Bank Alpha has an inventory of AAA-rated, 15-year zero-coupon bonds with a face value of $400 million. The bonds currently are yielding 9.5 percent in the over-the-counter market.
 
　　a. What is the modified duration of these bonds?
 
　　MD = D/(1 + R) = 15/(1.095) = 13.6986.
 
　　b. What is the price volatility if the potential adverse move in yields is 25 basis points?
 
　　Price volatility = (MD) x (potential adverse move in yield)
 
　　= (13.6986) x (.0025) = 0.03425 or 3.425 percent.
 
　　c. What is the DEAR?
 
　　Daily earnings at risk (DEAR) = ($ value of position) x (Price volatility) Dollar value of position = $400m./(1 + 0.095)15 = $102,529,350. Therefore,
 
　　DEAR = $102,529,350 x 0.03425 = $3,511,279.
 
　　d. If the price volatility is based on a 90 percent confidence limit and a mean historical change in daily yields of 0.0 percent, what is the implied standard deviation of daily yield changes?
 
　　The potential adverse move in yields = confidence limit value x standard deviation value. Therefore, 25 basis points = 1.65 x standard deviation, and standard deviation = .0025/1.65 = .001515 or 15.15 basis points.

 
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