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A)	a measure of the sensitivity of a security’s return to the market return.

B)	a standardized measure of the total risk of a security.

C)	the covariance of a security’s returns with the market return, divided by the variance of market returns.

Beta is a standardized measure of the systematic risk of a security. β = Cov_r,mkt / σ²_mkt. Beta is multiplied by the market risk premium in the CAPM: E(R_i) = RFR + β[E(R_mkt) – RFR].

Which of the following statements regarding the Capital Asset Pricing Model is least accurate?

A)	It is when the security market line (SML) and capital market line (CML) converge.

B)	It is useful for determining an appropriate discount rate.

C)	Its accuracy depends upon the accuracy of the beta estimates.

The CML plots expected return versus standard deviation risk. The SML plots expected return versus beta risk. Therefore, they are lines that are plotted in different two-dimensional spaces and will not converge.

Todd Karabon, a junior analyst for investment boutique Marsh & Sons, has just been assigned his first security-analysis project. Before he starts crunching numbers, Karabon decides to review his portfolio theory.

Karabon starts with a look at capital market theory. He remembers that the theory requires a number of assumptions, and he jots some of them down:

The market portfolio is key to modern portfolio theory, its existence creating a new strategy for maximizing portfolio return. As a refresher, Karabon records some thoughts about the market portfolio:

Marsh & Sons has provided Karabon with data sheets on a number of companies. The first one the analyst considers is Ofin Finance, a consumer-lending company. The sheet contains the following data: expected returns for the stock, the market risk premium, beta, and the risk-free rate of return. Karabon attempts to graph the SML to determine whether the stock is cheaply priced.

The analyst follows up his analysis of Ofin with a review of a half-dozen other stocks. While the SML is a useful tool for assessing valuation, Karabon is not satisfied. He decides to tweak his valuation model by relaxing some of the assumptions used to calculate the SML.

First, Karabon assumes that investors cannot borrow or lend at the risk-free rate. Eliminating the assumption changes the look of the SML graph. Next, Karabon goes down the list of assumptions and determines that every time he relaxes one of the CAPM assumptions, the SML changes dramatically.

When Karabon relaxed one of the CAPM assumptions, the SML looked different depending on the size of the stock. He was relaxing the assumption of:

Relaxing the assumption of no transaction costs and taxes turns the SML into a band, not a line. But since smaller stocks may have a higher liquidity premium than larger stocks, the band may be wider for the smaller stocks. The efficient-market hypothesis is not relevant here.

A)	All investors make investment decisions for the same reasons, considering only expected return and standard deviation.

B)	Every investor has the same time horizon.

C)	Investors can borrow at the risk-free rate and know in advance about their real cash flows.

While investors who theoretically borrow at the risk-free rate would certainly know their nominal cash flows, real cash flows cannot be guaranteed. A number of events, such as a change in the inflation rate, could affect real cash flows.

A)	needed to calculate the CML.

B)	needed to calculate beta.

C)	the point at which the SML intercepts the y-axis.

The SML intercepts the y-axis at a point equal to the risk-free rate of return, and that asset is needed to change the efficient frontier from a curve into a line, the CML. However, beta is calculated using the standard deviation, covariances, and correlations.

A)	the covariance between the returns for Ofin Finance and the market portfolio.

B)	expected market returns.

C)	no data beyond what he already possesses.

To calculate the SML for an asset, we need expected returns of that asset and the market, the asset’s beta, the risk-free return, and the market risk premium. However, since the market risk premium equals the expected market return minus the risk-free rate, we can calculate any one of the three variables if we are given the other two. By using the market risk premium and the risk-free rate, Karabon can calculate the expected market return.

A)	The risk of the market portfolio is measured in both standard deviation and systematic risk.

B)	No portfolio along the Markowitz efficient frontier has a higher Sharpe ratio than the market portfolio.

C)	The market portfolio is uninvestable.

The market portfolio’s risk is generally measured by standard deviation. Systematic risk is used to calculate the SML. Both of the other statements are correct.

How does eliminating the ability to lend and borrow at the risk-free rate change the nature of the SML?

In order to make the SML equation work, a zero-beta portfolio must exist. If we cannot borrow or lend at the risk-free rate, the zero-beta portfolio has a higher expected return than the risk-free rate, which makes the y-intercept higher. The higher return for the zero-beta portfolio also lowers, or flattens, the slope.

An analyst has developed the following data for two companies, PNS Manufacturing (PNS) and InCharge Travel (InCharge). PNS has an expected return of 15% and a standard deviation of 18%. InCharge has an expected return of 11% and a standard deviation of 17%. PNS’s correlation with the market is 75%, while InCharge’s correlation with the market is 85%. If the market standard deviation is 22%, which of the following are the betas for PNS and InCharge?

Beta_i = (s_i/s_M) ′ r_I,MBeta_PNS = (0.18/0.22) x 0.75 = 0.6136
Beta_InCharge = (0.17/0.22) x 0.85 = 0.6568

If the standard deviation of the market’s returns is 5.8%, the standard deviation of a stock’s returns is 8.2%, and the covariance of the market’s returns with the stock’s returns is 0.003, what is the beta of the stock?

Which of the following statements about a stock's beta is TRUE? A beta greater than one is:

A)	riskier than the market, while a beta less than one is less risky than the market.

B)	risky, while a beta less than one is risk-free.

C)	undervalued, while a beta less than one is overvalued.

Beta is a measure of the volatility of a stock. The overall market's beta is one. A stock with higher systematic risk than the market will have a beta greater than one, while a stock that has a lower systematic risk will have a beta less than one.

Given a beta of 1.10 and a risk-free rate of 5%, what is the expected rate of return assuming a 10% market return?

The expected rate of return is twice the 12% expected rate of return from the market. What is the beta if the risk-free rate is 6%?

24 = 6 + β (12 ? 6)

18 = 6β

β = 3

Which of the following statements about asset pricing models is most accurate?

A)	According to the Capital Asset Pricing Model (CAPM), the expected rate of return of a portfolio with a beta of 1.0 is the market expected return.

B)	Assuming assets are not perfectly positively correlated, the systematic risk of a portfolio decreases as more assets are added.

C)	Adding the risk-free asset to a portfolio will reduce return and total risk.

Diversification reduces unsystematic, or unique risk. With the risk-free asset and a portfolio of risky assets, the equation for the expected standard deviation is linear: w_As_A. A combination of the risk free asset and a portfolio always gives more return for a given level of risk. Risk tends to be reduced, but assuming that assets are not perfectly positively correlated, an investor can achieve the benefits of diversification by adding just one security (Markowitz). Studies have shown that approximately 18-30 stocks are needed for proper diversification. The main point is that the number of stocks required is small and is significantly less than all securities (and significantly less than 1,000 securities).

Given the following data, what is the correlation coefficient between the two stocks and the Beta of stock A?

correlation coefficient = 0.00109 / (0.0205)(0.1004) = 0.5296.

beta of stock A = covariance between stock and the market / variance of the market

Beta = 0.002 / 0.0301² = 2.2

Which of the following statements about the capital market line (CML) is least accurate?

A)	Investors choose a portfolio on the CML by varying their weightings of the risk-free asset and the market portfolio.

B)	The CML will not be a linear relationship if investors' borrowing and lending rates are not equal.

C)	The market portfolio lies on the CML and has only unsystematic risk.

The first part of this statement is true - the market portfolio does lie on the CML. However, the market portfolio is well diversified and thus has no unsystematic risk. The risk that remains is market risk, or nondiversifiable, or systematic risk.

The CML measures standard deviation (or total risk) against returns. The CML will “kink” if the borrowing rate and lending rate are not equal. Investors choose a portfolio on the CML by lending or borrowing at the risk-free rate to vary the weighting of their investments in the risk-free asset and the market portfolio.

A basic assumption of the capital asset pricing model (CAPM) is that there are no transaction costs. If this assumption is relaxed, which of the following would be the least likely to occur?

A)	All securities will plot very close to the security market line.

B)	Each investor can have a unique view of a security market line.

C)	Diversification benefits will be realized up to the point that they offset transactions costs.

If the assumption of “no transaction cost” is relaxed, then investors will correct mispricing only up to the point where transaction costs begin to offset potential excess return. As a result, all securities will plot within a band around the SML. It also would impact diversification, since at some point the transaction cost will offset the benefits of diversification.

21st Century Investments manages a portfolio, Z, that has zero correlation with the market index and examines the prospects for AMI Enterprises, a manufacturer of laptop batteries. 21^st Century Investments derives the following market forecasts:

Using the zero-beta form of the capital asset pricing model (CAPM), the equilibrium expected return for AMI is closest to:

The zero beta form of the CAPM replaces the risk-free rate with the return on a zero beta portfolio. Portfolio Z has zero correlation with the market portfolio. Therefore, the beta for portfolio Z also equals zero. Recall the formula for beta:

where cov_im is the covariance between any asset i and the market index m, σ_i is the standard deviation of returns for asset i, σ_m is the standard deviation of returns for the market index, and ρ_im is the correlation between asset i and the market index. Therefore, the beta will equal zero if the correlation equals zero.

The equation for the zero-beta CAPM is:

E(R) = E(R_z) + β[E(R_m) – E(R_z)] = 0.08 + 1.50[0.14 – 0.08] = 0.17 = 17%

Andrew Howell uses the security market line (SML) to make investment decisions. His firm incurs 2% transaction costs on all purchases. How does the existence of the 2% transaction cost change the intercept and slope of the SML for stock purchases faced by Howell’s firm?

Increase by 2%

No change

Increase by 2%

No change

The existence of transaction costs causes the SML to change from a line to a thick band. The width of the band equals the transactions cost (2% above the line for purchases, and 2% below the line for sales). The question asks about purchases, so the intercept will increase by 2%. There is no change in the slope if the 2% transaction applies to all stocks as stated in the question.

The security market line (SML) will resemble a band, rather than a line, if some of its underlying assumptions are lifted. About which of the following assumptions is this least accurate?

A)	No transactions costs.

B)	Heterogeneous investor expectations.

C)	Unequal borrowing and lending rates.

If investors have heterogeneous expectations, or if transaction costs are not assumed to be zero, the SML becomes a band rather than a line. Differences in borrowing and lending rates can be assumed to be appropriate and used in the construction of the capital market line (CML). The result is a CML that is bent around the market portfolio. The portion of the CML connecting the risk-free asset and market portfolio will have a steeper slope than the portion of the CML extending beyond the market portfolio.

Which of the following assumptions associated with the capital asset pricing model (CAPM), when relaxed, will be least likely to result in turning the security market line (SML) into a band rather than a line?

A)	A single holding period.

B)	No transaction costs.

C)	Equal borrowing and lending rates.

If the assumption of equal borrowing and lending rates is relaxed then the CAPM cannot be derived since there is no unique market portfolio. In effect, the CML will become kinked.