What Solutions Are Possible to the Free Rider Problem, Both Inside and Outside of Government
161
Outline of the Chapter
• Bond pricing and sensitivity of bond pricing to interest rate changes • Duration analysis
– What is duration? – What determines duration?
• Convexity • Passive bond management
– Immunization
• Active bond management
162
Interest Rate Risk
• There is an inverse relationship between interest rates (yields) and price of the bonds. • The changes in interest rates cause capital gains or losses. • This makes fixedincome investments risky.
163
Interest Rate Risk (Continued)
164
Interest Rate Risk (Continued)
• What factors affect the sensitivity of the bonds to interest rate fluctuations? • Malkiel’s (1962) bondpricing relationships
– Bond prices and yields are …show more content…
Convexity (Continued)
• The duration rule is a good approximation for small changes in bond yields. • The duration approximation always understates the value of the bond.
• It underestimates the increase in price when yields fall. • It overestimates the decline in prices when yields rise. •Due to the curvature of the true priceyield relationshipconvexity
1617
Convexity (Continued)
• Convexity is the rate of change of the slope of the priceyield curve, expressed as a fraction of the bond price.
– Higher convexity refers to higher curvature in the priceyield relationship. – The convexity of noncallable bonds are usually positive. – The slope of the cuve that shows the priceyield relation increases at higher yields.
Convexity
1 P (1 y ) 2
n t 1
CFt (t 2 t ) (1 y )t
1618
Convexity (Continued)
• We can improve the duration approximation for bond price changes by taking into account for convexity. • The new equation becomes:
P P
D
y
1 [Convexity ( y ) 2 ] 2
• The convexity becomes more important when potential interest rate changes are larger.
1619
Convexity (Continued)
• Why convexity is important? • In the figure bond A is more convex than bond B. •The price increases are more in A when interest rates fall. •The price decreases are less in A when interest rates rise.
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