[2008] Topic 72: The Capital Asset Pricing Model and Its Application to Perfo only, standard, returns

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AIM 1: List the CAPM’s underlying assumptions.

1、The assumption that returns are normally distributed means that investors:

A) are risk averse.

B) have the same horizon.

C) do not need to consider transactions costs.

D) only consider the mean and standard deviation of the returns.

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The correct answer is D

If a distribution is normally distributed, then it is completely described by the mean and standard deviation. Then, these are the only two parameters in the investors’ utility functions.

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

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

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

C) 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.

D) It is difficult for the individual investor to achieve the benefits from diversification because significantly reducing risk requires the purchase of approximately 1,000 securities.

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The correct answer is C

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: wAsA .  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).

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3、According to the capital asset pricing model, a negative risk premium:

A) is an impossibility.

B) would only occur if the covariance of a security’s return with the return on the market is positive.

C) would only occur if the covariance of a security’s return with the return on the market is negative.

D) would only occur if the covariance of a security’s return with the return on the market is zero.

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The correct answer is C

A negative risk premium would occur if the beta of the security was negative, which would occur if the covariance of a security's return with the return on the market is negative.

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4、All of the following are assumptions of the capital asset pricing model EXCEPT:

A) investors can borrow and lend at the same risk-free rate.

B) each investor seeks to maximize the expected utility of wealth at the end of his horizon.

C) the time horizons of investors are normally distributed.

D) investors have the same expectations concerning returns.

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The correct answer is C

The CAPM assumes that investors all have the same horizon (as well as expectations). This means that the distribution of the horizons is not normal because normality implies a bell-shaped curve distribution, which would have a positive variance and, hence, dispersion.

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5、Under the CAPM, which of the following can investors choose for their portfolios?

I.           The risk-free asset.

II.         The market portfolio.

III.        Assets that maximize return relative to asset-specific risk.

IV.      A portfolio (other than the market portfolio) on the efficient frontier of risky portfolios.

A) I and II only.

B) I only.

C) II and III only.

D) I, II and IV only.

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The correct answer is A

All investors will combine the market portfolio with the risk-free asset. Asset-specific risk is not important and is actually eliminated with the choice of the market portfolio.