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 A $210,000 1.47 B 315,000 0.61 C 525,000 1.16 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 16 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 enter the beta rounded to 3 decimal places Expected rate of return?

Answer 1

Beta of the portfolio is computed as follows:

= Beta of stock A x weight of stock A + Beta of stock B x weight of stock B + beta of stock C x weight of stock C

Total investment is computed as follows:

= $ 210,000 + $ 315,000 + $ 525,000

= $ 1,050,000

So, the beta will be as follows:

= 1.47 x ($ 210,000 / $ 1,050,000) + 0.61 x ($ 315,000 / $ 1,050,000) + 1.16 x ($ 525,000 / $ 1,050,000)

= 0.294 + 0.183 +0.58

= 1.057

So, the expected return will be as follows:

= risk free rate + Beta x (return on market - risk free rate)

= 8% + 1.057 x (16% - 8%)

= 16.46%

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