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Unformatted text preview: Answers to Sample Questions in Spiral Bound Book Lecture Topics 15 Lecture 1: 1. The Fisher equation tells us that the nominal rate on a debt instrument is set by the adding expected inflation to the required real rate of return. We can rewrite the Fisher equation to get the required real rate from expected inflation and the nominal contract rate. In this example, the contract rate is 5.75 and expected inflation is 3, so the required real rate is 5.753 or 2.75%. 2. If your parents hold a 9% TVA bond now, it must be selling at a premium because these trade at yields very close to those of Treasuries, which have much lower yields. So 9% is quite a nice coupon to be receiving these days. If you don’t quite see this, write down the cash flows on a 9% bond (pick a short one with annual coupons to save work) and start out with a price of par (discount rate of 9%). Now make the interest rate lower (say 5%) and look at the new price of the bond. You should get a number that is larger than $1000. If the TVA bonds are worth a premium over face value, your parents would not choose to cash them in for their face value (if they needed the money for your education they could take them to a bond dealer and get a better price). 3. The expectations theory of the yield curve says that the rate on a long term instrument is a geometric average of the yields on one year instruments between now and the end of the maturity of the long term debt. (A geometric average is calculated by multiplying the various expected rates (using 1+r, not r) and then taking the nth root of the product.) If we are talking about a two year note, we take today’s one year rate, multiply it by next year’s one year rate (the rate that is expected), and then take the square root. With a thirty year bond, we need to multiply out all those future rates, which in this case are nearly identical, and then raise the product of the rates to the power 1/30. In this question, you could actually calculate the rate that people expect the oneyear bill to change to, but were not asked such detail. All you need to know for the answer is that if the long bond has a higher rate than today’s, then it must be (according to the expectations theory) that there is an increase in one year rates. 4. (c). The FF rate would increase in the near future. The expectations theory of the yield curve states that longer maturity bonds’ yields are based on expectations of future one year rates. So a two year bond yield should be a geometric average of today’s one year rate and what people expect the one year rate to be in a year. If the yield curve is steep, people are expecting rates to go up in the future, either because of higher inflation or higher real rates from the Fed tightening. Answers (a) and (b) are wrong because both would imply lower future rates, which gives a flat or inverted yield curve. Answer (d) suggests future rates would be lower because of supply and demand factors, again giving the wrong shape to the yield curve. shape to the yield curve....
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 Spring '04
 HELWEGE
 Debt, required real rate

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