FINA 475 Chapter 4: Week 4
26 Sep 2017
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Macaulay duration = [c/(1+y) + 2c/(1+y)2 + nc/(1+y)n + m/(1+y)n]/p. Weighted average time to maturity to receive cash flows weighted by present value of cash flows. Modified duration = macd/(1+y) = -change in price/change in yield * 1/p. Relates approximate percentage price change for a given yield change. Longer maturity bonds have greater price volatility and higher duration value. 25 year bond, 6% coupon, 9% yield, price is . 357, modd is 10. 62. Approximate % change in price = -10. 62*. 001 = -0. 0106 (-1. 06%) %price change due to convexity: change in price/price = 1/2*convexity* y2. The convexity measure refers to quantification of the relationship. Approximate % change in price from convexity depends on the 1/2, convexity measure, and y2. In practice, the software varies the method and output. 25 year bond, 6% coupon, 9% yield, 10. 62 modd. If the yield increases by 200 basis points. %price change from duration: -. 02*10. 62 = -0. 2124 (-21. 24%) %price change from convexity: 1/2*(182. 92)*(. 02)^2 = 0. 0366 (3. 66%)
