Consider an asset X with payoff x at t=2 which is uniformly distributed between [a, 200]. The probability density is f(x)=1/(200-a). This asset is used as collateral to back a security s(x). The interest rate is r=0%. All investors are risk neutral. Suppose s(x) is a bond with given face value 100, i.e. sB(x)=min[x,100]. a) For a=80, what is the expected payoff of the bond? [4 Points] b) For a=40, what is the expected payoff of the bond? [2 Points] Suppose at t=0, an investor with wealth w=100 wants to buy a bond with price p=100. Since r=0%, a tradable bond has a price equals expected payoff, i.e. p=E[sB(x)]. c) For a=80, what is the face value of the bond such that E[sB(x)]=p=100? [4 Points] d) For a=40, what is the face value of the bond such that E[sB(x)]=p=100? [2 Points] Suppose the bond is traded at price p=E[sB(x)] in the case of (c) and (d). e) What is the information sensitivity of the bond for a=40 and a=80? [6 Points] f) What is the intuition that the information sensitivity is higher if a=40? [2 Points]