Financial Risk Manager Part 1
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You have been given the following asset weights and betas for a 4-asset portfolio:
| Asset | Beta | Portfolio Weight |
|---|---|---|
| 1 | 1.3 | 30% |
| 2 | 0.97 | 23% |
| 3 | 1.7 | 37% |
| 4 | 1.4 | 10% |
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TTanishq
A
Calculate the portfolio beta
B
Calculate the portfolio standard deviation
C
Calculate the portfolio variance
D
Calculate the portfolio expected return
E
Calculate the portfolio Sharpe ratio
F
Calculate the portfolio tracking error
Explanation:
Explanation
To calculate the portfolio beta, we use the weighted average of the individual asset betas:
Portfolio Beta = Σ(Weight_i × Beta_i)
Let's calculate step by step:
- Asset 1: 30% × 1.3 = 0.30 × 1.3 = 0.39
- Asset 2: 23% × 0.97 = 0.23 × 0.97 = 0.2231
- Asset 3: 37% × 1.7 = 0.37 × 1.7 = 0.629
- Asset 4: 10% × 1.4 = 0.10 × 1.4 = 0.14
Total Portfolio Beta = 0.39 + 0.2231 + 0.629 + 0.14 = 1.3821
Therefore, the portfolio beta is approximately 1.38.
This calculation is appropriate because:
- Beta measures systematic risk relative to the market
- Portfolio beta is the weighted average of individual asset betas
- The weights sum to 100% (30% + 23% + 37% + 10% = 100%)
- The result indicates the portfolio is more volatile than the market (beta > 1)
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