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?
 
　　b. What is the price volatility if the potential adverse move in yields is 25 basis points?
　　c. What is the DEAR?
　　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?
       Answer:
 
　　a.MD = D/(1 + R) = 15/(1.095) = 13.6986.
　　b.Price volatility = (MD) x (potential adverse move in yield)
　　= (13.6986) x (.0025) = 0.03425 or 3.425 percent.
 
　　c.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.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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