Financial Risk Manager Part 1
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Two portfolios have the following characteristics:
| Portfolio | Return | Beta |
|---|---|---|
| A | 8% | 0.7 |
| B | 7% | 1.1 |
Given a market return of 10% and a risk-free rate of 4%, calculate Jensen's Alpha for both portfolios and comment on which portfolio has performed better.
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TTanishq
A
-0.2% and -3.6% respectively
Portfolio A has performed better than Portfolio B.
B
-0.2% and -3.6% respectively
Portfolio B has performed better than Portfolio A.
C
0.2% and 3.6% respectively
Portfolio B has performed better than Portfolio A.
D
3.6% and 0.2% respectively
Portfolio A has performed better than Portfolio B.
Explanation:
Explanation
Jensen's Alpha measures the excess return of a portfolio compared to its expected return based on the Capital Asset Pricing Model (CAPM). The formula is:
Jensen's Alpha = Rp - [Rf + βp(Rm - Rf)]
Where:
- Rp = Portfolio return
- Rf = Risk-free rate
- βp = Portfolio beta
- Rm = Market return
Calculations:
For Portfolio A:
- Rp = 8% = 0.08
- Rf = 4% = 0.04
- βp = 0.7
- Rm = 10% = 0.10
Jensen's Alpha = 0.08 - [0.04 + 0.7(0.10 - 0.04)] = 0.08 - [0.04 + 0.7(0.06)] = 0.08 - [0.04 + 0.042] = 0.08 - 0.082 = -0.002 = -0.2%
For Portfolio B:
- Rp = 7% = 0.07
- Rf = 4% = 0.04
- βp = 1.1
- Rm = 10% = 0.10
Jensen's Alpha = 0.07 - [0.04 + 1.1(0.10 - 0.04)] = 0.07 - [0.04 + 1.1(0.06)] = 0.07 - [0.04 + 0.066] = 0.07 - 0.106 = -0.036 = -3.6%
Interpretation:
- Both portfolios have negative alphas, meaning they underperformed their expected returns based on CAPM
- Portfolio A has a higher alpha (-0.2%) than Portfolio B (-3.6%)
- A higher Jensen's Alpha indicates better risk-adjusted performance
- Therefore, Portfolio A has performed better than Portfolio B
Key Insight: Even though both portfolios underperformed expectations, Portfolio A's underperformance is much smaller than Portfolio B's, making it the relatively better performer.
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