Fin330 7 corporate bonds fin330 8 moodys aaa 30 year

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Fin330 7
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Corporate bonds Fin330 8 Moody's Aaa 30-year Corporate Bond Yield. Source: https://www.stlouisfed.org/
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Interest rate futures l Interest rate futures are derivatives with an interest- bearing instrument as the underlying asset. l It allows the buyer and seller to lock in the price of the interest-bearing asset for a future date. l It is used to hedge against the risk that interest rates will move in an adverse direction. l Example: Eurodollars are time deposits denominated in U.S. dollars and held at banks outside the U.S. l Other examples: EuroYen, T-bill futures. Fin330 9
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Overview 1. Types of rates 2. Measuring interest rates 3. Bond pricing: 1. Zero coupon bond and Zero Rate 2. Bond’s Yield 3. Term structure of interest rates Fin330 10
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Measuring Interest Rates l The interest rate on one-year deposits is R % per annum. What is the payoff at the end of one year? l The answer depends on the way the interest rate is measured. l Simple Interest is calculated on the original principal only . l Compound Interest is calculated each period on the original principal and all interest accumulated during past periods: l Annual compounding ( R %); l Semiannual compounding ( R /2 % every six months); l Quarterly compounding ( R /4 % every three months); l Monthly compounding ( R /12 % every month); l Continuous compounding (R/ % every month). Fin330 11
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Measuring Interest Rates l Notation: A 0 = initial investment; R = quoted interest rate per annum; m = compounding frequency (the number of times interest rate is compounded per annum); t = number of years; l The terminal value of the investment is: l The present value of the investment is: Fin330 12 A t = A 0 1 + R m mt A 0 = A t 1 + R m mt
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Example l The interest rate on a one-year deposit is 10 % per annum. What is the payoff at the end of one year if we invest $100? l Answer: l Annual compounding: $110. l Semiannual compounding: $110.25. l Quarterly compounding: $110.38. l Monthly compounding: $110.47. Fin330 13
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Example Fin330 14
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Continuous Compounding 15 l If the compounding frequency goes to infinity, we have continuous compounding . l The terminal value of investment is: l The present value of investment is: A t = lim m →∞ A 0 (1 + R m ) mt = A 0 e Rt Fin330 A 0 = A t e Rt
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Interest Rate Compounding 16 l Notation: R = quoted interest rate per annum m = compounding frequency (the number of times interest rate is compounded per annum) l Effective annual interest rate R e : mt t e m R R ) / 1 ( ) 1 ( + = + Fin330
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