A bank has invested $5 million in a four-year, zero coupon bond. The bond is trading at a yield to maturity of 4%. The historical change in yields are normally distributed and the standard deviation is 10 bps. 

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 is the daily earnings at risk (Dear) of this bond at 5% level? 

e). What is the VaR if the holding period is ten (30) days?rn