Question

Assume that you manage a risky portfolio with an expected rate of return of 17.7% and a standard deviation of 27.1%. The T-bill rate is 6.5%.

   

Required:
(a)	Your client chooses to invest 75% of a portfolio in your fund and 25% in a T-bill money market fund. What is the expected return and standard deviation of your client's portfolio? (Round your answers to 1 decimal place. Omit the "%" sign in your response.)

    

Expected return	%	per year
Standard deviation	%	per year

  

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

  

Stock A	27%
Stock B	35%
Stock C	38%

    

What are the investment proportions of your client’s overall portfolio, including the position in T-bills?(Round your answers to 1 decimal place. Omit the "%" sign in your response.)

    

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?(Round your answers to 4 decimal places.)

     

Your Reward-to-variability ratio
Client's Reward-to-variability ratio

Answer 1

a) Expected return = 17.7% x 0.75 + 6.5% x 0.25 = 14.9%

Now, T-bill is risk free, therefore, its standard deviation is zero.

So, Standard deviation of client's portfolio = 27.1% x 0.75 = 20.325% or 20.33%

b)

Security	Investment Proportion
T-bill	25%
Stock A	75% x 0.27 = 20.3%
Stock B	75% x 0.35 = 26.2%
Stock C	75% x 0.38 = 28.5%
Total	100%

Note : Stock A and B are rounded off, so it could be possible that stock A is 20.2% and stock B is 26.3%. Try this in case you see the above as incorrect.

c) Your Reward-to-variability ratio = (Expected return - Risk free rate) / Standard deviation = (17.7% - 6.5%) / 27.1% = 0.413284 or 0.4133

Client's Reward-to-variability ratio = (Expected return - Risk free rate) / Standard deviation = (14.9% - 6.5%) / 20.325% = 0.413182 or 0.4133

Note : For part c try 0.4132 for both in case you get incorrect answer.