Class Note 11_F2011

Class Note 11_F2011 - RSM 330 - Investments Class Note 11...

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RSM 330 - Investments Class Note 11 – Bond Portfolio Management December 1, 2011 Maureen Stapleton, CFA 1 RSM 330_week 12_Fall2011
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2 Plan for Today Office hours before the exam? Final project due December 8 at 4 pm Rotman 469 (REVISED!) Measuring Interest Rate Risk – Duration and Convexity Active Strategies for Managing Bond Portfolios Barbells and Bullets – Riding the Yield Curve - Sector swaps - Anomaly Trading Recap of the course RSM 330_week 12_Fall2011
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The Relationship between Bond Price & YTM is not linear 3 RSM 330_week 12_Fall2011
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4 y 1 ) y 1 ( D P P + + - = y 1 D D * + = y D P P * - = Bond prices move inversely with interest rates …. . The price change of a bond is proportional to its duration and not its term to maturity More precisely,  if we denote D = modified duration  Duration/Price Relationship: RSM 330_week 12_Fall2011
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5 Over time, there are three determinants of the bond price. P = f(y, cash flow, T) Your holding period return is impacted by a change in interest rates: P + ∆P = f(y + ∆y) and ∆ y ∆ P. Measures of sensitivity to interest rate risk: dP dP 1 dy or dy P For example, suppose that dP/dy = −6000 and dP 1/dy P = −10. Then for a small change ∆y, the price change is roughly ∆P = −6000∆y and the percentage price change is ∆ P/P = −10∆y. RSM 330_week 12_Fall2011
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6 Duration Macaulay Duration : “the average time at which you receive the cash flows from bond”; Alternatively, it’s the time at which you receive half the PV of cashflows Macaulay Duration = 1 · w 1 + 2 · w 2 + · · · + T · w T where the weights are and CF t is the cash flow at date t . Note that So the weights sum up to 1. P y CF P CF PV w t t t t 1 ) 1 ( ) ( + = = T t y CF y CF y CF P ) 1 ( ..... ) 1 ( 1 2 2 1 + + + + + + = RSM 330_week 12_Fall2011
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7 8% Bond Time years Coupon  (CF) PV of CF (10%) Weight Time X Weight .5 40 38.095 .0395 .0198 1 40 36.281 .0376 .0376 1.5 2.0 40 1040 sum 34.553 855.611 964.540 .0358 .8871 1.000 .0537 1.7742 1.8853 Calculate Macaulay Duration 2 year bond, 8% coupon, YTM =10% (semiannual pay) RSM 330_week 12_Fall2011
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8 0 200 400 600 800 1000 1200 1 2 3 4 5 6 7 8 Year Cash flow Bond Duration = 5.97 years Example: 8-year, 9% annual coupon bond Properties of Duration FULCRUM = duration What is duration of a zero-coupon bond? • Holding time to maturity constant, when
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Class Note 11_F2011 - RSM 330 - Investments Class Note 11...

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