Question

Q3. Follow Bank has a S1 million position in a five-year, zero-coupon bond with a face value of $1,402,552. The bond is trading at a yield to maturity of 7.00 percent. The historical mean change in daily yields is 0.0 percent and the standard deviation is 12 basis points a. What is the modified duration of the bond? What is the maximum adverse daily yield move given that we desire no more than a 5 percent chance that yield changes will be greater than this maximum? b. c. What is the daily earnings at risk for this bond?

Answer 1

1.MODIFIED DURATION OF THE BOND.

MD=D/(1+r)=5/1.07=4.6729 years

2.Potential adverse move in yield at 5%.

=1.65 $\sigma$ =1.65*standard deviation=1.65×0.0012=0.00198

3.Price volatility.

Price volatility=MD*Potential adverse move in yield

Price volatility=4.6729*0.00198=0.009252 or 0.9252 Percent

4.Daily earnings at the risk of this bond(DEAR).

DEAR=($ value of position)*(price volatility)

DEAR=$1,000,000*0.009252=$9252.