Follow Bank has a $1 million position in a five-year, zero-coupon bond with a fa
ID: 2797956 • Letter: F
Question
Follow Bank has a $1 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.
What is the modified duration of the bond?
What is the maximum adverse daily yield move given that we desire no more than a 1 percent chance that yield changes will be higher than this maximum?
What is the price volatility of this bond?
What is the daily earnings at risk for this bond?
Explanation / Answer
a.
Modified duration = year/(1+ rate)
= 5/(1.07)
=4.6729 years
b.
potentian adverse move in yield at 1 % = 2.33 * standard deviation
= 2.33 * 0.0012
= 0.002796
c.
price volatility = Modified duration * adverse move in yield
= 4.6729 * 0.002796
=1.3065%
d.
Daily earnings at risk = Amount * price volatility
= 1,000,000 * 1.3065%
= $13065