Question

Assume that you manage a risky portfolio with an expected rate of return of 12% and a standard deviation of 47%. The T-bill rate is 4%. Your risky portfolio includes the following investments in the given proportions: Stock A 31 % Stock B 31 % Stock C 38 % Your client decides to invest in your risky portfolio a proportion (y) of his total investment budget with the remainder in a T-bill money market fund so that his overall portfolio will have an expected rate of return of 10%.

a. What is the proportion y? (Round your answer to 3 decimal places.)

b. What are your client's investment proportions in your three stocks and the T-bill fund? (Round your intermediate calculations and final answers to 2 decimal places.)

Security Investment Proportions

T-Bills %

Stock A %

Stock B %

Stock C %

c. What is the standard deviation of the rate of return on your client's portfolio? (Round your intermediate calculations and final answer to 2 decimal places.)

Standard deviation % per year=

Answer 1

a) Weighted average return of individual components of a portfolio is total return of portfolio.

In this question, investor wants 10% or return.

Now, for the question,

10% = 12% * y + 4% * (1 - y)

0.10 = 0.12y + 0.04 - 0.04y

0.06 = 0.08y

y = 0.06/0.08

y = 75%

b) Proportion of fund in risky portfolio = 75%, in T-bills = 25% {= 1 - 75%}

T-Bills: 25%

Stock A %: 31% * 75% = 23.25%

Stock B %: 31% * 75% = 23.25%

Stock C %: 38% * 75% = 28.5%

c) standard deviation or volatility of portfolio is measurable by formula:

Now, for T-bill, standard deviation, ? = 0

So, substitution values:

std deviation % = 35.25%