Calculation Explanation

To calculate the diversified VaR at 95% confidence level, we need to:

1. Calculate individual VaRs:

   • VaR_X = Investment_X × Volatility_X × Z-score
   • VaR_Y = Investment_Y × Volatility_Y × Z-score

   For 95% confidence level, Z-score = 1.645

   VaR_X = 1,800,000 × 0.08 × 1.645 = $236,880 VaR_Y = 3,200,000 × 0.04 × 1.645 = $210,560

2. Calculate portfolio VaR using correlation:

   Portfolio VaR = √[VaR_X² + VaR_Y² + 2 × ρ × VaR_X × VaR_Y]

   Where ρ = 15% = 0.15

   Portfolio VaR = √[(236,880)² + (210,560)² + 2 × 0.15 × 236,880 × 210,560]

   = √[56,112,134,400 + 44,335,513,600 + 14,958,051,840]

   = √[115,405,699,840]

   = $339,722

Verification:

• Option A ($14,074) is too small
• Option B ($206,500) is approximately the average of individual VaRs
• Option C ($404,740) is close to the undiversified VaR (sum of individual VaRs)
• Option D ($339,722) matches our calculation

The portfolio VaR is less than the sum of individual VaRs ($447,440) due to diversification benefits from the 15% correlation.