Question

You manage equity fund with an expected risk premium of 12% and a standard deviation of 14%. The rate on T-bill is 4%. Your client chooses to invest $80,000 her portfolio in your equity fund and $20,000 in T-bill money market fund

What are the expected return and standard deviation of return on your client's portfolio?

13.60% and 11.20%

What is the reward-to-volatility ratio (Sharpe Ratio) for this equity fund?

0.8571

QUESTION:

Suppose your risky portfolio includes the following investments in the given proportions:

Stock A: 25%
Stock B: 35%
Stock C: 40%

What are the investment proportions of your client's overall portfolio, including the position in T-bills?

Question 1 options:

	6% in Stock A, 32% in Stock B, 42% in Stock C, 20% in T-Bill
	20% in Stock A, 28% in Stock B, 32% in Stock C, 20% in T-Bill
	25% in Stock A, 35% in Stock B, 40% in Stock C, 20% in T-Bill
	5% in Stock A, 7% in Stock B, 8% in Stock C, 80% in T-Bill

Answer 1

Expected return on equity fund = risk premium + risk free rate = 12%+ 4%= 16%

The Client invested 80% of his/her wealth in Equity fund and 20% in T- Bills

Since The return of a portfolio is the weighted return of the constituent stocks

So Return of this portfolio = 0.8* 16% +0.2 *4% = 13.2%

The standard deviation of a portfolio is given by

Where Wi is the weight of the security i,

is the standard deviation of returns of security i.

and is the correlation coefficient between returns of security i and security j

As T Bills have a Standard deviation of 0

So, standard deviation of portfolio =0.8 *14% = 11.2%

Reward to volatility ratio = (13.2%- 4%)/11.2% = 0.8571

Investment Proportions in the three stocks and T bills are

Stock A = 25%* 80% =20%

Stock B = 35%* 80% =28%

Stock C = 40%* 80% =32%

T- Bills = 20% (2nd option is correct)