Question

Using the following information to answer the next three questions:

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

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

	12.75% and 11.20%
	16.00% and 13.60%
	13.60% and 11.20%
	15.40% and 12.25%

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

	0.8211
	0.7710
	0.8991
	0.8571

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

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

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

	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

We have been given: Expected Risk Premium (RP) = 12%, Standard Deviation () = 14% , T-Bill Rate (R_f) = 4%

Weights in which client allocted his/her money : Equity (Wm) = 80,000/100,000

= 0.80

Debt (Wf) = 0.20

According to CAPM:-

Note: We have not been given Beta of the portfolio hence we are assuming that it's a market portfolio and therefore it's beta is 1.

%

Part 1. i.)

  %

ii)

  

Therfore Part 1 Answer is opetion C. 13.60% and 11.20%

Part 2.

  

  

Therefore Part 2 Answer is option D. 0.8571

Part 3. Now we are told that Equity Portfolio contains Stocks A, B and C.

So Investment Proportion Mix of clients overall portfolio :

Therefore answer for Part 3 is option B. 20% in Stock A, 28% in Stock B, 32% in Stock C, 20% in T-Bill

Explanation:

Asset prices are determind by Discounted Cash Flow technique, where

Since CF₁ ,CF₂ .................CF_n are uncertain, the discount rate i.e. R_e should be risk adjusted.

Re is derived by Capital Asset Price Model (CAPM). CAPM Model is an Addative Model. That's why we added Rf and Risk Premium*Beta in above formula.

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