Investments Chap 16
Convexity
- the relationship between bond prices and yields is not linear- slope would equal modified duration -duration rule is a good approximation for only small changes in bond yields (with greater changes in Y it becomes more of an exaggeration) -bonds with greater convexity have more curvature in the price-yield relationship
Duration
-A measure of the effective maturity of a bond -The weighted average of the times until each payment is received, with the weights proportional to the present value of the payment (PV of payment/price) -It is shorter than maturity for all bonds, and is equal to maturity for zero coupon bonds -higher coupon = greater amount comes earlier, lower duration
Why do investors like convexity?
-Bonds with greater curvature gain more in price when yields fall than they lose when yields rise -The more volatile interest rates, the more attractive this asymmetry -Bonds with greater convexity tend to have higher prices and/or lower yields, all else equal
What determines Duration?
-Rule 1 : The duration of a zero-coupon bond equals its time to maturity -Rule 2: Holding maturity constant, a bond's duration is higher when the coupon rate is lower (higher coupons earlier lower life) -Rule 3: Holding the coupon rate constant, a bond's duration generally increases with its time to maturity -Rule 4: Holding other factors constant, the duration of a coupon bond is higher when the bond's yield to maturity is lower -Rules 5: The duration of a level perpetuity is equal to: (1 + y) / y
Negative Convexity
-not desirable -you lose when interest rates go up and don't get as much when they go down
Duration-Price Relationship
-price change is proportional to duration and not to maturity -measure of the interest rate sensitivity - change p/p = -D*(change Y) D*= modified duration (duration/(1 + r)) -change P/P would be an exact relationship if everything was linear -bonds with equal D have the same interest rate sensitivity
Interest Rate Sensitivity
1. Bond prices and yields are inversely related 2. An increase in a bond's yield to maturity results in a smaller price change than a decrease of equal magnitude (decreases have a bigger impact on price) 3. Long-term bonds tend to be more price sensitive than short-term bonds 4. As maturity increases, price sensitivity increases at a decreasing rate (increases become smaller and smaller, less than proportional) 5. Interest rate risk is inversely related to the bond's coupon rate (0 coupon bonds have the highest int. rate risk, higher coupons have a lower effective maturity) 6. Price sensitivity is inversely related to the yield to maturity at which the bond is selling (the lower the yield, the higher the interest rate risk)
Two passive portfolio strategies
1. Indexing- select the entire bond market and replicate it 2. Immunization- applicable to financial institutions, can calculation the duration of any loan; make it the same for assets and liabilities; shield overall financial status from interest rate risk
Duration Calculation
W= CF/(1 + y)^t/Price D = SUM: t X w CF = cash flow at time t
