Question

What is the expected return of a portfolio with two stocks that has 3,200 shares of stock A, which has a price of 25.1 dollars per share and an expected return of 5.97 percent, and 75,300 dollars of stock B, which has a beta of 1.13? The market has an expected return of 13.51 percent, the inflation rate is 2.1 percent, and the risk-free rate is 3.01 percent. Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Answer 1

Here we will consider that risk free rate of 3.01% is nominal as it has not been mentioned that it is real.

Thus expected return of B = risk free rate + (beta*market risk premium)

= 3.01% + 1.13*(13.51% - 3.01%)

= 14.88%

Value of A = 3200*25.1 = $80,320

Value of B = $75,300

Thus weight of A = 80,320/(80,320+75,300) = 51.6129%. Thus weight of B = 1-51.6129% = 48.3871%

Thus expected return of the portfolio = 51.6129% * 5.97% + 48.3871% * 14.88%

= 0.1028

(Note that if risk free rate is implied as real risk free rate then return of B = 3.01%+2.1% + 1.13*(13.51%-3.01%-2.1%) = 14.60%. In this case the portfolio return will be = 0.1015)