- 10 Marks
FM – L2 – Q27a – Portfolio Theory and CAPM
Question
Apex Enterprises has a mixture of investment portfolios, Stock A and Stock B. The historical performance return on the stocks are as follows:
| Year | Stock A Return | Stock B Return |
|---|---|---|
| 20X5 | -10% | -3% |
| 20X6 | 18% | 21% |
| 20X7 | 39% | 44% |
| 20X8 | 14% | 4% |
| 20X9 | 33% | 28% |
Required:
(a) Calculate the average rate of return for each stock during the period of 20X5 to 20X9.
(b) Calculate the average return on the portfolio during the period if Apex Enterprises held 50% each of Stock A and Stock B.
(c) Calculate the return of the portfolio using standard deviation approach.
Answer
(a) Average return Stock A
(-10% + 18% + 39% + 14% + 33%) / 5 = 18.8%
Stock B
(-3% + 21% + 44% + 4% + 28%) / 5 = 18.8%
(b) The realized rate of return/average return of portfolio
RA (% of Stock A) + RB (% of Stock B), then average these yearly return.
| 20X5 | (-10% + -3%) / 2 | -6.5% |
| 20X6 | (18% + 21%) / 2 | 19.5% |
| 20X7 | (39% + 44%) / 2 | 41.5% |
| 20X8 | (14% + 4%) / 2 | 9% |
| 20X9 | (33% + 28%) / 2 | 30.5 |
| | 94 / 5 | 18.8% |
Alternatively
= aR_A + bR_B
= (0.5 * 18.8) + (0.5 * 18.8)
= 9.4 + 9.4 = 18.8%
(c) Standard deviation
Stock A
√A = √[(-10% – 18.8)^2 + (18 – 18.8)^2 + (39% – 18.8)^2 + (14% – 18.8)^2 + (33 – 18.8)^2] / (5 – 1)
= √1.46280 / 4 = 19.12%
Stock B
√B = √[(-3% – 18.8)^2 + (21 – 18.8)^2 + (44 – 18.8)^2 + (4% – 18.8)^2 + (28 – 18.8)^2] / (5 – 1)
= √1.418 / 4 = 18.83%
√AB = √[(-6.5 – 18.8)^2 + (19.5 – 18.8)^2 + (41.5 – 18.8)^2 + (9 – 18.8)^2 + (30.5 – 18.8)^2] / (5 – 1)
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