City bank has six-year zero coupon bonds with a total face value of $20 million. The current market yield on the bonds is 10 percent. What is the daily value at risk (VaR) of this bond portfolio?

Question

Quizplus · Accepted Answer

To calculate the VaR, we need to determine the standard deviation of the portfolio. Since these are zero coupon bonds, the only risk factor is the change in interest rates. Using the duration formula, we can calculate the duration of the portfolio as follows:

Duration = (6 years)(1 - 1/(1+0.10)^6) / 0.10 = 4.968 years

The standard deviation of the portfolio can be calculated as follows:

SD = Duration x Portfolio Value x Yield Volatility = 4.968 x $20 million x 0.01 = $993,600

Assuming a 99% confidence level and a normal distribution, we can calculate the VaR as follows:

VaR = -1.29 x SD = -$1,279 x $993,600 = -$1,271,494

The daily VaR is therefore equal to VaR / sqrt(252) = -$218,180.

City Bank Has Six-Year Zero Coupon Bonds with a Total