Problem Solving Activity•A bank has a $1 million position in a five year, zero coupon bond. The bond is trading at a yield to maturity of 7%. The historical mean change in daily yields is 0%, and the standard deviation is 12 bp

The complete question is: "A 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?

b. 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?

c. What is the daily earnings at risk for this bond? "

a. Modified duration = D/(1+r)

Modified duration = 5 / (1+7%)

Modified duration = 5/1.07

Modified duration = 4.6729 years

b. Maximum adverse daily yield  = 1.65\б = 1.65 * Standard deviation = 1.65 * 0.0012 = 0.00198

d. Price volatility = Modified duration * Potential adverse move in yield  = 4.6729 * 0.00198 = 0.009252 =  0.9252%

Daily earnings at the risk of this bond = Value of position * Price volatility) = $1,000,000*0.009252 = $9,252