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Explanation:
B is correct. We can derive marginal VaR as:
Marginal VaR of asset i = (VaRₚ/Valueₚ) * Betaᵢ
Since VaRₚ/Valueₚ will be the same for all the assets, marginal VaRs of assets can be compared based on their betas.
Jensen’s Alpha measure is calculated as:
Jensen’s Alpha = Actual return – Expected return based on systematic risk
= Actual return – (risk-free rate + (Market return – risk-free rate)*Beta)
Note that the market risk premium = expected market return – risk-free rate = 0.08 – 0.03 = 5%
Thus, among those assets whose Jensen’s Alphas are greater than or equal to market risk premiums, Asset JKL has the lowest Marginal VaR:
| Asset | Portfolio weight | Actual return | Beta to the portfolio | Marginal VaR | Expected return | Jensen’s Alpha |
|---|---|---|---|---|---|---|
| BDE | 0.35 | 14% | 1.20 | 1.2W | 9.0% | 5.0% |
| JKL | 0.30 | 13% | 0.90 | 0.9W | 7.5% | 5.5% |
| MNO | 0.25 | 13% | 1.00 | 1.0W | 8.0% | 5.0% |
| STU | 0.10 | 10% | 0.80 | 0.8W | 7.0% | 3.0% |
where W = VaRₚ/Valueₚ.
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| Asset | Portfolio weight | Return | Volatility of return | Beta to the portfolio |
|---|---|---|---|---|
| BDE | 0.35 | 14% | 19% | 1.20 |
| JKL | 0.30 | 13% | 18% | 0.90 |
| MNO | 0.25 | 13% | 16% | 1.00 |
| STU | 0.10 | 10% | 10% | 0.80 |
The portfolio manager wants to select the asset that has the lowest marginal VaR as long as its Jensen’s alpha is greater than or equal to the market risk premium. Assuming the risk-free interest rate is 3% and the market return is 8%, which asset should the portfolio manager select?
A
Asset BDE
B
Asset JKL
C
Asset MNO
D
Asset STU