Question

Assume that you manage a risky portfolio with an expected rate of return of 12% and a standard deviation of 39%. The T-bill rate is 6%A client prefers to invest in your portfolio a proportion (y) that maximizes the expected return on the overall portfolio subject to the constraint that the overall portfolio's standard deviation will not exceed 30%. a. What is the investment proportion, y

Answer 1

Answer:

y = 0.76923076923  or  76.923076923%  rounded off to 76.92%

So, 76.92% of the portfolio should be invested in risky portfolio.

Explanation:

The portfolio standard deviation for a portfolio consisting of two securities with one of them being the risk free security is calculated by multiplying the standard deviation of the risky security by the weightage of investment in the risky security as a proportion of the overall investment in portfolio. The formula can be written as follows,

Portfolio STDEV = Weight of Risky Asset  *  STDEV of risky asset

30% = y  *  39%

30% / 39% = y

y = 0.76923076923  or  76.923076923%  rounded off to 76.92%