benefits of diversification further, Dursham chooses Capital Commodities Mutual fund, which invests in assets related to the production of raw materials and other commodities. The recent return and standard deviation of Capital Commodities has been 8% and 18% respectfully. The correlation of Capital Commodities with the other two stocks is effectively zero. Dursham computes the return and standard deviation of a portfolio consisting of 50% IntMarket, 30% Granite Bank, and 20% Capital Commodities.
Dursham takes time to explain the principle and assumptions behind mean-variance analysis and why it is important. He says the four underlying principals are i) investors are risk averse, ii) necessary statistics of returns can be calculated, iii) the returns have a normal distribution, and iv) the tax rate is fixed at some positive rate like 28%. During the discussion, Litner says she thinks the three stocks IntMarket Corporation, Granite Bank, and Capital Commodities may be all she needs in her portfolio. She asks Dursham to choose the weights for those three stocks that will minimize the variance and let that be her portfolio. If they desire a higher return, she adds using terms she has just learned, they can just leverage up that portfolio.If the recent return of the market was 14%, and the risk-free rate is 3%, using the market model what was the alpha of IntMarket Corporation?

+4.4%.

+1.4%.

+1.6%.

When using the market model, alpha is the difference between the realized return and that predicted by the product of the beta and the market return. The risk-free rate is not a part of the computation. The recent return of IntMarket was 24%. The predicted return based upon a beta equal to 1.6 and a market return of 14% is the product of these values: 22.4%. Thus the alpha is 24% − 22.4% = 1.6%. (Study Session 18, LOS 60.g)

Of Dursham’s list of the assumptions underlying mean-variance analysis, which of the following is the least likely to be one of the generally accepted assumptions?

A)	Necessary statistics of returns can be calculated.

B)	The tax rate is fixed at some positive rate like 28%.

C)	The returns have a normal distribution.

The assumption should be that there are no taxes and that there are no transactions costs. (Study Session 18, LOS 60.g)

A portfolio invested 50% in IntMarket and 50% in Granite Bank would have an expected return:

A)	lower than that of Granite Bank and a higher standard deviation than that of Granite Bank.

B)	greater than that of Granite Bank and a lower standard deviation than that of Granite Bank.

C)	greater than that of Granite Bank and a higher standard deviation than that of Granite Bank.

The average will obviously be higher than that of Granite Bank. The average is 18% = (0.5 × 24%) + (0.5 × 12%). The variance of the 50/50 portfolio is 1413 = (0.5 × 0.5 × 60 × 60) + (0.5 × 0.5 × 30 × 30) + (2 × 0.5 × 0.5 × 576); the standard deviation is about 37.6%, which is greater than the 30% standard deviation of Granite Bank. (Study Session 18, LOS 60.a)

The portfolio that Dursham recommends using the two stocks and the mutual fund would have a standard deviation that is closest in value to:

36.0%.

34.2%.

36.7%.

Since the return of Capital Commodities is uncorrelated with the returns of the two stocks, the variance of the portfolio is 1166.8 = (0.5 × 0.5 × 60 × 60) + (0.3 × 0.3 × 30 × 30) + (0.2 × 0.2 × 18 × 18) + (2 × 0.5 × 0.3 × 576) The standard deviation is √34.2%. (Study Session 18, LOS 60.a)

When compared to all other possible portfolios, the portfolio that has the smallest variance, which Litner requests, would have a Sharpe ratio that:

A)	may or may not be the highest of all possible portfolios; there is no general rule.

B)	is the highest of all possible portfolios.

C)	could not be the highest of all possible portfolios.

Minimizing the variance does not produce the portfolio with the highest Sharpe ratio. A point along the efficient frontier above the minimum variance portfolio will have both a higher return and standard deviation, but it will have a higher Sharpe ratio. (Study Session 18, LOS 60.b)

The portfolio that Litner requests, the one that has the smallest variance of all possible portfolios, would best be described as the:

A)	market portfolio.

B)	global minimum variance portfolio.

C)	efficient variance portfolio.

This is the definition of the global minimum variance portfolio. (Study Session 18, LOS 60.b)

作者: bapswarrior 时间: 2012-4-2 18:52

Michael Carr and Karen Bocock are analysts for the Portfolio Optimization Group. Carr and Bocock are discussing the firm’s mean variance optimization model for equity holdings and the pros and cons of using market model estimates or historical estimates as inputs to the model.

Carr states, “One of the main concerns I have about the model is that whether we are using market model estimates or historical estimates, we are implicitly assuming that the historical relationship between the stock and the market is indicative of the future.”
Bocock replies, “One of the main advantages to using the market model estimates is the fact that there are fewer parameters to estimate.”

With regard to their statements about methods for computing the inputs for a mean-optimization model:

A)	both are incorrect.

B)	only one is correct.

C)	both are correct.

Carr’s statement is correct. Using historical estimates and market model estimates both involve the implicit assumption that the historical relationship between a stock and the market is indicative of the future relationship. The historical estimate method uses direct historical means, variances, and correlations as inputs to the model. The market model method regresses historical returns against returns for the market and assumes that returns for each asset are correlated with returns to the market. Since both methods use some form of historical data, both assume that history is indicative of the future.
Bocock is also correct. The historical estimate method requires a large number of estimates, especially for computing the covariances between every stock in a portfolio. The market model estimate method simplifies the process significantly (resulting in fewer parameters) since all stock returns are assumed to be correlated with the market.

作者: bapswarrior 时间: 2012-4-2 18:52

The single-factor market model assumes there are how many sources of risk in asset returns?

Two.

One.

Three.

The market model assumes that there are two sources of risk in asset returns, unanticipated macroeconomic events and firm-specific events.

作者: bapswarrior 时间: 2012-4-2 18:53

Bill Tanner is a new associate at Global Western Investments. Tanner approaches his supervisor, Eric Simms, with some questions about risk. Specifically, Tanner lacks a complete understanding of many portfolio concepts, including the following:

How the presence of a risk-free asset will affect the efficient frontier.
The difference between total risk, systematic risk, and unsystematic risk.
Market and Macroeconomic models.

Tanner is concerned with providing the best investment advice possible for his clients. He seeks advice from some of his former Midwestern college friends who now happen to be CFA charterholders. One of his old roommates suggests that he look into using the market model or a multifactor model based on the arbitrage pricing theory (APT).
Tanner researches alternative pricing models and starts to become confused as all the equations look similar. He writes down the following notes from memory:

The intercept for the market model is derived from the APT.
The intercept for the APT is the risk free rate.
The intercept for a macroeconomic factor model is the expected return on the stock when there are no surprises to the factors.

Simms makes the predictions for Tanner shown in Exhibit 1.

Exhibit 1: Simm’s Predictions for Tanner

Beta for Stock B 1.10
Beta for Stock C 1.50
Correlation between Stock A and the S&P 500 0.50
Standard deviation for Stock A 28%
Standard deviation for the S&P 500 20%
1-year Treasure bill rate 5%
Expected return on the S&P 500 12%

Tanner uses the market model predictions (and the S&P 500 as a proxy for the market portfolio) to calculate the covariance of Stock B and C at 0.33. Using the market model, he also determines that the systematic component of the variance for Stock B is equal to 0.048.
Next, he heads out to meet a friend, Del Torres, for lunch. Torres excitedly tells Tanner about his latest work with tracking and factor portfolios. Torres says he has developed a tracking portfolio to aid in speculating on oil prices and is working on a factor portfolio with a specific set of factor sensitivities to the Russell 2000.Which of the following is the most appropriate response to Tanner’s question about the presence of a risk-free asset and the Markowitz efficient frontier? The presence of a risk-free asset changes the characteristics of the Markowitz efficient frontier by:

A)	converting the Markowitz efficient frontier from a curve into a linear risk/return relationship.

B)	reducing the total risk and the systematic risk of the market portfolio.

C)	allowing risk averse investors to include in their portfolios an asset that is negatively correlated with stocks, thereby reducing the risk related to investing in equities.

The presence of a risk-free asset changes the characteristics of the Markowitz efficient frontier by converting the Markowitz efficient frontier from a curve into a straight line called the capital market line (CML). (Study Session 18, LOS 60.b)

Which of the following statements best describes the concept of systematic risk? Systematic risk:

A)	remains even for a well-diversified portfolio.

B)	is approximately equal to total risk divided by unsystematic risk.

C)	as measured by the standard deviation is the only risk rewarded by the market.

Systematic risk remains even if a portfolio is well diversified. (Study Session 18, LOS 60.g)

Are Tanner’s notes on the intercepts for the pricing models correct?

A)	No, because the intercept for the market model is the return on the stock when the return on the market is zero.

B)	No, because the intercept for the APT is the stock’s alpha.

C)	No, because the intercept for the market model is the risk-free rate.

Tanner is incorrect with regard to the market model. The intercept is equal to the return when the market return is zero. Tanner’s other two comments on intercepts are correct. (Study Session 18, LOS 60.g)

The beta of Stock A is closest to:

0.70.

0.36.

0.50.

(Study Session 18, LOS 60.h)

According to the predictions of the market model, did Tanner correctly calculate the covariance of Stock B and C and Stock B’s systematic component of variance?

Covariance

Systematic component

Yes

Tanner incorrectly calculated the covariance and correctly calculated the systematic variance component.
According to the market model, the covariance between any two stocks is calculated as the product of their betas and the variance of the market portfolio. Here, the S&P 500 is a proxy for the market portfolio.

Here, CovB,C = 1.10(1.50)(0.2)2 = 0.066. Tanner incorrectly used the standard deviation of the market.The variance of the returns on asset i consists of two components: a systematic component related to the asset’s beta,

, and an unsystematic component related to firm-specific events,

.
For Stock B, the systematic component = 1.102(0.2)2 = 0.048 (Study Session 18, LOS 60.a)

Did Torres correctly describe tracking and factor portfolios?

Tracking

Factor

Yes

Torres reversed the concepts and is thus incorrect on both counts. A factor portfolio is a portfolio with a factor sensitivity of 1 to a particular factor and zero to all other factors. It represents a pure bet on one factor, and can be used for speculation or hedging purposes. A tracking portfolio is a portfolio with a specific set of factor sensitivities. Tracking portfolios are often designed to replicate the factor exposures of a benchmark index like the Russell 2000. (Study Session 18, LOS 60.m)

作者: bapswarrior 时间: 2012-4-2 18:54

Adjusted betas were developed in an effort to compensate for:

A)	traditional beta’s limitations in assessing the risk of extremely volatile stocks.

B)	the weaknesses of standard deviation as a risk measurement.

C)	inaccurate forecasts for the efficient frontier based on traditional beta.

Adjusted beta was developed to compensate for the beta instability problem, or the tendency of historical betas to generate inaccurate forecasts. Extreme volatility is not an issue; nor is standard deviation.

作者: bapswarrior 时间: 2012-4-2 18:54

Conner Cans shares have a beta of 0.8. Assuming α1 is 40%, Conner’s adjusted beta is closest to:

1.12.

0.92.

0.88.

Adjusted beta = α0 + α1 × beta where α0 and α1 must sum to 1, so α0 = 60%.
Adjusted beta = 60% + 40% × 0.8 = 0.92.

作者: bapswarrior 时间: 2012-4-2 18:54

Martz & Withers Enterprises has a beta of 1.6. We can most likely assume that:

A)	the future beta will be less than 1.6 but greater than 1.0.

B)	calculating an adjusted beta will ease the downward pressure on the forecasted beta.

C)	the standard error on the future beta forecast is positive.

The standard error is always expected to be zero, and the beta has nothing to do with that estimate. In the case of Martz & Withers, adjusted beta will almost certainly be lower than the current beta. Most adjusted beta calculations are as follows: adjusted beta = 1/3 + (2/3 × historical beta). In this case, adjusted beta is 1.2. Not everyone will use the two-thirds/one-third relationship, but any adjusted-beta equation will result in a value between 1.0 and 1.6.

作者: bapswarrior 时间: 2012-4-2 18:55

Analysts attempting to compensate for instability in the minimum-variance frontier will find which of the following strategies least effective?

A)	Reducing the frequency of portfolio rebalancing.

B)	Gathering more accurate historical data.

C)	Eliminating short sales.

Constraining portfolio weights through the elimination of short sales and avoiding rebalancing until significant changes occur in the efficient frontier can be effective strategies for limiting instability. However, even the best historical data is often of limited use in forecasting future values. Gathering more accurate historical data would help, compensate for instability, but not as much as the other two options.

作者: bapswarrior 时间: 2012-4-2 18:55

Responses to instability in the minimum variance frontier are least likely to include:

A)	improving the statistical quality of inputs.

B)	adding constraints against short sales.

C)	reducing the skew of the probability distribution of the sample mean.

Improving the statistical quality of inputs and adding constraints against short sales are valid methods for reducing instability in the minimum variance frontier.

作者: bapswarrior 时间: 2012-4-2 18:55

An analyst is constructing a portfolio for a new client. During an optimization procedure, it becomes apparent that small changes in input assumptions lead to broad changes in the efficient frontier. This is most likely a result of instability:

A)	of the point estimate of the sample mean.

B)	in the minimum variance frontier.

C)	of the point estimates of the covariances.

When small changes in input assumptions lead to broad changes in the efficient frontier, instability in the minimum variance frontier and the efficient frontier is indicated.

作者: bapswarrior 时间: 2012-4-2 18:56

What happens to the minimum-variance frontier when:

Return forecasts fall?

Covariance forecasts fall?

Curve shifts left

Curve shifts down

Curve shifts left

When the expected return forecast declines, the minimum-variance frontier moves down. A decline in covariance forecasts will cause the curve to shift to the left.

作者: bapswarrior 时间: 2012-4-2 18:56

Analysts trying to compensate for instability in the efficient frontier are least concerned about:

A)	small changes in expected returns.

B)	a sharp rise in earnings restatements.

C)	uncertainty in the forecast of variances and returns.

Small changes in expected returns can have a large effect on the efficient frontier – in some cases analysts or money managers will take actions to compensate for those effects. Uncertainty in forecasts is of paramount importance to analysts, since an accurate portrayal of the efficient frontier is impossible without accurate estimates. While historical data is often used to extrapolate future values, analysts realize the limitations of such data in forecasting. As such, changes to historical statistics, such as those caused by a flood of restatements, would be of some concern, but less than the other choices.

作者: bapswarrior 时间: 2012-4-2 18:57

Orb Trust (Orb) has historically leaned towards a passive management style of its portfolios. The only model that Orb’s senior management has promoted in the past is the Capital Asset Pricing Model (CAPM). Now Orb’s management has asked one of its analysts, Kevin McCracken, CFA, to investigate the use of the Arbitrage Pricing Theory model (APT).
McCracken has determined that a two-factor APT model is adequate where the factors are the sensitivity to changes in real GDP and changes in inflation. McCracken’s analysis has led him to the conclusion that the factor risk premium for real GDP is 8 percent while the factor risk premium for inflation is 2 percent. He estimates for Orb’s High Growth Fund that the sensitivities to these two factors are 1.25 and 1.5 respectively. Using his APT results, he computes the expected return of the fund. For comparison purposes, he then uses fundamental analysis to also compute the expected return of Orb’s High Growth Fund. McCracken finds that the two estimates of the Orb High Growth Fund’s expected return are equal.
McCracken asks a fellow analyst, Sue Kwon, to provide an estimate of the expected return of Orb’s Large Cap Fund based upon fundamental analysis. Kwon, who manages the fund, says that the expected return is 8.5 percent above the risk-free rate. McCracken then applies the APT model to the Large Cap Fund. He finds that the sensitivities to real GDP and inflation are 0.75 and 1.25 respectively.
Kwon wants to learn more about the APT and discusses McCracken’s results with him. McCracken says “the APT model is a variation of the CAPM.” Kwon comments that “extending the CAPM to an APT framework must require additional assumptions.”
Craig Newland joins the conversation. Newland says that the APT really is just another ad hoc multifactor model. All a researcher needs to do to compose an APT model, according to Newland, is to find a few macroeconomic factors that are correlated with stock returns and do a simple linear regression for each asset. McCracken says that it really is not that easy. For one thing, according to McCracken, the coefficients in the APT have a different interpretation from that of a basic multifactor model.
McCracken’s manager at Orb, Jay Stiles, asks McCracken to compose a portfolio that has a unit sensitivity to real GDP growth but is not affected by inflation. McCracken is confident in his APT estimates for the High Growth Fund and the Large Cap Fund. He then computes the sensitivities for a third fund, Orb’s Utility Fund, which has sensitivities equal to 1.0 and 2.0 respectively. McCracken will use his APT results for these three funds to accomplish the task of creating a portfolio with a unit exposure to real GDP and no exposure to inflation. He calls the fund the “GDP Fund.” Stiles says such a GDP Fund would be good for clients who are retirees who live off the steady income of their investments. McCracken says that the fund would be a good choice if upcoming supply-side macroeconomic policies of the government are successful. McCracken’s estimate of the expected return of Orb’s High Growth Fund would be:

A)	the risk-free rate plus 10%.

B)	the risk-free rate plus 13%.

10%.

The formula is: expected return = RF + 0.08 × 1.25 + 0.02 × 1.5 = RF + 13% (Study Session 18, LOS 66.j)

With respect to McCracken’s APT model estimate of Orb’s Large Cap Fund and the information Kwon provides, an arbitrage profit could:

A)	be earned by buying the High Growth Fund and selling short the Large Cap Fund.

B)	be earned by buying the Large Cap Fund and selling short the High Growth Fund.

C)	not be earned.

Based on the sensitivities to real GDP and inflation of 0.75 and 1.25, McCracken would calculate the expected return for the Orb Large Cap Fund to be:

expected return = RF + 0.08 × 0.75 + 0.02 × 1.25 = RF + 8.5%

Therefore, Kwon’s fundamental analysis estimate is congruent with McCracken’s APT estimate. If we assume that both Kwon’s and McCracken’s estimates of the return of Orb’s High Growth Fund are accurate, then no arbitrage profit is possible. Had Kwon provided an estimate of the Orb Large Cap Fund’s expected return that was less than 8.5 percent, for example, then we would consider selling that fund short and purchasing the High Growth Fund with the proceeds. (Study Session 18, LOS 66.l)

With respect to McCracken and Kwon’s comments concerning the relationship of the APT to the CAPM:

A)	McCracken is correct and Kwon is wrong.

B)	both McCracken and Kwon are wrong.

C)	Kwon is correct and McCracken is wrong.

McCracken is correct in saying the APT is a variation of the CAPM. Both the APT and the CAPM are equilibrium asset-pricing models. For example, both models assume there are no arbitrage opportunities available. The APT requires fewer (not more) assumptions, however, e.g., the APT does not assume all investors will hold the same portfolio and have the same expectations. (Study Session 18, LOS 66.n)

In the conversation between Newland and McCracken concerning the relationship of multifactor models in general and the APT:

A)	McCracken was correct and Newland was wrong.

B)	Newland was correct and McCracken was wrong.

C)	they were both wrong.

The APT is a special case of a multifactor model. Two of the most important distinguishing characteristics are that the coefficients in the APT are not simply regression coefficients from a regression of returns over time on some factors that have been selected ad hoc. In the APT the coefficients are premiums for an asset’s exposure to certain types of risk. Their values represent a no-arbitrage condition, which is an important assumption in the APT that a general multifactor model does not require. (Study Session 18, LOS 66.j)

The GDP Fund composed from the other three funds would have a weight in Utility Fund equal to:

-3.2.

-2.2.

0.3.

In order to eliminate inflation, the following three equations must be solved simultaneously, where the GDP sensitivity will equal 1 in the first equation, inflation sensitivity will equal 0 in the second equation and the sum of the weights must equal 1 in the third equation.

1. 1.25wx + 0.75wy + 1.0wz = 1
2. 1.5wx+ 1.25wy + 2.0wz = 0
3. wx + wy + wz = 1

Here, “x” represents Orb’s “High Growth Fund”, “y” represents “Large Cap Fund” and “z” represents “Utility Fund.” By multiplying equation 1 by 2.0 and subtracting equation 2 from the result, McCracken will get wx + 0.25wy = 2. McCracken can also subtract equation 3 from equation 1 and get 0.25wx – 0.25wy = 0. This means wx = wy. Thus, the equation wx + 0.25wy = 2 becomes 1.25wy = 2 and wy = wx = 1.6. It follows from any of the other equations that wz = -2.2.

(Study Session 18, LOS 66.j)

With respect to the comments of Stiles and McCracken concerning for whom the GDP Fund would be appropriate:

A)	McCracken was correct and Stiles was wrong.

B)	both were correct.

C)	Stiles was correct and McCracken was wrong.

Since retirees living off a steady income would be hurt by inflation, this portfolio would not be appropriate for them. Retirees would want a portfolio whose return is positively correlated with inflation, to preserve value, and less correlated with the variable growth of GDP. Thus, the fund would not be appropriate for retirees and Stiles is wrong. McCracken is correct in that supply side macroeconomic policies are generally designed to increase output at a minimum of inflationary pressure. Increased output would mean higher GDP, which in turn would increase returns of a fund positively correlated with GDP. (Study Session 18, LOS 66.j)

作者: bapswarrior 时间: 2012-4-2 18:57

In a multi-factor macroeconomic model the mean-zero error term represents:

A)	the portion of the individual asset's return that is not explained by the systematic factors.

B)	sampling error in estimating factor sensitivities.

C)	the no-arbitrage condition imposed in multi-factor models.

The mean-zero error term represents the unsystematic, firm-specific, diversifiable risks that are not explained by the systematic factors.

作者: bapswarrior 时间: 2012-4-2 18:58

The macroeconomic factor models for the returns on Omni, Inc., (OM) and Garbo Manufacturing (GAR) are:

ROM = 20.0% +1.0(FGDP) + 1.4(FQS) + εOM
RGAR = 15.0% +0.5(FGDP) + 0.8 (FQS) + εGAR

What is the expected return on a portfolio invested 60% in Omni and 40% in Garbo?

A)

20.96%.
B)

18.0%.
C)

19.96%.

Since the expected factor suprises and expected errors are all 0 by definition, the macroeconomic factor model for the portfolio is:

RP = [(0.6)(20.0%) + (0.4)(15.0%)]
+ [(0.6)(−1.0) + (0.4)(−0.5)] (0)
+ [(0.6)(1.4) + (0.4)(0.8)] (0)
+ [(0.6) εOM + (0.4)εGAR]

= 18.0% −0.80(0) + 1.16(0) + (0.6)(0) + (0.4)(0)

作者: bapswarrior 时间: 2012-4-2 18:58

Which of the following statements concerning the macroeconomic multi-factor model for returns on stock j {Rj = 12% + 1.4F1 – 0.8F2 + εj} is least accurate?

A)	The expected return on stock j is 12%.

B)	The return on stock j will decrease as factor 2 is expected to increase.

C)	F1 and F2 represent priced risk.

In a macroeconomic multi-factor model, only unexpected changes in systematic factors are priced in the sense that they affect stock returns. The return on stock j will decrease only if factor 2 increases unexpectedly (because the factor sensitivity is less than zero). Expected increases will NOT cause stock j returns to decrease.

作者: bapswarrior 时间: 2012-4-2 18:58

The factor models for the returns on Omni, Inc., (OM) and Garbo Manufacturing (GAR) are: ROM = 20.0% − 1.0(FCONF) + 1.4(FTIME) + εOM
RGAR = 15.0% − 0.5(FCONF) + 0.8 (FTIME) + εGAR What is the factor sensitivity to the time-horizon factor (TIME) of a portfolio invested 20% in Omni and 80% in Garbo?

0.92.

-0.60.

0.16.

The factor model for the portfolio is:
RP = [(0.2)(20.0%) + (0.8)(15.0%)]
+ [(0.2)(-1.0) + (0.8)(-0.5)] (FCONF)
+ [(0.2)(1.4) + (0.8)(0.8)] (FTIME)
+ [(0.2) εOM + (0.8)εGAR]
= 16.0% −0.60(FCONF) + 0.92(FTIME) + (0.2)εOM + (0.8)εGAR

作者: bapswarrior 时间: 2012-4-2 18:59

Assume you are considering forming a common stock portfolio consisting of 25% Stonebrook Corporation (Stone) and 75% Rockway Corporation (Rock). As expressed in the two-factor returns models presented below, both of these stocks’ returns are affected by two common factors: surprises in interest rates and surprises in the unemployment rate.

RStone = 0.11 + 1.0FInt + 1.2FUn + εStone
RRock = 0.13 + 0.8FInt + 3.5FUn + εRock

Assume that at the beginning of the year, interest rates were expected to be 5.1% and unemployment was expected to be 6.8%. Further, assume that at the end of the year, interest rates were actually 5.3%, the actual unemployment rate was 7.2%, and there were no company-specific surprises in returns. This information is summarized in Table 1 below:

Table 1: Expected versus Actual Interest Rates and Unemployment Rates

Actual
Expected
Company-specific returns surprises

Interest Rate
0.053
0.051
0.0

Unemployment Rate
0.072
0.068
0.0

What is the expected return for Stonebrook?

11.0%.

13.0%.

13.2%.

The expected return for Stonebrook is simply the intercept return (ai) of 0.11, or = 11.0%. (Study Session 18, LOS 66.j, k)

What is the expected return for Rockway?

13.0%.

17.3%.

11.0%.

The expected return for Rockway is simply the intercept term (ai) of 0.13, or 13%. (Study Session 18, LOS 66.j, k)

What is the portfolio’s sensitivity to interest rate surprises?

0.95.

0.25.

0.85.

The portfolio composition is 25% Stonebrook and 75% Rockway. The interest rate sensitivities for Stonebrook and Rockway are 1.0 and 0.8, respectively. Thus, the portfolio's sensitivity to interest rate surprises is: (0.25)(1.0) + (0.75)(0.8) = 0.85. (Study Session 18, LOS 66.k)

What is the portfolio’s sensitivity to unemployment rate surprises?

2.625.

1.775.

2.925.

The portfolio composition is 25% Stonebrook and 75% Rockway. The unemployment rate sensitivities for Stonebrook and Rockway are 1.2 and 3.5, respectively. Thus, the portfolio's sensitivity to unemployment rate surprises is: (0.25)(1.2) + (0.75)(3.5) = 2.925. (Study Session 18, LOS 66.k)

What is the expected return of the portfolio?

12.5%.

11.5%.

2.75%.

The portfolio composition is 25% Stonebrook and 75% Rockway. The expected returns for Stonebrook and Rockway are 11% and 13%, respectively. Thus, the portfolio’s expected return is (0.25)(0.11) + (0.75)(0.13) = 12.5%. (Study Session 18, LOS 66.k)

What is the predicted return for Stonebrook?

0.40%.

11.68%.

11.00%.

The predicted return uses the unemployment and interest rate surprises as follows:
The returns for a stock that are correlated with surprises in interest rates and unemployment rates can be expressed using a two-factor model as:

Ri = ai+ bi,1FInt + bi,2FUn + εi

where:
Ri = the return on stock i
ai = the expected return on stock i
bi,1 = the factor sensitivity of stock i to unexpected changes in interest rates
FInt = unexpected changes in interest rates (the interest factor) = .053 − .051 = .002
bi,2 = the factor sensitivity of stock i to unexpected changes in the unemployment rate
FUn = unexpected changes in the unemployment rate (the unemployment rate factor) = .072 − .068 = .004
εi = a mean-zero error term that represents the part of asset i’s return not explained by the two factors.

Thus the predicted return is: 0.11 + (1.0)(0.002) + (1.2)(0.004) = 0.1168 or 11.68% (Study Session 18, LOS 66.j)

作者: bapswarrior 时间: 2012-4-2 19:00

Examples of macroeconomic variables that create systematic risk include:

A)	all of these choices are correct.

B)	variability in the growth of the money supply.

C)	changes in GDP growth rates.

Systematic risk factors are those variables that: (1) exhibit correlation with other variables and (2) explain the returns of many different assts. GDP growth and the money supply are each examples of systematic risk factors.

作者: bapswarrior 时间: 2012-4-2 19:00

A multi-factor model that identifies the portfolios that best explain the historical cross-sectional returns or covariances among assets is called a:

A)	fundamental factor model.

B)	covariance factor model.

C)	statistical factor model.

A statistical factor model identifies the portfolios that best explain the historical cross-sectional returns or covariances among assets. The returns on these portfolios represent the factors. In fundamental factor models, the factors are characteristics of the stock or the company that have been shown to affect asset returns, such as book-to-market or price-to-earnings ratios.

作者: bapswarrior 时间: 2012-4-2 19:00

Identify the most accurate statement regarding multifactor models from among the following.

A)	Macrofactor models include explanatory variables such as real GDP growth and the price-to-earnings ratio and fundamental factor models include explanatory variables such as firm size and unexpected inflation.

B)	Macrofactor models include explanatory variables such as firm size and the price-to-earnings ratio and fundamental factor models include explanatory variables such as real GDP growth and unexpected inflation.

C)	Macrofactor models include explanatory variables such as the business cycle, interest rates, and inflation, and fundamental factor models include explanatory variables such as firm size and the price-to-earnings ratio.

Macrofactor models include multiple risk factors such as the business cycle, interest rates, and inflation. Fundamental factor models include specific characteristics of the securities themselves such as firm size and the price-to-earnings ratio.

作者: bapswarrior 时间: 2012-4-2 19:00

A two-stock portfolio consists of the following:

The portfolio consists of stock of Green Company (portfolio weight 30%) and Blue Company (portfolio weight 70%).
Green’s expected return is 12%, Blue’s is 8%.
Interest rates are expected to be 6%.
Oil prices are expected to rise 2%.
The two-factor model for Green Company is R(green) = 12% − 0.5 Fint − 0.5 Foil + egreen
The two-factor model for Blue Company is R(blue) = 8% + 0.8 Fint + 0.4 Foil + eblue

If interest rates are actually 9% and oil prices do not rise, the return on the portfolio will be:

10.17%.

12.89%.

10.55%.

R(green) is [12 − (0.5 × 3) − (0.5 × (−2))] = 11.5%.
R(blue) is [8 + (0.8 × 3) + (0.4 × (−2))] = 9.6%.
The portfolio return is [(0.30)(11.5) + (0.70)(9.6)] = 10.17%.

作者: bapswarrior 时间: 2012-4-2 19:01

multi-factor model that uses unexpected changes (surprises) in macroeconomic variables (e.g., inflation and gross domestic product) as the factors to explain asset returns is called a:

A)	fundamental factor model.

B)	macroeconomic factor model.

C)	statistical factor model.

Macroeconomic factor models use unexpected changes (surprises) in macroeconomic variables as the factors to explain asset returns. One example of a factor in this type of model is the unexpected change in gross domestic product (GDP) growth. In fundamental factor models, the factors are characteristics of the stock or the company that have been shown to affect asset returns, such as book-to-market or price-to-earnings ratios. A statistical factor model identifies the portfolios that best explain the historical cross-sectional returns or covariances among assets. The returns on these portfolios represent the factors.

作者: bapswarrior 时间: 2012-4-2 19:01

Carla Vole has developed the following macroeconomic models:

Return of Stock A = 6.5% + (9.6 × productivity) + (5.4 × growth in number of businesses)
Return of Stock B = 18.7% + (2.5 × productivity) + (3.7 × growth in number of businesses)

Assuming a portfolio contains 60% Stock A and 40% Stock B, the portfolio’s sensitivity to productivity is closest to:

4.72.

6.76.

5.34.

To calculate the portfolio’s factor sensitivity, we need the weighted average of the factor sensitivity of each stock: (9.6 × 60%) + (2.5 × 40%) = 6.76.

作者: bapswarrior 时间: 2012-4-2 19:02

Colonial Capital leans heavily on the capital asset pricing model (CAPM) in its investment-making decisions, but the company’s analysts find it difficult to use. In an effort to make the calculations easier, Colonial has modified the CAPM to use the S&P 1500 SuperComposite Index as a benchmark.
Colonial recently hired high-powered money manager Marjorie Kemp away from a rival company in an effort to boost its lagging returns. Kemp understands the appeal of the CAPM but likes to use multiple valuation methods for the purposes of comparison.
In her first act as chief investment officer of Colonial, Kemp sent a memo to all portfolio managers instructing them to start using alternative methods for valuing assets. She opened by touting the benefits of other forms of asset valuation.

“The CAPM requires a lot of unrealistic assumptions. Arbitrage Pricing Theory’s (APT) assumptions are far less restrictive.”
“A major benefit of multifactor models relative to the CAPM is their ability to be effectively tested using real-life data.”
“Under APT, risk is easier to calculate than is the case with the CAPM, for which beta must be estimated based on unobservable returns.”
“Neither multifactor models nor APT require an estimation of the market risk premium.”

Kemp then called a meeting of Colonial’s analysts to discuss asset-valuation strategies. The debate grew quite spirited.
A longtime Colonial analyst named Smathers said the company had experimented with multifactor models years earlier and could not come up with a model that satisfied everyone. He then proposed creating a number of multifactor models for different sectors. The responses were as follows:

Florio said he didn’t like APT because it did not indicate what the risk factors were.
Garcia said he liked APT because it acknowledged that arbitrage opportunities occasionally exist.
Inge said he disliked APT because it did not allow analysts to consider the market portfolio.

After about 30 minutes, Kemp realized nothing productive would occur, so she set everyone to work analyzing a valuation model. She wrote the following equation on a blackboard:

Expected stock return = expected S&P 1500 Index return / 2 + capacity utilization / 15 + 1.5 × GDP growth − 2 × inflation

Which factors, taken in combination, would create the best multifactor model for utility stocks?

A)	Projected change in energy prices, interest rate term structure, estimated GDP growth, projected market return.

B)	Projected winter low temperature, projected change in energy prices, projected change in inflation, projected market return.

C)	Projected winter low temperature, interest rate term structure, housing starts, price/earnings factor.

Without knowing the accuracy of the factor sensitivities or actually looking at the numbers generated by the equation, we can only assess the value of a multifactor model by considering whether the individual factors are relevant. Winter low temperatures and energy prices are particularly relevant to utilities, the first on the revenue side, and the second on the cost side. Because utilities tend to be heavily leveraged, interest rates affect them. Inflation rates are relevant for most companies, as are price/earnings ratios. Housing starts are relevant for utilities, as houses are larger than apartments and more expensive to heat and cool. However, utilities are considered diversifiers, and their returns are less correlated to those of the broader market than are the returns of stocks in other sectors. The sector is also less correlated to economic growth than most. As such, models that consider GDP growth or market returns are probably of less value than the one model that considers neither.

Which statement represents Kemp’s weakest argument?

A)	“Under APT, risk is easier to calculate than is the case with the CAPM, for which beta must be estimated based on unobservable returns.”

B)	“The CAPM requires a lot of unrealistic assumptions. APT’s assumptions are far less restrictive.”

C)	“Neither multifactor models nor APT require an estimation of the market risk premium.”

It is debatable whether risk is easier to calculate under APT. True, the beta of the unobservable market portfolio is not needed, but the risk factors required for the APT equation are not provided. The analyst must select them. As such, the statement about the ease of calculating risk is open for interpretation. Both remaining statements are factually accurate, with no interpretation required.

Kemp’s equation is closest to:

A)	arbitrage pricing theory.

B)	a microeconomic multifactor model.

C)	a macroeconomic multifactor model.

The arbitrage pricing theory and the capital asset pricing model equations use the risk-free return, so Kemp’s equation is not an APT. That leaves factor models. The market return is technically neither a macroeconomic or microeconomic variable, but it can be used with multifactor models. Since the other three variables represent macro factors, the equation is closest to a macroeconomic multifactor model.

Which analyst made the most sense?

Garcia.

Inge.

Florio.

Florio’s statement about risk factors is correct, and reflects a weakness in APT. Garcia’s statement is incorrect, because one of the assumptions inherent in the APT is that arbitrage opportunities do not exist. Inge is mistaken because, while APT does not require the use of the market portfolio, an analyst can certainly use the market portfolio as a factor if desired.

作者: bapswarrior 时间: 2012-4-2 19:02

The Adams portfolio contains 35% Khallin Equipment stock and 65% Giant Semiconductor stock. Analyst Joe Karroll estimates that 40% of Khallin’s return variance is determined by cost trends and 60% is determined by purchasing trends. Karroll also estimates that Giant’s return variance is 75% determined by cost trends and 25 percent determined by purchasing trends. Assuming an estimated return of 7% for Khallin and 16% for Giant and a cost factor of –0.07 and a purchasing factor of 0.0325, the Adams portfolio’s expected return is closest to:

12.9%.

8.0%.

9.7%.

When we have data points for the macroeconomic model, we use the model to calculate expected returns, rather than falling back on the estimated returns of the individual stocks. To calculate portfolio returns using the macroeconomic models, we simply use the weighted average of the models. Here are the models:

Return-Khallin = 0.07 + (0.4 × -0.07) + (0.6 × 0.0325)
Return-Giant = 0.16 + (0.75 × -0.07) + (0.25 × 0.0325)

Assuming a 35% weighting for Khallin stock and a 65% weighting for Giant, the portfolio return = 0.129 + (0.628 × -0.07) + (0.373 × 0.0325) = 12.9% - 4.4% + 1.2% = 9.7%.

作者: bapswarrior 时间: 2012-4-2 19:02

Mary Carruthers has created the following macroeconomic model for stock in Magma Metro Systems and Clampett Pharmaceuticals:

R-Magma = 12% + (6.3 × GDP growth) + (0.056 × population growth) + error.
R-Clampett = 18% + (1.2 × GDP growth) – (0.231 × population growth) + error.

The expected return for a portfolio containing 65% Magma Metro Systems and 35% Clampett Pharmaceuticals is closest to:

14%.

16%.

13%.

Given no information about GDP and population growth, we cannot calculate returns using the detailed model. As such, we fall back on the traditional assumption that the factors and random error in a macroeconomic model are expected to equal zero. As such, the expected return for the portfolio is the weighted average of the intercepts: 65% × 12% = 7.8% and 35% × 18% = 6.3% thus 7.8% + 6.3% = 14.1%.

作者: bapswarrior 时间: 2012-4-2 19:03

Which of the following statements about multifactor models is CORRECT?

A)	The multifactor model is a cross-sectional equilibrium pricing model that explains variation across assets.

B)	The intercept term in a macroeconomic factor model is the risk-free rate.

C)	The multifactor model is a time-series regression that explains variation in one asset.

The multifactor model is a time-series regression that explains variation in one asset. APT is a cross-sectional equilibrium pricing model that explains variation across assets. The intercept term in a macroeconomic factor model is the asset's expected return.

作者: bapswarrior 时间: 2012-4-2 19:03

Given a three-factor arbitrage pricing theory APT model, what is the expected return on the Freedom Fund?

The factor risk premiums to factors 1, 2, and 3 are 10%, 7% and 6%, respectively.
The Freedom Fund has sensitivities to the factors 1, 2, and 3 of 1.0, 2.0 and 0.0, respectively.
The risk-free rate is 6.0%.

30.0%.

33.0%.

24.0%.

The expected return on the Freedom Fund is 6% + (10.0%)(1.0) + (7.0%)(2.0) + (6.0%)(0.0) = 30.0%.

作者: bigredhockey55 时间: 2012-4-2 19:07

Jennifer Watkins, CFA, is a portfolio manager at Q-Metrics. She has derived a 2-factor arbitrage pricing theory (APT) model of expected returns she intends to use in her portfolio management strategies. The two-factor APT equation, in which the two factors are confidence risk and industrial production, is:

E(RP) = RT-bill + 0.06βp,CONF + 0.09βp,PROD

Watkins determines the sensitivity to each of the two factors for three diversified portfolios as well as for her benchmark, the Wilshire 5000. The results of her analysis are shown in the table below.

Portfolio Sensitivity to Conf. Risk Factor Sensitivity to Indust. Prod. Factor
J 1.50 1.00
K 0.80 1.20
L 1.00 2.00
Wilshire 5000 1.00 1.50

βp,CONF: a market confidence factor
βp,PROD: industrial production factor

RT-bill: the Treasury bill rate of return, assumed equal to 4%.

Watkins compares her data and results to that of a colleague who uses the Capital Asset Pricing Model (CAPM) to analyze the same portfolios. She determines that her analysis is more appropriate for the given portfolios.
What is the expected return on Portfolio K according to the APT equation?

19.6%.

15.6%.

22.0%.

The β's in the APT equation are the factor sensitivities. The expected return on portfolio K is E(RK) = 0.04 + 0.06(0.80) + 0.09(1.20) = 19.6%.

Which of the following would be a valid reason for concluding that the APT analysis of Watkins is more appropriate than the CAPM analysis of her colleague?

A)	Investors have quadratic utility functions.

B)	Investors can borrow and lend at the risk-free rate.

C)	The APT model is less restrictive than the CAPM.

The true market portfolio contains all securities. The CAPM is a more restrictive model and requires that such a portfolio be mean/variance efficient while the APT does not. The Wilshire 5000 is a very diversified portfolio, but it does not contain all securities.

Which of the following is least likely one of the three equations needed to solve for the Industrial Production factor portfolio combination of J, K and L?

A)	1.50wJ + 0.80wK + 1.00wL = 0.

B)	wJ + wK + wL = 1.

C)	1.50wJ + 1.20wK + 2.00wL = 0.

A factor portfolio has a sensitivity of one to one factor and a sensitivity of zero for all other factors (in this case, a pure bet on industrial production). We need to create a factor portfolio (a combination of portfolios J, K and L) that has a factor sensitivity of zero to the confidence risk factor and a sensitivity of one to the industrial production factor. The three simultaneous equations to solve are:
Equation 1: wJ + wK + wL = 1 (portfolio weights sum to 1)
Equation 2: 1.50wJ + 0.80wK + 1.00wL = 0 (confidence risk portfolio sensitivity equals 0)
Equation 3: 1.00wJ + 1.20wK + 2.00wL = 1 (production portfolio sensitivity equals 1)

作者: bigredhockey55 时间: 2012-4-2 19:08

Carrie Marcel, CFA, has long used the Capital Asset Pricing Model (CAPM) as an investment tool. Marcel has recently begun to appreciate the advantages of arbitrage pricing theory (APT). She used reliable techniques and data to create the following two-factor APT equation:

E(RP) = 6.0% + 12.0%βp,ΔGDP – 3.0%βp,ΔINF

Where ΔGDP is the change in GDP and ΔINF is the change in inflation. She then determines the sensitivities to the factors of three diversified portfolios that are available for investment as well as a benchmark index:

Portfolio
Sensitivity to ΔGDP
Sensitivity to ΔINF
Q
2.00
0.75
R
1.25
0.50
S
1.50
0.25
Benchmark Index
1.80
1.00

Marcel is investigating several strategies. She decides to determine how to create a portfolio from Q, R, and S that only has an exposure to ΔGDP. She also wishes to create a portfolio out of Q, R, and S that can replicate the benchmark. Marcel also believes that a hedge fund, which is composed of long and short positions, could be created with a portfolio that is equally weighted in Q, R, S and the benchmark index. The hedge fund would produce a return in excess of the risk-free return but would not have any risk.

Which of the following statements least likely describes characteristics of the APT and the CAPM?

A)	The APT is more flexible than the CAPM because it allows for multiple factors.

B)	Both models assume firm-specific risk can be diversified away.

C)	Both models require the ability to invest in the market portfolio.

The CAPM can be thought of as a subset of the APT, multifactor model. Therefore, fewer assumptions are needed for the APT model than the CAPM. Although it could be included as a factor, the APT does not require an investment in the market portfolio. APT can be thought of as a k factor model, while the CAPM is based on the risk-free asset and the market portfolio.

What is the APT expected return on a factor portfolio exposed only to ΔGDP?

18.0%.

12.0%.

15.0%.

A factor portfolio is a portfolio with a factor sensitivity of one to a particular factor and zero to all other factors. The expected return on a “factor 1” portfolio is E(RR) = 6.0% + 12.0% (1.00) − 3.0%(0.00) = 18.0%.

作者: bigredhockey55 时间: 2012-4-2 19:08

Given a three-factor arbitrage pricing theory (APT) model, what is the expected return on the Premium Dividend Yield Fund?

The factor risk premiums to factors 1, 2 and 3 are 8%, 12% and 5%, respectively.
The fund has sensitivities to the factors 1, 2, and 3 of 2.0, 1.0 and 1.0, respectively.
The risk-free rate is 3.0%.

33.0%.

50.0%.

36.0%.

The expected return on the Premium Dividend Yield Fund is 3% + (8.0%)(2.0) + (12.0%)(1.0) + (5.0%)(1.0) = 36.0%.

作者: bigredhockey55 时间: 2012-4-2 19:09

Which of the following assumptions is NOT necessary to derive the APT?

A)	The factor portfolios are efficient.

B)	Investors can create diversified portfolios with no firm-specific risk.

C)	A factor model describes asset returns.

The APT is an equilibrium model that assumes that investors can create diversified portfolios and that a factor model describes asset returns. It does NOT require that factor portfolios (nor, as in the capital asset pricing model [CAPM], the market portfolio) be efficient. In effect, the APT assumes investors simply like more money to less, while the CAPM assumes they care about expected return and standard deviation and invest in efficient portfolios. The APT makes no reference to mean-variance analysis or assumptions about efficient portfolios. This weaker set of assumptions is an advantage of the APT over the CAPM.

作者: bigredhockey55 时间: 2012-4-2 19:09

Which of the following is NOT an underlying assumption of the arbitrage pricing theory (APT)?

A)	Asset returns are described by a K factor model.

B)	There are a sufficient number of assets for investors to create diversified portfolios in which firm-specific risk is eliminated.

C)	A market portfolio exists that contains all risky assets and is mean-variance efficient.

The APT makes no assumption about a market portfolio.

欢迎光临 CFA论坛 (http://forum.theanalystspace.com/)

Expected Return/Correlation	Variance	Weight
E(R1) = 10%	Var(1) = 9%	w1 = 30%
E(R2) = 15%	Var(2) = 25%	w2 = 70%
r1,2 = 0.4

	Equity Fund A	Equity Fund B	Equity Fund C
Average Return	12%	9%	8%
Variance	0.0256	0.0196	0.0172
Correlation of A & B is 0.50 Correlation of A & C is 0.38 Correlation of B & C is 0.85

Expected Return and Risk for Selected Investments
Investment	Expected Return	Standard Deviation
Stock A	12%	30%
Stock B	15%	35%
Stock C	11%	40%
S&P 500	12%	22%
Treasury Bills	3%	0%
Correlation Coefficient for Stocks A and B equals 0.4. Correlation Coefficient for Stocks A and C equals -0.5. Correlation Coefficient for Stocks B and C equals 0.1.

	The Washington Fund	The Jefferson Fund
Expected Return	30%	36%
Variance	0.0576	0.1024
Investment	$2,000,000	$6,000,000
Correlation	0.40

	Current Client Portfolio	New Horizon	Hi Rise Real Estate	Quality Commodity	Beta Naught
Average	10%	20%	10%	6%	4%
Std. Dev.	16%	50%	16%	16%	25%
Beta	0.8	0.9	0.4	-0.2	0

Portfolio	A	B	C	D	E	F	G	H
(Rp)	10%	12.5%	15%	16%	17%	18%	18%	20%
sp	23%	21%	25%	29%	29%	32%	35%	45%

Correlation Matrix
Fund	Amgen	WW	XX	ZZ
Amgen	1.0
WW	0.5	1.0
XX	0.1	-0.2	1.0
YY	0.3	0.4	0.8
ZZ	0.0	0.8	0.9	1.0

Stock Correlations
	X	Y	Z
X	1.00	0.15	0.70
Y	0.15	1.00	0.51
Z	0.70	0.51	1.00

Stock	Beta	F(R)
A	0.5	0.065
B	1.0	0.095
C	1.5	0.115
Risk-free	0.0	0.030
Market	1.0	0.090

Stock	Ohio	Texas	Montana
Beta	0.50	XX%	1.50
Required Return	10.5%	11.0%	XX%
Expected Return	12.0%	10.0%	15.0%
Expected S&P 500 return	14.0%

Stock	Price Today	Forecasted Price*	Dividend	Beta
Alpha	25	31	2	1.6
Omega	105	110	1	1.2
Lambda	10	10.80	0	0.5
*Forecast Price = expected price one year from today.

Point 1:	Using the historical estimate is far simpler and involves fewer computations than the market model method.
Point 2:	The use of market model estimates implicitly assumes that the market itself is mean-variance efficient.
Point 3:	Both the use of market model estimates and historical estimates rely on historical data to some degree.
Point 4:	One of the problems with using market model estimates for estimating returns is that the market model implicitly assumes the market index is representative of the entire market.

Beta for Stock B	1.10
Beta for Stock C	1.50
Correlation between Stock A and the S&P 500	0.50
Standard deviation for Stock A	28%
Standard deviation for the S&P 500	20%
1-year Treasure bill rate	5%
Expected return on the S&P 500	12%

	Actual	Expected	Company-specific returns surprises
Interest Rate	0.053	0.051	0.0
Unemployment Rate	0.072	0.068	0.0

Portfolio	Sensitivity to Conf. Risk Factor	Sensitivity to Indust. Prod. Factor
J	1.50	1.00
K	0.80	1.20
L	1.00	2.00
Wilshire 5000	1.00	1.50

Portfolio	Sensitivity to ΔGDP	Sensitivity to ΔINF
Q	2.00	0.75
R	1.25	0.50
S	1.50	0.25
Benchmark Index	1.80	1.00