AIM 1: Describe how the covariance/correlation of returns between securities affects the returns distribution of a portfolio of securities.

1、Mital Tiene’s investment portfolio currently consists of stocks in two companies, 40 percent in Drysdahl Banking and the remaining amount in Clampett Oil. Performance measurement information for these two stocks is given in the table below:  

The covariance between the two stocks is 0.001. Tiene is considering adding a third stock, Hilbilee Investors. Hilbilee Investor’s correlation coefficient with the current portfolio is 0.38.

Which of the following statements is least accurate?

A) With Hilbilee added to the portfolio, the variance could be 0.026.  

B) As Tiene diversifies, he will reduce the portfolio's unsystematic risk. 

C) The standard deviation of returns for the current portfolio is 15.5%.  

D) The expected return of Tiene's current portfolio is approximately 14.1%.

The correct answer is A

Since Hilbilee’s correlation coefficient with the existing portfolio is less than 1, there are benefits to diversification, and adding it to the existing portfolio would reduce the variance below the current level of 0.024. (See calculations below). The other choices are correct.

ER_Portfolio = (w_Drysdahl × ER_Drysdahl) + (w_Clampett × ER_Clampett) = (0.40 × 10.5%) + (0.60 × 16.55%) = 14.13%.

The equation for the standard deviation = σ_1,2 = [(w₁²)(σ₁²) + (w₂²)(σ₂²) + 2w₁w₂σ₁σ₂ρ_1,2]^1/2,

Here stock 1 = Drysdahl and stock 2 = Clampett, and r_1,2 = cov_1,2 / (σ₁ × σ₂) = 0.001 / (0.085 × 0.25) = 0.047

σ_Portfolio = [(0.40² × 0.085²) + (0.60² × 0.25²) + (2 × 0.40 × 0.60 × 0.085 × 0.25 × 0.047)]^1/2 = 0.024^1/2, or 0.155 = 15.5%. (The variance is 0.024).

2、 investor owns the following three-stock portfolio today.

Stock                       Market Value                 Expected Annual Return 

K                         $4,500                                       14% 

L                         $6,300                                        9% 

M                        $3,700                                        12%  

The expected portfolio value two years from now is closest to:

A) $16,150.  

B) $14,960. 

C) $17,975. 

D) $17,870.

The correct answer is C

The easiest way to approach this problem is to determine the value of each stock two years in the future and to sum up the total values of each stock.

Stock           Market Value  ×       Expected Annual Return     =   Total

K                 $4,500   ×               1.14 × 1.14       =   5,848.20

L                  $6,300   ×               1.09 × 1.09       =   7,485.03

M                 $3,700   ×               1.12 × 1.12       =   4,641.28

                                                   Total                =   17,974.51

3、If the correlation between assets is less than one, the portfolio variance is less than the weighted average of the variances of the individual securities. This is an example of the:

A) benefits of diversification.  

B) limits of VAR. 

C) variance mapping effect. 

D) variance/covariance effect.

The correct answer is A

The reduction in variance through the combination of instruments with a correlation of less than one is an example of the benefits of diversification.

4、Which of the following statements regarding risk is FALSE? The:

A) expected return for a portfolio is calculated as a weighted average where the weights are based on percentage of asset allocation in each security.  

B) standard deviation of a portfolio is calculated as a weighted average of individual standard deviations where the weights are based on the percentage of asset allocation in each security. 

C) risk for the portfolio is based on dispersion of returns around the expected return.  

D) portfolio's variance or standard deviation is a good measure of total risk.

The correct answer is B

The standard deviation of a portfolio is calculated using the Markowitz equation. Security correlations are the key to diversification benefits. For a two-asset portfolio the expected return for the portfolio is simply based on the weighted-average return and is a linear relationship based on the percentage allocated in each asset. However, if two assets are not perfectly correlated, the standard deviation or total risk for the portfolio will be reduced based on how the assets are correlated with each other.

AIM 2: Describe the efficient frontier and the asset allocation decision both with and without the presence of a riskless asset.

1、All portfolios on the capital market line are:

A) distinct from each other.  

B) unrelated except that they all contain the risk-free asset. 

C) perfectly negatively correlated.  

D) perfectly positively correlated. 

The correct answer is D

The introduction of a risk-free asset changes the Markowitz efficient frontier into a straight line. This straight efficient frontier line is called the capital market line (CML). Since the line is straight, the math implies that any two assets falling on this line will be perfectly, positively correlated with each other. Note: When ra,b = 1, then the equation for risk changes to sport = WAsA + WBsB, which is a straight line.

2、 An investor is evaluating the following possible portfolios. Which of the following portfolios would least likely lie on the efficient frontier?

A) C, D, and E.  

B) A, E, and F. 

C) A, B, and C.  

D) B, C, and F.

The correct answer is D

Portfolio B cannot lie on the frontier because its risk is higher than that of Portfolio A's with lower return. Portfolio C cannot lie on the frontier because it has higher risk than Portfolio D with lower return. Portfolio F cannot lie on the frontier cannot lie on the frontier because its risk is higher than Portfolio D.

3、The capital market line results from combining the efficient frontier with a risk-free asset. Given the availability of risky assets and a risk-free asset, the best combinations of risk and return are represented by:

A) the efficient frontier of risky assets.  

B) combinations of the market portfolio and risk-free borrowing or lending. 

C) combinations of the minimum variance portfolio of risky assets and the risk-free asset.  

D) combinations of the market portfolio and minimum variance portfolio of risky assets.

The correct answer is B

The best combinations of risk and return are represented by combinations of the market portfolio and risk-free borrowing or lending.

4、The intercept and slope of the capital market line are:

A) RM and [E(RP) ? RF] / σP, respectively.  

B) RF and [E(RM) ? RF] / σM, respectively. 

C) RF and [E(RP) ? RF] / σM, respectively.  

D) RM and [E(RM) ? RP] / σM, respectively.

The correct answer is B

The CML is expressed by the following equation:

The line begins at the vertical axis at R_F. With each increase in σ_P, the expected return increases by [E(R_M) ? R_F] / σ_M.

AIM 3: Summarize the concepts of beta, the security market line (SML), and the capital asset pricing model (CAPM), and describe how they are related to the determination of the expected return of a security or portfolio of securities.

1、The beta of stock D is -0.5. If the expected return of Stock D is 8%, and the risk-free rate of return is 5%, what is the expected return of the market?

A) -1.0%.  

B) +3.0%. 

C) +3.5%.  

D) -4.0%.

The correct answer is A

RRStock = Rf + (RMarket ? Rf) × BetaStock, where RR = required return, R = return, and Rf = risk-free rate

A bit of algebraic manipulation results in:

RMarket = [RRStock ? Rf ? (BetaStock × Rf)] / BetaStock = [8 ? 5 ? (-0.5 × 5)] / -0.5 = 0.5 / -0.5 = -1%

2、Total Quality Inc. has a beta of 1.15. If the expected return on the market is 12 percent, and the risk-free rate is 6 percent, what is the expected return for Total Quality?

A) 12.90%.  

B) 10.15%. 

C) 11.69%.  

D) 14.00%.

The correct answer is A

Expected return = Rf + β(RM – Rf) = 6 + 1.15 (12-6) = 12.90%

3、Jim Sheehan manages a diversified portfolio containing forty stocks. The portfolio beta is 1.05. Jim is considering adding the stock of ABC Inc. to the portfolio, and would fund the purchase with cash already in the portfolio. ABC Inc. has a beta of 1.20, and is currently not part of the portfolio. Which statement about the resulting portfolio is TRUE?

A) Systematic risk would decrease, but the unsystematic risk would be unchanged.  

B) Both systematic risk and unsystematic risk would be unchanged. 

C) Systematic risk would increase, but the unsystematic risk would be unchanged.   

D) Both systematic risk and unsystematic risk would both increase. 

The correct answer is C

Since the portfolio is well diversified, the assumed level of unsystematic risk is zero. The addition of ABC Inc will increase the portfolio beta, and, hence, the level of systematic risk.

4、A security’s systematic risk is proportional to:

A) the standard deviation of its return.  

B) the variance of its return. 

C) its diversifiable risk.   

D) the covariance of its return with the return on the market portfolio.

The correct answer is D

The measure of systematic risk is beta, and beta is proportional to the covariance of a security’s return with the return on the market portfolio.

5、The expected rate of return is 1.5 times the 16% expected rate of return from the market. What is the beta if the risk free rate is 8%?

A) 2.  

B) 4. 

C) 3.  

D) 5.

The correct answer is A

24 = 8 + β (16 ? 8)

24 = 8 + 8β

16 = 8β

16 / 8 = β

β = 2

6、An analyst collected the following data for three possible investments.

The expected return on the market is 12% and the risk-free rate is 4%.

According to the security market line (SML), which of the three securities is correctly priced?

A) Alpha.  

B) Omega. 

C) Lambda.  

D) None of the securities are correctly priced.

The correct answer is C

In the context of the SML, a security is underpriced if the required return is less than the holding period (or expected) return, is overpriced if the required return is greater the holding period (or expected) return, and is correctly priced if the required return equals the holding period (or expected) return.

Here, the holding period (or expected) return is calculated as: (ending price – beginning price + any cash flows / dividends) / beginning price. The required return uses the equation of the SML: risk free rate + Beta × (expected market rate ? risk free rate).

§ For Alpha: ER = (31 – 25 + 2) / 25 = 32%, RR = 4 + 1.6 × (12 ? 4) = 16.8%. Stock is underpriced.

§ For Omega: ER = (110 – 105 + 1) / 105 = 5.7%, RR = 4 + 1.2 × (12 ? 4) = 13.6%. Stock is overpriced.

§ For Lambda, ER = (10.8 – 10 + 0) / 10 = 8%, RR = 4 + 0.5 × (12 ? 4) = 8%. Stock is correctly priced.

Which of the three securities identified by Williams would plot on the capital market line(CML)?

A) Alpha.  

B) Omega. 

C) Lambda.  

D) None of the securities would plot on the CML.

The correct answer is D

By definition, all stocks and portfolios (other than the market portfolio) fall below the CML. (Only the market portfolio is efficient).

7、Which of the following statements about the security market line (SML) is least accurate?

A) The market portfolio consists of all risky assets.  

B) Securities that plot above the SML are undervalued. 

C) Securities that plot on the SML have no intrinsic value to the investor.  

D) The risk-free rate defines where the SML intersects the vertical axis.

The correct answer is C

Securities that fall on the SML are properly priced. They have value to an investor in that they still earn a return.

8、Consider the expected returns and standard deviations for the following portfolios:

Relative to the other portfolios, the portfolio that is not mean variance efficient is:

A) Portfolio 2.  

B) Portfolio 3. 

C) Portfolio 1.  

D) Portfolio 4.

The correct answer is C

Portfolio 1 is not efficient because it has a lower expected return and higher risk than both Portfolios 2 and 3.

AIM 4: Explain why diversification strategies do not increase firm value.

1、In perfect capital markets, the firm cannot create value by hedging risks because:

A) risk is transferred costlessly.  

B) it is costly to transfer risk. 

C) the cost of bearing any risk does not vary across individuals or institutions.  

D) only systematic risk matters.

The correct answer is C

In perfect capital markets, the firm cannot create value by hedging risks because shareholders can hedge at the same cost as the firm. They will not pay the firm to do something that they can do on their own account at the same price.

2、In perfect capital markets, managers will be rewarded by shareholders for decreasing the firm’s diversifiable risk:

A) regardless of the cost.  

B) under no conditions. 

C) if the cost of reducing diversifiable risk is zero.  

D) if the cost of reducing diversifiable risk is sufficiently low.

The correct answer is B

In perfect capital markets, shareholders can eliminate diversifiable risk through their own diversification at zero cost.

AIM 6: Demonstrate, using arbitrage and hedging, that hedging price risk with respect to output will not affect firm value.

1、In perfect capital markets, the only exception to the idea that firm hedging activities do not increase firm value is when:

A) diversifiable risk is decreased.  

B) systematic risk is decreased.  

C) there are no exceptions.   

D) risk premiums are very high.

The correct answer is C

In perfect capital markets, there is no exception to the rule that hedging will NOT increase firm value. Assuming perfect markets, shareholders can hedge at the same cost as the firm. They will not pay the firm to do something that they can do on their own account at the same price.