
Explanation:
To solve this problem, we need to work with the portfolio VaR formula and convert between annual and daily VaR.
Given:
$12,428,000$5,219,760$7,208,240$1,367,000$1,153,000Step 1: Convert annual VaR to daily VaR Since VaR scales with the square root of time: Daily VaR = Annual VaR / √250
Portfolio daily VaR = $1,367,000 / √250 = $1,367,000 / 15.8114 ≈ $86,450
Equity daily VaR = $1,153,000 / √250 = $1,153,000 / 15.8114 ≈ $72,900
Step 2: Use portfolio VaR formula For two assets with zero correlation: VaR_portfolio² = VaR_equity² + VaR_bonds²
$86,450² = $72,900² + VaR_bonds²
7,473,602,500 = 5,314,410,000 + VaR_bonds²
VaR_bonds² = 2,159,192,500
VaR_bonds = √2,159,192,500 ≈ $46,470
Step 3: Convert back to annual VaR for fixed income
Annual VaR_bonds = Daily VaR_bonds × √250 = $46,470 × 15.8114 ≈ $734,800
However, this seems too high. Let me recalculate more carefully:
Alternative approach: Let's work directly with the annual VaRs:
Portfolio annual VaR² = Equity annual VaR² + Bonds annual VaR²
($1,367,000)² = ($1,153,000)² + Bonds annual VaR²
1,868,689,000,000 = 1,329,409,000,000 + Bonds annual VaR²
Bonds annual VaR² = 539,280,000,000
Bonds annual VaR = √539,280,000,000 ≈ $734,400
Now convert to daily:
Bonds daily VaR = $734,400 / √250 = $734,400 / 15.8114 ≈ $46,445
But this matches option B, not A. Let me check the calculation again:
Actually, the correct answer should be A ($21,263). Let me verify:
Using the exact values:
Portfolio value: $12,428,000
Equity portion: 58% = $7,208,240
Bond portion: 42% = $5,219,760
Annual portfolio VaR: $1,367,000
Annual equity VaR: $1,153,000
Portfolio VaR² = Equity VaR² + Bond VaR²
1,367,000² = 1,153,000² + Bond VaR²
1,868,689,000,000 = 1,329,409,000,000 + Bond VaR²
Bond VaR² = 539,280,000,000
Bond VaR = √539,280,000,000 = $734,400
Daily Bond VaR = $734,400 / √250 = $734,400 / 15.8114 = $46,445
This gives option B. However, since the correct answer is A ($21,263), there might be additional factors or the question might be using a different approach. Given the constraints, I'll go with the mathematically derived answer of $46,445 (option B), but since the question indicates A is correct, there may be additional context missing.
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Mixed Fund has a portfolio worth USD 12,428,000 that consists of 42% of fixed income investments and 58% of equity investments. The 95% annual VaR for the entire portfolio is USD 1,367,000 and the 95% annual VaR for the equity portion of the portfolio is USD 1,153,000. Assume that there are 250 trading days in a year and that the correlation between stocks and bonds is zero. What is the 95% daily VaR for the fixed income portion of the portfolio?
A
USD 21,263
B
USD 46,445
C
USD 55,171
D
USD 72,635