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Chapter 2 Tuckman Lecture - CHAPTER 2 TUCKMAN BOND PRICES...

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CHAPTER 2 TUCKMAN BOND PRICES, SPOT RATES, and FORWARD RATES SEMIANNUAL COMPOUNDING A complete description of a fixed income investment includes the annual rate and how often that rate will be compounded during the year. Depends when the interest is compounded: Can be done semiannually, quarterly, or monthly. Semiannually = Interest Rate / 2 Monthly = Interest Rate / 12 T-bonds pay interest semi-annually. To calculate principal and interest for semi-annual compounding: See Equation 2.3 on page 24. T = years r = annual rate 2T = an investment for T years compounded semiannually is an investment for 2T six month periods To calculate a semi-annual compounded holding period return: See Equation 2.6 on page 25. w = Future value x = Present value r = Holding period return or Return on a percentage basis T = years 2 = semi-annual compounding periods Do Class Problems 1 and 2. 1
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SPOT RATES The spot rate is the rate on a spot loan = a loan agreement where the lender loans money to the borrower at the moment the loan contract or agreement is made. t-year spot rate is r(t). Here will assume that rates are compounded semi-annually. If quote a C-STRIPS on February 15, 2001, that matures on February 15, 2011, at 58.779, then using the equation to calculate a semi-annual compounded holding period return: See page 25, Equation 2.8. Here, the price of this particular STRIPS implies that r(10) = 5.385%. 10 denotes time from February 15, 2001, to February 15, 2011. To calculate the discount factor: See page 26, Equation 2.10. See Table 2.1 on page 26. Shows the calculation of spot rates based on the discount factors reported in Table 1.2 of Chapter 1. Spot Rate starts at 5% and decreases, and then slowly increases, even as the discount factor decreases. The relationship between spot rates and maturity, or term, is the term structure of spot rates.
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