Question

You have just invested in a portfolio of three stocks. The amount of money that you invested in each stock and its beta are summarized below. Stock Investment Beta $198,000 1.45 297,000 0.62 495,000 1.32 Calculate the beta of the portfolio and use the Capital Asset Pricing Model (CAPM) to compute the expected rate of return for the portfolio. Assume that the expected rate of return on the market is 14 percent and that the risk-free rate is 8 percent. (Round beta answer to 3 decimal places, e.g. 52.750 and expected rate of return answer to 2 decimal places, e.g. 52.75%.) Beta of the portfolio Expected rate of return

Answer 1

Total Portfolio value = Value of A + Value of B + Value of C

=198000+297000+495000

=990000

Weight of A = Value of A/Total Portfolio Value

= 198000/990000

=0.2

Weight of B = Value of B/Total Portfolio Value

= 297000/990000

=0.3

Weight of C = Value of C/Total Portfolio Value

= 495000/990000

=0.5

Beta of Portfolio = Weight of A*Beta of A+Weight of B*Beta of B+Weight of C*Beta of C

Beta of Portfolio = 1.45*0.2+0.62*0.3+1.32*0.5

Beta of Portfolio = 1.136

As per CAPM

expected return = risk-free rate + beta * (expected return on the market - risk-free rate)

Expected return% = 8 + 1.136 * (14 - 8)

Expected return% = 14.82