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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