Explanation

To calculate the maximum possible daily 95% VaR, we need to consider the worst-case scenario for portfolio diversification, which occurs when the correlation between the two funds is +1 (perfect positive correlation).

Step 1: Calculate daily volatilities

• Alpha daily volatility = 20% / √252 = 20% / 15.8745 = 1.2599%
• Omega daily volatility = 25% / √252 = 25% / 15.8745 = 1.5749%

Step 2: Calculate portfolio weights

Since the portfolio is equally invested:

• Weight in Alpha = 0.5
• Weight in Omega = 0.5

Step 3: Calculate portfolio volatility with ρ = +1

When correlation is +1, portfolio volatility is simply the weighted sum: σ_portfolio = w₁σ₁ + w₂σ₂ = 0.5 × 1.2599% + 0.5 × 1.5749% = 1.4174%

Step 4: Calculate daily 95% VaR

Given μ = 0 (as specified), and using z-score for 95% confidence level = 1.645: VaR = Portfolio Value × σ_portfolio × z-score VaR = 1,000,000 × 1.4174% × 1.645 = 1,000,000 × 0.014174 × 1.645 = USD 23,316

Verification

The maximum possible VaR occurs when correlation is +1 because there is no diversification benefit. If correlation were less than +1, the portfolio volatility would be lower, resulting in a smaller VaR.

Therefore, the maximum possible daily 95% VaR is USD 23,316.