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Unformatted text preview: 81CHAPTER 8: PRINCIPLES OF SPOT PRICINGENDOFCHAPTER 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 longand shortterm markets determine whether long or shortterm rates will be higher. In thisexample, the Treasury is shifting toward more longterm borrowing which should, if nothing elsechanges, cause longterm rates to increase and shortterm rates to decrease.b.The expectations theory. This theory says that the expectation of increasing interest rates isrevealed by the fact that longterm rates are higher than shortterm 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 shortterm loansand require a risk premium to be willing to make longterm 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 oneperiodahead 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 longerterm loan is equivalent toa series of shorterterm loans.a.A twoyear spot loan is equivalent to a oneyear 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 threeyear spot loan is equivalent to a oneyear 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 threeyear spot loan is equal to a twoyear spot loan plus a forward loan starting at the end ofyear 2 to be paid back at the end of year 3.82[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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 Fall '08
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 Interest Rates, Spot price

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