Assume that you manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 34%. The T-bill rate is 5.5%.

Your risky portfolio includes the following investments in the given proportions:

Stock A 32%

Stock B 36%

Stock C 32% 

 

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 17%.

 

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

 

Proportion y=       

 

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

Expected return on an investment refers to the expected value of its return. Standard deviation is a measure of the volatility of the returns.

The value of y proportion is 0.920 or 92%.

The client's investment in T-bill is 8%

The investment proportion in Stock A is 29.44%

The investment proportion in Stock B is 33.12%

The investment proportion in Stock C is 29.44%

The standard deviation of the rate of return on the client's portfolio is 31.28%

Part a:

Expected return of the risky portfolio is 18% or 0.18 and the T-bill rate is 5.5% or 0.055.

Now, the client decides to invest "y" proportion in the risky portfolio and remainder in a T-bill.

So, investment in the T-bill will be "1-y".

On investing "y" proportion in the risky portfolio and "1-y" in T-bill the expected rate of return is 17% or 0.17

?=>y×0.18+(1−y)×0.055=0.17?

?=>y×0.18+1×0.055−y×0.055=0.17?

?=>y×0.18−y×0.055+0.055=0.17?

?=>(0.18−0.055)×y=0.17−0.055?

?=>(0.125)×y=0.115?

?=>y=0.1250.115??

=0.920 or 92%

Answer: Hence, the value of y proportion is 0.920 or 92%

Part b:

Client's investment in T-bill is:

?=1−y=1−0.92?

=0.08 or 8%

Answer: Hence, the client's investment in T-bill is 8%

Given that the risky portfolio includes the following investments in the given proportions:

Stock A 32% or 0.32

Stock B 36% or 0.36

Stock C 32% or 0.32

We have determined that the client's investment in the risky portfolio is 92% or 0.92.

Client's investment proportions in the three stocks is calculated as:

Investment proportion in Stock A is calculated as:

?=0.32×0.92?

=0.2944 or 29.44%

Answer: Hence, the investment proportion in Stock A is 29.44%

Investment proportion in Stock B is calculated as:

?=0.36×0.92?

=0.3312 or 33.12%

Answer: Hence, the investment proportion in Stock B is 33.12%

Investment proportion in Stock C is calculated as:

?=0.32×0.92?

=0.2944 or 29.44%

Answer: Hence, the investment proportion in Stock C is 29.44%

Part c:

Given that the standard deviation of the risky portfolio is 34% or 0.34

As T-bill is a risk free asset, the standard deviation of T-bill will be zero. 

So, the standard deviation of the client's portfolio will be:

?=(Weightoftheportfolio)×(Standarddeviationoftheportfolio)?

?=(0.92)×(0.34)?

=0.3128 or 31.28%

Answer: Hence, the standard deviation of the rate of return on the client's portfolio is 31.28%