Assume that yT is normally distributed at time 0. It is not expected to be different from yo,T, i.e. E[31,T] = Yo,T for all T, and the variance is the same for all maturities, Voy1,T] =2 for all T>1. Denote the expected one-period return (from time 0 to time 1) of a zero-coupon bond with maturity T by E(r. 1). Assume ro +1 = 1.01 (Gross return) and = 0.1. We will consider expected returns on zero-coupon bonds for different assumptions about investor behavior. Suppose investors are risk-neutral, i.e., expected bond returns are equalized across all maturities: E(+1) = r = 1.01 for all T. (a) Why must expected returns be equalized across maturities?3 (b) How is E(+1) related to yo, and y,T? Derive an expression for E(+1) in terms of yo, and y,T, and then explain the idea behind that expression intuitively.4 (c) Use E(r) = r++ to solve for yoT as a function of T. (d) Draw the yield curve, i.e., the continuously compounded yield yo, as a function of maturity T for T > 1. Is the yield curve upward or downward sloping? 3 Hint: Think about the usual risk-return tradeoff. Does it apply in this scenario? 4 Hint: Try to express the price of the bond at time 0 and time 1 using the yield at each time.