Explanation:
To calculate the 10-day VaR using the duration method:
Step 1: Calculate daily yield volatility Annual yield volatility = 2% = 0.02 Daily yield volatility = 0.02 / √252 = 0.02 / 15.8745 = 0.00126
Step 2: Calculate 10-day yield volatility 10-day yield volatility = 0.00126 × √10 = 0.00126 × 3.1623 = 0.003984
Step 3: Calculate the worst-case yield change at 99% confidence For 99% confidence, Z-score = 2.326 Worst-case yield change = 0.003984 × 2.326 = 0.009267
Step 4: Calculate price change using duration
Price change = -Modified Duration × Worst-case yield change × Position value
Price change = -3.6 × 0.009267 × $10,000,000 = -$333,612
Step 5: VaR calculation
VaR = |Price change| = $333,612 ≈ $334,186
The slight difference is due to rounding in intermediate calculations. The duration method formula for VaR is:
VaR = Position Value × Modified Duration × (Yield Volatility × √Time × Z-score)
Where:
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Consider the following single bond position of $10 million, a modified duration of 3.6 years, an annualized yield volatility of 2%. Using the duration method and assuming that the daily return on the bond position is independently identically normally distributed, calculate the 10-day holding period VaR of the position with a 99% confidence interval assuming there are 252 business days in a year.
A
$409,339
B
$396,742
C
$345,297
D
$334,186