Assume that you manage a risky portfolio with an expected rate of return of 15%
ID: 2650734 • Letter: A
Question
Assume that you manage a risky portfolio with an expected rate of return of 15% and a standard deviation of 47%. The T-bill rate is 5%. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund.
What is the expected return and standard deviation of your client's portfolio? (Round your answers to 2 decimal places.)
Suppose your risky portfolio includes the following investments in the given proportions:
31%
What are the investment proportions of your client’s overall portfolio, including the position in T-bills?(Round your answers to 2 decimal places.)
What is the reward-to-volatility ratio (S) of your risky portfolio and your client's overall portfolio? (Round your answers to 4 decimal places.)
Assume that you manage a risky portfolio with an expected rate of return of 15% and a standard deviation of 47%. The T-bill rate is 5%. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund.
Explanation / Answer
Solution:
1. Expected Return = r1 .w1 + r2 .w2
where,
ri = rate of return of an asset class (i=1,2,3)
wi = weight of asset class in the portfolio (i=1,2,3).
ER = (15%) * (70%) + (5%) * (30%)
= 10.50% + 1.50%
= 12%
Standard Deviation (S.D.) = s1 .w1 + s2 .w2
where,
si = standard deviation of an asset class (i=1,2,3)
wi = weight of asset class in the portfolio (i=1,2,3).
S.D. = (47%) * (70%) + (0) * (30%)
= 32.90%
Expected Returns (ER) = 12%
Standard Deviation (S.D.) = 32.90%.
2. Investment Proportion of Stock A = 31% *70 /100 = 0.217
Investment Proportion of Stock B = 31% *70 /100 = 0.217
Investment Proportion of Stock C = 38% *70 /100 = 0.266
Investment Proportion of T-Bills = 30%.
3. Reward-to-Volatility Ratio = (rp - rf) / sp.
where,
rp = expected return on portfolio,
rf = risk free rate,
sp = standard deviation of portfolio.
Reward-to-Volatility Ratio of Risky Portfolio = (15% - 5%) / 47% = 21.28%
Reward-to-Volatility Ratio of Client's Overall Portfolio = (12% -5%) / 32.90% = 21.28%.