Question

You invest 50% in a risky portfolio, and 50% in a treasury bill. The risky portfolio has an expected return of 15% and a standard deviation of 25%. The treasury bill pays 7%. Suppose that your risky portfolio includes the following investments in the given proportions:

Stock A 30%

Stock B 30%

Stock C 30%

Stock D 10%

What are the investment proportions in the complete portfolio, including stock A, B, C, D and the Treasury bill & What is the expected return and standard deviation of your complete portfolio?

Answer 1

a) Proportion of investments

Stock A: 50% * 30% = 15%

Stock B: 50% * 30% = 15%

Stock C: 50% * 30% = 15%

Stock D: 50% * 10% = 5%

Treasury bill: 50%

b) Expected return is the weighted average of the returns of individual components within the group.

E(R) = w1 * R1 + w2 * R2

E(R) = 50% * 7% + 50% * 15% = 11.00%

c) Standard deviation of portfolio is mathematically represented as:

Standard deviation of Treasury bill (since it is a risk free asset) and its correlation with risky portfolio = 0.

Standard deviation = 12.50%