In: Finance
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 | |
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 |