Financial Risk Manager Part 2

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Question A fund manager, who has recently obtained a modest sum of new capital, intends to allocate this capital into a current fund that is indexed to a benchmark. Instead of investing in a new asset to be added to the fund, the manager is considering increasing the investment in one of the fund's four existing assets. Details about these assets and their performance during the latest evaluation period are provided below:

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 fund manager is looking to choose the asset with the lowest marginal Value at Risk (VaR), provided that its Jensen's alpha is at least equal to the market's risk premium. Assume a risk-free interest rate of 3% and a market return of 8%. Which asset should the fund manager opt for?

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

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Explanation:

The portfolio manager should select Asset JKL. The decision is based on the comparison of marginal Value at Risk (VaR) and Jensen's Alpha for each asset. Marginal VaR can be determined by the formula: Marginal VaR of asset i = (VaRp/Valuep) * Betai. Since the VaRp/Valuep ratio is constant for all assets, the comparison of marginal VaRs can be made solely based on the assets' betas.

Jensen's Alpha, a measure of the asset's performance relative to the market, is calculated using the formula: Jensen's Alpha = Actual return - Expected return based on systematic risk, which is further broken down to Actual return - (risk-free rate + (Market return - risk-free rate) * Beta). The market risk premium is calculated as the expected market return minus the risk-free rate, which in this case is 5% (0.08 - 0.03).

Among the assets, the one with the lowest marginal VaR and a Jensen's Alpha greater than or equal to the market risk premium is selected. After calculating both metrics for each asset, it is determined that Asset JKL has the lowest marginal VaR and a Jensen's Alpha of 5.5%, which is greater than the market risk premium. Therefore, Asset JKL is the correct choice for the portfolio manager.