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Debt Instrument

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Debt Instruments and Markets Professor Carpenter Solutions to Problem Set 2: Rate of Return and Yield to Maturity Please do all calculations in Excel and put your answers in the blue cells. Please do not move or reformat the blue cells. Names: Question 1 On November 14, 1995, a customer could have purchased a 1-year STRIP at a zero rate of 5.45%, or a 1.5-year STRIP at a zero rate of 5.47%. Using the information from the table below, calculate the realized rate of return (semi-annually compounded) on each security over the subsequent year. STRIPS pricing on November 14, 1996: Maturity Ask Rate Ask Price Bid Price in Bid Price in Bid Rate 0.5 5.29% in 97.4232 32nds 97:13 Decimal 97.4063 5.33% 1 5.44% 94.7742 94:24 94.7500 5.47% 1.5 5.58% 92.0762 92:01 92.0313 5.61% 1-year STRIP 5.45% 1.5-year STRIP 5.54% Reference Cells 1-year STRIP 1.5-year STRIP Rate 5.45% 5.47%

1-year STRIP: cost = 1/(1+0.0545/2)2 = 0.947649 payoff = 1 growth factor (payoff/cost) = 1/0.947649 = 1.055243 semi-annually compounded rate of return = 2x[(1.055243)0.5 - 1] = 5.45% 1.5-year STRIP: cost = 1/(1+0.0547/2)3 = 0.922242 payoff = 0.974063 (from bid price of 0.5-year STRIP on November 14, 1996) growth factor (payoff/cost) = 0.974063/0.922242 = 1.05619 semi-annually compounded rate of return = 2x[(1.05619)0.5 - 1] = 5.54% Question 2 Suppose that at time 0 you buy a 6%-coupon 30-year bond priced at par, and at time 0.5 you sell this bond at a price of 90% of par value. a) What is your time 0.5 payoff per $1 of initial investment? $0.93 Two approaches, giving same answer: #1) Sell bond immediately after coupon payment: payoff = coupon + sale proceeds = coupon + ex-coupon bond price payoff = 0.06/2 + 0.90 = 0.93 #2) Sell bond immediately before coupon payment: payoff = sale proceeds = coupon + ex-coupon bond price = 0.93 b) What is the rate of return on your investment (annualized, with semi-annual

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