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]. Suppose at t=0, an investor with wealth w=100 wants to use it to buy equity instead of a bond. An equity contract is sE(x)=x. Since r=0%, a tradable equity has a price equal expected payoff, i.e. p=E[sE(x)].

a) For a=80, what fraction of payoff does the investor obtain for p=100? [4 Points] b) For a=40, what fraction of payoff does the investor obtain for p=100? [2 Points] Suppose equity is traded at price p=E[sE(x)]. c) What is the information sensitivity of the equity for a=40 and a=80? [6 Points] d) Suppose a=40. Compare the information sensitivity of equity with the bond in 1(e). What is the intuition for the result? [3 Points] e) Suppose a<200 and a bond and equity have the same expected payoff. A bond always has smaller information sensitivity than equity and other securities. Is this correct? [3 Points]