Chap015 - Chapter 15 - The Term Structure of Interest Rates...

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Chapter 15 - The Term Structure of Interest Rates CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS. 1. In general, the forward rate can be viewed as the sum of the market’s expectation of the future short rate plus a potential risk (or ‘liquidity’) premium. According to the expectations theory of the term structure of interest rates, the liquidity premium is zero so that the forward rate is equal to the market’s expectation of the future short rate. Therefore, the market’s expectation of future short rates (i.e., forward rates) can be derived from the yield curve, and there is no risk premium for longer maturities. The liquidity preference theory, on the other hand, specifies that the liquidity premium is positive so that the forward rate is less than the market’s expectation of the future short rate. This could result in an upward sloping term structure even if the market does not anticipate an increase in interest rates. T he liquidity preference theory is based on the assumption that the financial markets are dominated by short-term investors who demand a premium in order to be induced to invest in long maturity securities. 2. True. Under the expectations hypothesis, there are no risk premia built into bond prices. The only reason for long-term yields to exceed short-term yields is an expectation of higher short-term rates in the future. 3. Uncertain. Expectations of lower inflation will usually lead to lower nominal interest rates. Nevertheless, if the liquidity premium is sufficiently great, long-term yields may exceed short-term yields despite expectations of falling short rates. 4. Maturity Price YTM Forward Rate 1 $943.40 6.00% 2 $898.47 5.50% (1.055 2 /1.06) – 1 = 5.0% 3 $847.62 5.67% (1.0567 3 /1.055 2 ) – 1 = 6.0% 4 $792.16 6.00% (1.06 4 /1.0567 3 ) – 1 = 7.0% 15-1
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Chapter 15 - The Term Structure of Interest Rates 5. The expected price path of the 4-year zero coupon bond is shown below. (Note that we discount the face value by the appropriate sequence of forward rates implied by this year’s yield curve.) Beginnin g of Year Expected Price Expected Rate of Return 1 $792.16 ($839.69/$792.16) – 1 = 6.00% 2 69 . 839 $ 07 . 1 06 . 1 05 . 1 000 , 1 $ = × × ($881.68/$839.69) – 1 = 5.00% 3 68 . 881 $ 07 . 1 06 . 1 000 , 1 $ = × ($934.58/$881.68) – 1 = 6.00% 4 58 . 934 $ 07 . 1 000 , 1 $ = ($1,000.00/$934.58) – 1 = 7.00% 6. a.A 3-year zero coupon bond with face value $100 will sell today at a yield of 6% and a price of: $100/1.06 3 =$83.96 Next year, the bond will have a two-year maturity, and therefore a yield of 6% (from next year’s forecasted yield curve). The price will be $89.00, resulting in a holding period return of 6%.
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This note was uploaded on 04/03/2010 for the course FEAS 311.01 taught by Professor Attilaodabaşı during the Spring '10 term at Boğaziçi University.

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Chap015 - Chapter 15 - The Term Structure of Interest Rates...

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