Question

Currently, we are investing 10 billion won of bonds (3 years maturity, 6% face value), with a maturity rate of 10% and a duration of 2.78 years.

When the annual volatility of the bond yield is 0.45%, calculate the annual VaR of the bond under the delta normal method at the 95% confidence level.

Answer 1

Z-factor for 95% confidence interval = 1.645

Duration = 2.78 years, YTM = 10%

we need to first calculate interest rate VAR, and then need to calculate delta normal standard deviation to convert interest rate VAR into Delta normal VAR.

1. Calculate Interest rate value at risk:

Interest rate value at risk ( rate VAR) = z-factor*standard deviation*square root of holding period

rate VAR = 1.645*0.45*square root of 10

= 2.34%

2. Calculate delta normal standard deviation using rate VAR:

Delta standard deviation using rate VAR = rate VAR*Duration*YTM

= 2.34*2.78*10

= 0.65%

3. Calculate annual delta normal VAR:

New delta normal value at risk (Delta normal) = Delta Std*z-factor*square root of holding period

= 0.65*1.645*square root of 10

= 3.38%