Financial Risk Manager Part 1

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.