Question
In: Finance
Assume that you manage a risky portfolio with an expected rate of return of 12% and...
|
Assume that you manage a risky portfolio with an expected rate of return of 12% and a standard deviation of 44%. The T-bill rate is 5%. Your client chooses to invest 80% of a portfolio in your fund and 20% in a T-bill money market fund. |
| a. |
What is the expected return and standard deviation of your client's portfolio? (Enter your answer as a percentage rounded to two decimal places.) |
| Expected return | % per year | |
| Standard deviation | % per year | |
| b. |
Suppose your risky portfolio includes the following investments in the given proportions: |
| Stock A | 28% |
| Stock B |
37% |
| Stock C | 35% |
|
What are the investment proportions of your client’s overall portfolio, including the position in T-bills? (Enter your answer as a percentage rounded to two decimal places.) |
| Security | Investment Proportions |
|
| T-Bills | % | |
| Stock A | % | |
| Stock B | % | |
| Stock C | % | |
| c. |
What is the reward-to-volatility ratio (S) of your risky portfolio and your client's overall portfolio? (Enter your answer as a decimal rounded to 4 decimal places.) |
| Reward-to-Volatility Ratio | |
| Your risky portfolio | |
| Client’s overall portfolio | |
Solutions
Expert Solution
a
| Weight of Risky portfolio = 0.8 |
| Weight of T bill = 0.2 |
| Expected return of Client portfolio = Weight of Risky portfolio*Expected return of Risky portfolio+Weight of T bill*Expected return of T bill |
| Expected return of Client portfolio = 12*0.8+5*0.2 |
| Expected return of Client portfolio = 10.6 |
| Weight of Risky portfolio = 0.8 |
| Weight of T bill = 0.2 |
| Std dev of Client portfolio = Weight of Risky portfolio*Std dev of Risky portfolio+Weight of T bill*Std dev of T bill |
| Std dev of Client portfolio = 44*0.8+0*0.2 |
| Std dev of Client portfolio = 35.2 |
b
Weight of T bill = 20%
Weight of stock A = Weight of risky portfolio*weight of stock A in risky portfolio=0.8*0.28=22.4%
Weight of stock B = Weight of risky portfolio*weight of stock B in risky portfolio=0.8*0.37=29.6%
Weight of stock C = Weight of risky portfolio*weight of stock C in risky portfolio=0.8*0.35=28%
c
Risky portfolio
| Sharpe ratio(reward to variability) | ||
| =(Return-risk free rate)/std dev | ||
| =(12-5)/44 | ||
| =0.1591 |
Client portfolio
| Sharpe ratio(reward to variability) | ||
| =(Return-risk free rate)/std dev | ||
| =(10.6-5)/35.2 | ||
| =0.1591 |
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