Question

The market index has average return 7% and standard deviation 30%. The
risk-free rate is 3%. A portfolio has beta 1.4, unsystematic variance of 0.03,
and an M2-measure of -0.01. What is the average return on the portfolio?

Answer 1

Total Variance of the portfolio= Beta^2*market variance + unsystematic variance

= 1.4^2*0.3^2+0.03

= 0.2064

Standard deviation of the portfolio = 0.2064^0.5 = 0.4543 or 45.43%

M2 = (return of portfolio (R) - risk free rate) * standard deviation of market/ standard deviation of portfolio - (Return on market - risk free rate)

= (R-0.03)*0.3/0.4543 - (0.07-0.03) = -0.01

=> (R-0.03) = 0.03*0.4543/0.3 = 0.04543

R = 0.07543 or 7.543%

So, average return on the portfolio is 7.543%