Ch8Sols - 8-1CHAPTER 8: PRINCIPLES OF SPOT...

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Unformatted text preview: 8-1CHAPTER 8: PRINCIPLES OF SPOT PRICINGEND-OF-CHAPTER QUESTIONS AND PROBLEMS1.A spot rate is a rate on a loan to be taken out immediately. The rate is negotiated today and the borrowerthen receives funds from the lender. A forward rate is a rate on a loan in which the rate is negotiatedtoday, but the loan is not taken out until a later date. A spot rate reflects current market conditions, whilea forward rate must reflect expected future market conditions.2.a.The market segmentation theory. This theory says that supply and demand conditions in long-and short-term markets determine whether long- or short-term rates will be higher. In thisexample, the Treasury is shifting toward more long-term borrowing which should, if nothing elsechanges, cause long-term rates to increase and short-term rates to decrease.b.The expectations theory. This theory says that the expectation of increasing interest rates isrevealed by the fact that long-term rates are higher than short-term rates. The forward rates thatare imbedded in the term structure are the market's expectations of future spot rates.c.The liquidity preference theory. This theory says that lenders prefer to make short-term loansand require a risk premium to be willing to make long-term loans.d.The local expectations theory. This theory is simply based on the principle that there are noarbitrage opportunities available across the term structure. The implication is that the one-periodahead forward rate will be an unbiased expectation of the future spot rate but only when the riskneutral probabilities, which are not the true probabilities, of interest rate movements are used.3.In each of the problems below we set up an equation that indicates that a longer-term loan is equivalent toa series of shorter-term loans.a.A two-year spot loan is equivalent to a one-year spot loan plus a forward loan starting at the endof year 1 to be paid back at the end of year 2.[1 + r(0, 2)]2= [1 + r(0,1)][1 + r(1, 2)]Solving for r(1, 2):r(1, 2) = {[1 + r(0, 2)]2/[1 + r(0, 1)]} - 1r (1, 2) = {[1.085]2/[1.08]} - 1 = .09b.A three-year spot loan is equivalent to a one-year spot loan plus a forward loan starting at the endof year 1 to be paid back at the end of year 3.[1 + r(0, 3)]3= {[1 + r(0, 1)][1 + r(1, 3)]2}r(1, 3) = {[1 + r(0, 3)]3/[1 + r(0, 1)]}1/2- 1r(1, 3) = {[1.09]3/[1.08]}1/2- 1 = .095c. A three-year spot loan is equal to a two-year spot loan plus a forward loan starting at the end ofyear 2 to be paid back at the end of year 3.8-2[1 + r(0, 3)]3= [1 + r(0, 2)]2[1 + r(2, 3)]r(2, 3) = {[1 + r(0, 3)]3/[1 + r(0, 2)]2} - 1r(2, 3) = {[1.09]3/[1.085]2} - 1 = .10014.P = [90(1 - (1.0894)-3)/.0894] + 1,000(1.0894)-3= 1,001.525.Find the price at a yield of 13.35 percent....
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Ch8Sols - 8-1CHAPTER 8: PRINCIPLES OF SPOT...

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