- 10 Marks
FM – L2 – Q25 – Portfolio theory and the capital asset pricing model (CAPM)
Question
Regal Enterprises Ltd. has a mixture of investment portfolios, Project 3 and Project 4. The historical performance return on the projects are as follows:
| Return | Probability | |
|---|---|---|
| Project 3 | 6.0 | 0.6 |
| 1.0 | 0.4 | |
| Project 4 | 8.0 | 0.5 |
| -1.0 | 0.5 |
Required:
(a) Calculate the expected return and standard deviation for Project 3 and Project 4. (6 marks)
(b) The divisional manager will invest in projects that are more risky if they offer a higher return. Advise which project the manager will invest in, considering the expected returns of Project 1 (3.6) and Project 2 (3.95).
Answer
(a)
Project 3
Expected return = (0.6 × 6) + (0.4 × 1) = +4.0
| Return r | Probability p | (r – r̄)² | p(r – r̄)² |
|---|---|---|---|
| 6.0 | 0.6 | 2.40 | 1.44 |
| 1.0 | 0.4 | 3.60 | 1.44 |
| Variance (σ²) | 6.00 |
Standard deviation (σ) = √6.00 = 2.45
Project 4
Expected return = (0.5 × 8) + (0.5 × -1) = +3.5
| Return r | Probability p | (r – r̄)² | p(r – r̄)² |
|---|---|---|---|
| 8.0 | 0.5 | 10.125 | 5.0625 |
| -1.0 | 0.5 | 10.125 | 5.0625 |
| Variance (σ²) | 20.250 |
Standard deviation (σ) = √20.250 = 4.5
(b) The divisional manager will invest in projects that are more risky if they offer a higher return.
The manager will not invest in Project 4 because it offers a lower expected return than Project 3 but higher risk.
The expected return from Project 1 is (0.8 × 4) + (0.2 × 2) = +3.6. The expected return from Project 2 is (0.7 × 5) + (0.3 × 1.5) = +3.95. The highest expected return is offered by Project 3, which has a higher return than Project 1 and Project 2. It would seem that the divisional manager will invest in Project 3 because he is prepared to take the higher risk for a higher expected return. However, Project 2 might seem more attractive: its expected return is almost as high as for Project 3 and the risk is much less.
- Tags: CAPM, expected return, Investment decisions, Portfolio theory, risk analysis, Standard deviation
- Level: Level 2
- Uploader: Samuel Duah