5.2.BKM Ch 16 (Duration & Convexity)
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6 general properties of bond prices
- Bond prices and yields are inversly related
- Incr in yield has smaller impact than comparable decr in yield
- Long term bonds are more sensitive to changes in yields
- Sensitivity to chg in yield incr at decr rate as mat incr
- High coupon bonds are less sensitive to chg in yield
- Sensitiviy of bond price to chg in yield is inversly related to yield at which it's currently selling
- Basic formulas
- D = ∑ ti (CFt / (1 + y)t) / B
- D* = D / (1 + y)
- ∆P/P = -D*∆y
- C = 1 / P(1 + y)² ∑[(CFt/(1 + y)t t(t+1)]
- ∆P/P = -D*∆y + ½C(∆y)²
- D* ≈ (P- - P+) / 2P∆y
- C ≈ (P- + P+ - 2P) / P(∆y)²
- Continuous compoundingD* = DD = ∑ ti (CFt e-yti) / B
- C = 1 / P ∑[ti² CFt e-yti]
Duration vs Convexity
Duration is only good for small changes in rates. For slightly higher changes, we use Convexity to adjust estimated change in price.
Why do investors like Convexity
It causes the price of bond to increase more when yield fall then they decrease when yield rises. This asymetry is desirable and causes an increase in E(r) for bonds as yield volatility increases.
Duration of a PF
Weighted avg of durations
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