Explanation

To solve this problem, we need to find the 95% daily VaR for the fixed income portion of the portfolio.

Step 1: Understand the given information

• Portfolio value: USD 12,428,000
• Fixed income portion: 42% → USD 5,219,760
• Equity portion: 58% → USD 7,208,240
• 95% annual VaR (portfolio): USD 1,367,000
• 95% annual VaR (equity): USD 1,153,000
• Correlation between stocks and bonds: 0
• Trading days per year: 250

Step 2: Convert annual VaR to daily VaR

Since VaR scales with the square root of time:

Daily VaR (portfolio) = Annual VaR (portfolio) / √250 = 1,367,000 / √250 = 1,367,000 / 15.8114 ≈ USD 86,450

Daily VaR (equity) = Annual VaR (equity) / √250 = 1,153,000 / √250 = 1,153,000 / 15.8114 ≈ USD 72,920

Step 3: Use portfolio VaR formula with zero correlation

When correlation = 0, the portfolio VaR formula simplifies to:

VaR²(portfolio) = VaR²(equity) + VaR²(fixed income)

Let VaR(fixed income) = x

86,450² = 72,920² + x²

7,473,602,500 = 5,318,126,400 + x²

x² = 7,473,602,500 - 5,318,126,400 x² = 2,155,476,100

x = √2,155,476,100 ≈ USD 46,445

Step 4: Verify the result

• Daily VaR (equity): USD 72,920
• Daily VaR (fixed income): USD 46,445
• Portfolio VaR: √(72,920² + 46,445²) = √(5,318,126,400 + 2,157,138,025) = √7,475,264,425 ≈ USD 86,450 ✓

Therefore, the 95% daily VaR for the fixed income portion is USD 46,445.