Question

The market portfolio currently has the expected return of 15% per annum and with the risk, as measured by standard deviation, of 10% per annum. The risk free rate is currently 5% per annum. You wish to form an investment portfolio with the expected return of 12% per annum. What will be the risk of your portfolio? Show all workings, including the weights to be invested in the Market portfolio and Risk-Free asset (and indicate whether you have to borrow or lend).

Answer 1

Let, Weight of Market Portfolio be x. Therefore, Weight of Risk Free Asset will be (1-x)

Expected Return is 12%

Therefore, Weighted Average of Portfolio should be 12%

Weighted Average = Sum of (Weights*Return)

12 = (x*15)+[(1-x)*5]

12 = 15x+5-5x

7 = 10x

Therefore, Weight of Market Portfolio = x = 7/10 = 70%

Therefore, Weight of Risk Free Asset = 1-70% = 30%

As, Weight of Risk Free Asset is Positive, Amount will be LENT.

Risk of Portfolio = Weighted Average Standard Deviation

Standard Deviation of Risk Free Asset = 0

Therefore, Risk of Portfolio = (Risk of Market*Weight of Market) + 0 = (10*70%) = 7%