| 1.You are constructing a portfolio of two assets, Asset A and Asset B. The expected returns of the assets are 13 percent and 16 percent, respectively. The standard deviations of the assets are 39 percent and 47 percent, respectively. The correlation between the two assets is 0.61 and the risk-free rate is 5.3 percent. What is the optimal Sharpe ratio in a portfolio of the two assets? What is the smallest expected loss for this portfolio over the coming year with a probability of 1 percent?(Negative amounts should be indicated by a minus sign. Round your Sharpe ratio answer to 4 decimal place & Probabilityanswer to 2 decimal places. Omit the “%” sign in your response.) |
| Sharpe ratio | |
| Smallest expected loss | % |
The Sharpe ratio is a ratio of return versus risk. The formula is:
(Rp-Rf)/p
where:
Rp = the expected return on the investor’s portfolio
Rf = the risk-free rate of return
p = the portfolio’s standard deviation, a measure of risk
here in this example we assume that both the assets have 50 % each weight in total portfollio
First of all let us find out expexted return
| Assets | Return | Weight | return |
| Assets A | 13 | 0.50 | 6.50% |
| Assets B | 16 | 0.50 | 8% |
| Expected Return | 14.50% |
Expected Return of the portfollio is 14.50%
Risk free rate of return is 5.3 %
Now we will find out portfollio’s standered deviation
Portfolio standard deviation σp for a two-asset portfolio is given by the following formula:
Portfolio Standard Deviation= ω2Aσ2Aω2Bσ2B2ωAωBσAσB
Where,
ωA = weight of asset A in the portfolio;
ωB = weight of asset B in the portfolio;
σA = standard deviation of asset A;
σB = standard deviation of asset B; and
ρ = correlation coefficient between returns on asset A and asset B.
50%239%2+50%247%2+50%50%39%47%0.61
38.62%
Sharp ratio =(0.145 – 0.053)/0.3862 = 0.238 =0.24
smallest expected loss for this portfolio over the coming year with a probability of 1 percent
= expected losses strictly exceeding VaR (also called Mean Excess Loss and Expected Shortfall)
=0.38-0.24
=0.14
