Bond duration and convexity formulas explained. Modified duration, Macaulay duration, effective duration, and convexity with calculation examples.
Measure of bond price sensitivity to yield changes. Higher duration = more price volatility. Approximate % price change for 1% yield change.
Weighted average time to receive cash flows. In years. Duration of zero-coupon = maturity.
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Modified Duration
Where: y = YTM, m = compounding periods per year
Price Change (Duration)
Where: First-order approximation
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Bond Price
PV of coupons + PV of par
Current Yield
Income return only
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Use when:
Avoid when:
If a bond has a modified duration of 6 and yields increase by 100 basis points, the approximate price change is:
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