Question

Assume that (i) the expected return on the stock market is 10% with a standard deviation of 20%, (ii) the expected return on gold is 5% with a standard deviation of 25%, and (iii) the risk-free rate is 2%. Further assume the correlation between returns on stocks and those on gold is -0.5. Which of the following is closest to the volatility of a portfolio that is 80% stocks and 20% gold? Group of answer choices

14.2%

15.0%

10.2%

21.0%

2.01%

Using the information in the previous problem (#8), which of the following is closest to the Sharpe ratio of each of stocks and gold?

Group of answer choices

Sharpe ratio of Stocks= 0.40, of gold=0.12

Sharpe ratio of Stocks= 0.50, of gold=0.20

Sharpe ratio of Stocks= 0.50, of gold=0.12

Sharpe ratio of Stocks= 0.40, of gold=0.20

Using the information in the problem #8, which of the following is closest to the Sharpe ratio of the (80%stocks, 20%gold) portfolio?

0.49

0.40

0.55

0.34

Answer 1

8.

We need to find the volatility (standard deviation) of the portfolio which contains 80% stocks and 20% Gold. Given returns and standard deviation of stocks is 10% and 20%. Returns and standard deviation of Gold is 5% and 25%. Correlation is -0.5 between them. So, volatility of the portfolio can be calculated by the formula square root of (W(s)^2*sd(s)^2+W(g)^2*sd(g)^2+(2*W(s)*W(g)*correlation*sd(s)*sd(g))). On substituting, we get square root of (0.8^2*0.2^2+0.2^2*0.25^2+(2*0.8*0.2*(-0.5)*0.2*0.25) which gives 14.17% which is closest to 14.2%.

9.

Sharp ratio is calculated by the formula, (expected return-risk free return)/standard deviation. Given that risk free rate is 2%.

So, Sharp ratio of stocks = 10%-2%/0.2= 0.4

Sharp ratio of gold is 5%-2%/0.25= 0.12

10.

For calculating sharp ratio of portfolio, we need to find expected returns. Expected return in the given portfolio = 0.8*(10%)+0.2*(5%)= 9%. Standard deviation is already calculated as 14.2%

So, sharp ratio of the portfolio is given by 9%-2%/14.2% = 0.49