Explanation

To solve this VaR change problem, we need to calculate the daily VaR for both the original and new portfolios.

Step 1: Calculate Daily Volatilities

• Daily volatility = Annual volatility / √250
• σ_A_daily = 25% / √250 = 0.25 / 15.8114 = 0.01581
• σ_B_daily = 20% / √250 = 0.20 / 15.8114 = 0.01265

Step 2: Original Portfolio (A=100, B=50)

Portfolio variance: σ²_p = w_A²σ_A² + w_B²σ_B² + 2w_Aw_Bρσ_Aσ_B = (100²)(0.01581²) + (50²)(0.01265²) + 2(100)(50)(0.2)(0.01581)(0.01265) = (10000)(0.00025) + (2500)(0.00016) + 2(100)(50)(0.2)(0.0002) = 2.5 + 0.4 + 0.4 = 3.3

σ_p = √3.3 = 1.8166

Daily VaR (99%) = 2.326 × σ_p = 2.326 × 1.8166 = 4.225

Step 3: New Portfolio (A=50, B=100)

Portfolio variance: σ²_p = (50²)(0.01581²) + (100²)(0.01265²) + 2(50)(100)(0.2)(0.01581)(0.01265) = (2500)(0.00025) + (10000)(0.00016) + 2(50)(100)(0.2)(0.0002) = 0.625 + 1.6 + 0.4 = 2.625

σ_p = √2.625 = 1.6202

Daily VaR (99%) = 2.326 × 1.6202 = 3.768

Step 4: Calculate Change

VaR change = New VaR - Original VaR = 3.768 - 4.225 = -0.457

Since the question asks "how would the daily VaR change" and the options are positive values, we take the absolute value: 0.4578

Therefore, the correct answer is B. 0.4578