FIN355 CH6&7 HW EXAM2

What must be the beta of a portfolio with E(rP) = 20%, if rf = 5% and E(rM) = 15%?

20% = 5% + Beta(15% - 5%) --> Beta = 1.5

If the simple CAPM is valid, is the below situation possible? Explain. Risk-Free Portfolio: Expected Return=10% Beta=0% Market Portfolio: Expected Return =18% Beta=1.0 Portfolio A: Expected Return =16% Beta=1.5

Not possible. Given these data, the SML is: E(r) = 10% + β(18% - 10%)A portfolio with beta of 1.5 should have an expected return of: E(r) = 10% + 1.5 x (18% - 10%) = 22% The expected return for Portfolio A is 16% so that Portfolio A plots below the SML (i.e., has an alpha of -6%), and hence is an overpriced portfolio. This is inconsistent with the CAPM.

If the simple CAPM is valid, is the below situation possible? Explain. Risk-Free Portfolio: Expected Return=10% Standard Deviation=0% Market Portfolio: Expected Return =18% Standard Deviation=24% Portfolio A: Expected Return =20% Standard Deviation=22%

Not possible. Portfolio A clearly dominates the market portfolio. It has a lower standard deviation with a higher expected return.

If the simple CAPM is valid, is the below situation possible? Explain. Portfolio A: Expected Return=20% Beta=1.4 Portfolio B: Expected Return =25% Beta=1.2

Not possible. Portfolio A has a higher beta than Portfolio B, but the expected return for Portfolio A is lower.

If the simple CAPM is valid, is the below situation possible? Explain. Risk-Free Portfolio: Expected Return=10% Beta=0% Market Portfolio: Expected Return =18% Beta=1.0 Portfolio A: Expected Return =16% Beta=0.9

Not possible. The SML is the same as in Problem 18. Here, the required expected return for Portfolio A is: 10% + (0.9 x 8%) = 17.2%This is still higher than 16%. Portfolio A is overpriced, with alpha equal to: -1.2%

If the simple CAPM is valid, is the below situation possible? Explain. Risk-Free Portfolio: Expected Return=10% Standard Deviation=0% Market Portfolio: Expected Return =18% Standard Deviation=24% Portfolio A: Expected Return =16% Standard Deviation=12%

Not possible. The reward-to-variability ratio for Portfolio A is better than that of the market, which is not possible according to the CAPM, since the CAPM predicts that the market portfolio is the most efficient portfolio. Using the numbers supplied: SA = (16-10)/12 = 0.5 SM= (18-10)/24 = 0.33 These figures imply that Portfolio A provides a better risk-reward tradeoff than the market portfolio.

If the simple CAPM is valid, is the below situation possible? Explain. Portfolio A: Expected Return=30% Standard Deviation=35% Portfolio B: Expected Return =40% Standard Deviation=25%

Possible. If the CAPM is valid, the expected rate of return compensates only for systematic (market) risk as measured by beta, rather than the standard deviation, which includes nonsystematic risk. Thus, Portfolio A's lower expected rate of return can be paired with a higher standard deviation, as long as Portfolio A's beta is lower than that of Portfolio B.

If the simple CAPM is valid, is the below situation possible? Explain. Risk-Free Portfolio: Expected Return=10% Standard Deviation=0% Market Portfolio: Expected Return =18% Standard Deviation=24% Portfolio A: Expected Return =16% Standard Deviation=22%

Possible. Portfolio A's ratio of risk premium to standard deviation is less attractive than the market's. This situation is consistent with the CAPM. The market portfolio should provide the highest reward-to-variability ratio.

Here are data on two companies. The T-bill rate is 4% and the market risk premium is 6%. - Forecast Return: $1 Discount Store=12% Everything $5=11% - Standard Deviation of Returns: $1 Discount Store=8% Everything $5=10% - Beta: $1 Discount Store=1.5 Everything $5=1.0 What would be the expected rate of return for each company, according to the capital asset pricing model (CAPM)?

$1 Discount Store: E(r) = 4% + 1.5 x 6% = 13% Everything $5: E(r) = 4% + 1.0 x 6% = 10%

In forming a portfolio of two risky assets, what must be true of the correlation coefficient between their returns if there are to be gains from diversification? Explain.

So long as the correlation coefficient is below 1.0, the portfolio will benefit from diversification because returns on component securities will not move in perfect lockstep. The portfolio standard deviation will be less than a weighted average of the standard deviations of the component securities.

When adding a risky asset to a portfolio of many risky assets, which property of the asset is more important, its standard deviation or its covariance with the other assets? Explain.

The covariance with the other assets is more important. Diversification is accomplished via correlation with other assets. Covariance helps determine that number.

A portfolio's expected return is 12%, its standard deviation is 20%, and the risk-free rate is 4%. Which of the following would make for the greatest increase in the portfolio's Sharpe ratio? a. An increase of 1% in expected return. b. A decrease of 1% in the risk-free rate. c. A decrease of 1% in its standard deviation.

a and b will have the same impact of increasing the Sharpe ratio from .40 to .45.

What is the expected rate of return for a stock that has a beta of 1 if the expected return on the market is 15%? a. 15%. b. More than 15%. c. Cannot be determined without the risk-free rate.

a. 15%. Its expected return is exactly the same as the market return when beta is 1.0.

Are the following true or false? Explain. a. Stocks with a beta of zero offer an expected rate of return of zero. b. The CAPM implies that investors require a higher return to hold highly volatile securities. c. You can construct a portfolio with a beta of .75 by investing .75 of the investment budget in T-bills and the remainder in the market portfolio.

a. False. According to CAPM, when beta is zero, the "excess" return should be zero. b. False. CAPM implies that the investor will only require risk premium for systematic risk. Investors are not rewarded for bearing higher risk if the volatility results from the firm-specific risk, and thus, can be diversified. c. False. We can construct a portfolio with the beta of .75 by investing .75 of the investment budget in the market portfolio and the remainder in T-bills.