Question

3. (8) Your grandpa is 60 years old. He shows you his portfolio:

Assets	Holdings
Cash	$ 50,000
S&P 500 Index Fund	100,000
Analog Devices Inc.	200,000

He asks you to forecast how much the portfolio will be worth in 5 years when he retires. The risk-free rate is 6% per year, the average return on the market portfolio is 12%, the beta of the S&P index is 1.0, and the beta of Analog Devices is 1.5.

1. What is the expected rate of return on the portfolio, assuming the CAPM holds?
2. What is the forecasted portfolio value after 5 years?
3. Your grandpa is not impressed with this CAPM “theory” since his portfolio has done much better than your forecasted return over the past five years. What would you say about that?

Answer 1

a. Cash will earn the risk-free rate = 6%. The return on the index or the market will be the average market return which is 12%. The return on Analog Devices will be calculated by CAPM.

R = Rf + Beta x (Rm - Rf) = 6 + 1.5 x (12 - 6) = 15%.

Hence, the average return will be the weighted average = 50/35 x 6 + 10/35 x 12 + 20/35 x 15 = 20.5714%.

b. The forecasted value after 5 years will be = 350,000 x 1.205714^5 = $891,845.3716

c. The reason of doing differently is that these are the average or the expected values. The actual values can be different for a short period of time but for an extended period of time, they will converge to these average. Also, the data viz. beta and market portfolio return may be backward-looking i.e. historical data. Hence, without forward-looking data, it is difficult to predict the actual values.