F520bond 2 holding the coupon rate constant for a

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F520_Bond 2. Holding the coupon rate constant, for a given change in market yields, percentage changes in bond prices are greater the longer the term to maturity. 3. The percentage price changes described in Theorem 2 increase at a decreasing rate as N increases 14
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F520_Bond 4. Holding N constant and starting from the same market yield, equal yield changes up or down do not results in equal percentage price changes. A decrease in yield increases prices more than an equal increase in yield decreases prices. In more formal terms, price changes are asymmetric with respect to changes in yield. 15
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F520_Bond 5. Holding N constant and starting from the same market yield, the higher the coupon rate, the smaller the percentage change in price for a given change in yield. 16
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F520_Bond Conclusions: Long-term securities and securities with lower coupon payments have higher price risk and lower reinvestment risk than short term securities and securities with higher coupon payments. The best measure of interest rate risk also accounts for convextity (the curvature in the bond pricing). IV. Duration is our basic measure of interest rate risk. Duration controls for Maturity D Level of coupon payments D Frequency of Coupon payments D Level of interest rate D Convexity of bond prices D ? (when using most precise measure) 17
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F520_Bond Macaulay Duration (D) is the weighted average term to maturity of the components of a bond’s cash flow, in which the time of receipt of each payment is weighted by the present value of that payment. P t t D T t t T t t T t t PV PV PV * * 1 1 1 Modified Duration (MD) is the an indication of the proportional sensitivity of the price of an asset/liability to changes in the market rate of interest. Modified duration = Macaulay Duration / (1+y) MD = D / (1+y) Modified duration is the approximate percentage price change for a 100 basis point change in yields. Modified Duration measures the sensitivity of our portfolio/balance sheet/assets to changes in market interest rates. 2/F-1238.pdf 18
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F520_Bond V. Calculation of Modified Duration A. You can calculate modified duration for any fixed income security using this general formula: D MD P t t D P t MD rearrange negative double drop t P MD t y P price Bond Derivative First Use y P P MD ice Bond y y C PV PV y C y y C y y C y y C y C y C y C y C T t t t T t t T t t T t t t T t t t T t t t T t t t n n 1 1 1 1 1 1 1 1 1 1 1 1 1 1 * * * 1 _ _& _ _ * 1 * 1 * 1 _ _ _ _ * 1 ... Pr 1 1 1 1 1 1 1 3 3 2 2 1 1 where C t = Cash flow received on the security at end of period t T
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