Cuhk Chapter 6 Assignment

Chapter 6

Q7

1. It is expected that the mean return of stock fund will be similar to the value computed in Spreadsheet 6.2, and the variance value of stock fund will be increased since the probabilities of the extreme outcome including Severe Recession and Boom are higher.

[pic 1]

[pic 2]

Covariance has dropped because the possibility of extreme scenario has increased, including severe recession and boom. In this case, the deviation of Stock return does not change much but the deviation of Bond Fund return become less dynamic, therefore the covariance dropped.

Q13

1. Even though it seems that gold is dominated by stocks, gold might still be an attractive asset to hold as a part of a portfolio. Given that the correlation between gold and stocks is sufficiently low, gold will be held as a component in a portfolio, specifically, the optimal tangency portfolio.
2. If the correlation between gold and stocks is 1, then no one will hold gold since gold would move exactly in the same direction of stocks and stocks dominate gold in terms of both return and standard deviation.

However, this situation will not last long because in case that no one desired gold in the market, the price of gold will fall and its expected rate of return will increase until it reaches the equilibrium in the market.

Q14

Since Stock A and Stock B are perfectly negatively related, we can create a risk free portfolio with stock A and stock B and this risk-free portfolio’s return can be considered as a risk-free rate.

To find the respective proposition of Stock A and Stock B, we assume that we will invest (WA) in Stock A and (1-WA) = WB in Stock B. Also, the standard deviation of the portfolio will be 0.

WA × 0.4 - (1-WA) × 0.6 = 0

0.4 WA - 0.6 + 0.6 WA = 0

WA = 0.6

WB = 0.4

Risk-free rate:

WA × 8% + WB × 13%

= 0.6 × 8% + 0.4 × 13%

=10%

Therefore, the equilibrium Risk-free rate can be equal to 10%, but not greater than 10%.

Q21

1. For a diversified investor, he is exposed to the systematic risk. Beta measures the systematic risk, which is reflected in the slope of the Security Characteristic Line (SCL), since the slope of SCL of Stock B is steeper, it implies the beta of Stock B is greater than Stock A and hence stock B is risker for this investor.
2. For an undiversified investor, he is exposed to the firm-specific risk. In this case, we can find that the deviation from the SCL, which is the vertical distance of each plot with the SCL, is larger for Stock A, compared to Stock B. Therefore, it implies Stock A is risker for this investor.

Chapter 7

Q3

1. False. We can still earn the Risk-free rate even though the stock has a zero beta.
2. False. Investors require a risk premium only for bearing systematic risk while total volatility includes non- systematic risk.
3. False. Given that the beta of market portfolio must be 1, if we would like to construct a portfolio with beta of 0.75, we should invest 75% of the investment budget in market portfolio and 25% in T-bills.

Q13

This case is not possible.

CAPM indicates that stock with a higher beta should be compensated with a higher expected return. Since Portfolio A has a lower expected return and higher beta when compared to Portfolio B, it contradicts with the CAPM theory.

Q14

This case is possible.

CAPM indicates that the expected return should be compensated for systematic risk only. For the standard deviation, it measures both systematic and non-systematic risk. Therefore, as long as the beta of Portfolio A is lower than the beta of Portfolio B, it is possible that Portfolio A has a higher expected return than Portfolio B.

Q15

This case is not possible.

CAPM indicates that the market is the most efficient portfolio. To compare the efficiency, we can compare the Sharpe ratio of both Portfolio A and Market Portfolio.

 = 0.5[pic 3]

 = 0.33[pic 4]

Since the Sharpe ratio of Portfolio A is better than the Market Portfolio, it violates the CAPM and this case is not possible.

Q16

This case is not possible.

Since Portfolio A dominates the Market Portfolio, in which Portfolio A has a higher return and a lower standard deviation, it violates the CAPM and this case is not possible.

Q18

This case is not possible.

Expected return with beta of 0.9:

= Risk-free rate + (Beta × Market Premium)

= 10% + 0.9 × (18% - 10%)

= 10% + 7.2%

= 17.2%

For the Portfolio with a beta of 0.9, it should have an expected return of 17.2% under the same SML. Since Portfolio A is plotted below the SML, it has a negative alpha of (17.2% - 16%) 1.2% and it is overpriced, in which it violates CAPM.

Q19

This case is possible.

CAPM indicates that the market is the most efficient portfolio. To compare the efficiency, we can compare the Sharpe ratio of both Portfolio A and Market Portfolio.

 = 0.27[pic 5]

 = 0.33[pic 6]

Since the Sharpe ratio of Portfolio A is not better than the Market Portfolio, it does not violate the CAPM and this case is possible.

Q24

1. We cannot tell which advisor was a better selector of individual stock because of the uncompleted information. To compare the performance, we need to examine the abnormal return, which is the difference between the actual realized return and the expected return from the SML line. Without the risk-free rate and the market return rate, there is no way for us the compare the advisor’s performance with the market, so that we cannot determine which advisor was a better selector.
2. Given that the T-bills rate was 6% and the market return is 14%, we can determine which advisor was the superior stock selector.

Advisor 1’s expected return: 6% + 1.5 × (14% - 6%) = 18%

Abnormal return of advisor 1: 19% - 18% = 1%

Advisor 2’s expected return: 6% + 1 × (14% - 6%) = 14%

Abnormal return of advisor 2: 16% - 14% = 2%

In this case, since advisor 2 achieves a higher abnormal return than advisor 1, it is believed that advisor 2 was the superior stock selector.