5.2.BKM Ch 16 (Duration & Convexity)

• 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 = ∑ t_i (CF_t / (1 + y)^_t) / B
• D* = D / (1 + y)
• ∆P/P = -D*∆y
• C = 1 / P(1 + y)² ∑[(CF_t/(1 + y)^t t(t+1)]
• ∆P/P = -D*∆y + ½C(∆y)²

• Approximations
• D* ≈ (P_- - P₊) / 2P∆y
• C ≈ (P_- + P₊ - 2P) / P(∆y)²

• Continuous compounding
• D* = D
• D = ∑ t_i (CF_t e^-yt_i) / B
• C = 1 / P ∑[t_i² CF_t e^-yt_i]

Duration is only good for small changes in rates. For slightly higher changes, we use Convexity to adjust estimated change in price.

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.

Weighted avg of durations