Assume that you manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 42%. The T-bill rate is 6%. Your client chooses to invest 85% of a portfolio in your fund and 15% in a T-bill money market fund.

a. What is the expected return and standard deviation of your client's portfolio? (Round your answers to 2 decimal places.)
b. Suppose your risky portfolio includes the following investments in the given proportions:

Stock A 26%
Stock B 35%
Stock C 39%

What are the investment proportions of your client

a. Expected Return = 16.20 %

   Standard Deviation = 35.70%

b. Stock A  = 22.10%

   Stock B  = 29.75%

   Stock C  = 33.15%

   T-bills  = 15%

Explanation:

a. To calculate the expected return of the portfolio, we simply multiply the Expected return of the stock with the weight of the stock in the portfolio.

Thus, the expected return of the client's portfolio is,

The standard deviation of a portfolio with a risky and risk free asset is equal to the standard deviation of the risky asset multiply by its weightage in the portfolio as the risk free asset like T-bill has zero standard deviation.

b. The investment proportions of the client is equal to his investment in T-bills and risky portfolio. If the risky portfolio investment is considered of the set proportion investment in Stock A, B & C then the 85% investment of the client will be divided in the following proportions,

1a)16.2% 1b)35.7% 2a.            2b.              2c

Explanation:

1a)Expected Return=Prop in risky*exp return+Prop in t-bill*return in t-bill

=(0.85*0.18)+(0.15*0.6)

=0.162/16.2%

1b) prop in Rsky *standard deviation of risky

    = 0.85*0.42

    =0.357/35.7%

2a. The prop invested in risky is 85% so

=0.85*0.26=0.221/21.2%

=0.85*0.35=0.2975/29.75%

=0.85*0.39=0.3315/33.15%

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