Question

Assume that you are managing a risky portfolio with expected rate of return of 18% and standard deviation of 28%. The T-bill rate is 8%. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund.

a) What is the expected value and standard deviation of the rate of return on his portfolio? [8 marks]

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

Stock A 25%, Stock B 32%, Stock C 43%

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

c) What is the reward-to-volatility ratio S of your risky portfolio? Calculate also this ratio for your client?

d) Draw the CAL (capital allocation line) of your portfolio on an expected return–standard deviation diagram. Show the position of your client on your fund’s CAL.

e) Suppose that your client decides to invest in your portfolio a proportion y of the total investment budget so that the overall portfolio will have an expected rate of return of 16%. What is the proportion y?

Answer 1

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Answer:

1)

Let c denote the client’s portfolio, let f denote the money-market fund and let p denote the risky portfolio. Then
E[r_c] = E[.7r_p + .3r_f ] = .7E[r_p] + .3r_f = .7 × .18 + .3 × .08 = 15%
Since σ_f = 0, the standard deviation of the client’s portfolio is given by
σ_c = .7σ_p = .7 × .28 = 19.6%

2).

Since portfolio c is 70 percent invested in p, this means
.7 × .25 = 17.5% in Stock A,
.7 × .32 = 22.4% in Stock B,
.7 × .43 = 30.1% in Stock C.
The fraction invested in T-bills is 30%.

(NOTE IF IN PERCENTAGES, IT IS (35.71%)

d)

e)

Calculate expected return on the client’s portfolio as shown below.

Let y be the proportion of the client’s portfolio invested in the risky portfolio. If the expected return on the client’s portfolio is 16%.

Find y by solving the following equation as shown below.

Proportion of the risky assets in client’s portfolio is 80%.