Suppose that the interest rate on a 1-year bond in 2000 is 10%. Interest rates are expected to fall. Suppose that the expected interest rate on one-year bonds in 2001, 2002, 2003, and 2004 are 8%, 6%, 4%, and 2%, respectively. In addition, suppose that the liquidity premium, i.e., the spread between the forward rate of interest and the expected one-year interest rate in 2001, 2002, 2003, and 2004 is constant at 4%. That is, fn = E(rn) + 4% for n = 2,3,4, and 5. Note: All the bonds considered in this exercise are zero-coupon bonds and their par value is $1,000.
(a) Calculate the forward rates in 2001, 2002, 2003, and 2004.
(b) If the yield curve is determined by both the expectations theory and the liquidity preference theory, calculate the yield to maturity of the five zero-coupon bonds issued today (2000) and which mature in 2001, 2002, 2003, 2004, and 2005, respectively.
(c) In the same graph, draw the expected returns, the forward rates, and the yield curve, all as a function of the maturity of the five bonds considered in this exercise.
(d) Inspecting the graph, what relation do you observe between the forwards rates fn and the yield curve?
(e) If the interest rates in 2001, 2002, 2003, and 2004 turned out to be equal to the forward rates in 2001, 2002, 2003, and 2004 that you calculated above, what would then the price in 2002 be of the 5-year maturity bond issued in year 2000? What would the price in 2003 be of the same bond issued in year 2000? Given those prices, what would the rate of return be from buying this bond in 2002 and selling it in 2003? Defend your answer and provide intuition for your result.

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