3. In our "Orange County's Investment Pool" mini-case study, suppose that Bob Citron's investment portfolio is composed of 5-year treasury bonds paying 3% coupons annually We can then treat his entire portfolio as holding one giant treasury coupon bond with a 5 year maturity and a 3% annual coupon rate (as said above, coupons are paid annually) The yield to maturity (yield) of this bond is also 5%, as in the mini-case. Assume the face value of the bond is $100. (a) Calculate the modified duration of this (giant) bond. (b) Bob Citron's investment portfolio was worth $20.5 billion in value, ie. he invested $20.5 billion in this bond (of course through aggressive short-term borrowing). Estimate a change in the yield of this bond that would cause Bob Citron's portfolio to suffer a loss of $1.6 billion in value. (Assume that during the move of the yield, Citron's portfolio holdings stay the same, thus % change in the bond price = % change in Citron's portfolio value)