Assume a flat yield curve with spot rate of 4.0% at all maturities and normally distributed yield volatility of 1.0%. We are mapping a two-bond portfolio. Both bonds have a $100 million face value and pay an ANNUAL 4% coupon. One bond has a one year maturity; the other has a five year maturity. If we use PRINCIPAL MAPPING what is the portfolio's 95% value at risk (VaR)?

a. $2.7 million

b. $4.9 million

c. $7.5 million

d. $9.5 million

Your answer was:

D- The 3-year zero-coupon bond (the primitive), under annual compounding, has modified duration = 3/(1+4%) = 2.885.

The Returns (%) VaR = 1% yield volatility * 1.645 deviate * 2.885 mod duration = 4.75% Risk (i.e., Returns VaR)

The 95% VaR = 4.75%* $200 MM = $9.49 million.

I did not understand the formula of the modified duration. I can see that we need to get the average maturity, however, no clue as to the equation 3/(1+4%).

Can you please explain.

Thanks

Imad