Follow Bank has a $1 million position in a five-year zero-coupon bond with a face value of

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.
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 price volatility of this bond?
d. What are the daily earnings at risk for this bond?
Solution: a) Modified duration of the bond It expresses the measurable change in the value of a security in response to a change in interest rates. The modified duration concept is based on the fact that interest rate and bonds price moves in opposite direction. Modified Duration = Time/(1 + Yield to Maturity) = 5/(1.07) = 4.6729 years b) In this part, we have calculated the expected adverse move in yeild at 5%. Potential adverse move in yield at 5 percent = 1.65* Basis boints = 1.65 x 0.0012 = .001980 c) Price volatility of this bond It describes how quickly or widely price can change. It is calculated by multiplying the modified duration with potential adverse move in yield. Price volatality =

odified duration x potential adverse move in yield = 4.6729 x .00198 = 0.009252 or 0.9252 percent d) Daily Earnings at Risk is defined as the estimated potential loss of a portfolios value over a one-day unwind period as a result of adverse moves in market conditions, such as changes in interest rates, foreign exchange rates, and market volatility. Hence, Daily Earnings at Risk (DEAR) = ($ value of position) x (price volatility) = $1,000,000 x 0.009252 = $9,252

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