Question

You currently have $55,000 invested in a portfolio that has an expected return of 11% and a volatility of 10%. Suppose the risk-free rate is 6%, and there is another portfolio has an expected return of 20% and a volatility of 13% a. What portfolio has a higher expected return than your portfolio but with the same volatility? b. What portfolio has a lower volatility than your portfolio but with the same expected return?

Answer 1

a). Let the proportion invested in the other portfolio be x.

Then, expected volatility = x*13%. This has to be same as the volatility of your portfolio which is 10%, so

13%x = 10%, x = 10%/13% = 76.92%

So, in order to have a volatlity of 10%, 76.92% of 55,000 = 42,307.69 has to be invested in the other portfolio and 12,692.31 in the risk-free investment.

Expected return of the portfolio = (76.92%*20%) + ((1-76.92%)*6%) = 16.77%

b). Let the proportion invested in the other portfolio be x.

In order to have the same expected return of 11% as your portfolio, the new expected return has to be

11% = 20%*x + 6%*(1-x)

11% = 14%*x + 6%

x = 5%/14% = 35.71%

So, invest 35.71%*55,000 = 19,642.86 in the other portfolio and 55,000 - 19,642.86 = 35,357.14 in the risk-free asset.

Volatility in this case, will be x*13% = 35.71%*13% = 4.64%