# What Solutions Are Possible to the Free Rider Problem, Both Inside and Outside of Government

2176 Words May 12th, 2013 9 Pages
CHAPTER 16 MANAGING BOND PORTFOLIOS

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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

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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 fixed-income investments risky.

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Interest Rate Risk (Continued)

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Interest Rate Risk (Continued)
• What factors affect the sensitivity of the bonds to interest rate fluctuations? • Malkiel’s (1962) bond-pricing relationships
– Bond prices and yields are
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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 price-yield relationshipconvexity
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Convexity (Continued)
• Convexity is the rate of change of the slope of the price-yield curve, expressed as a fraction of the bond price.
– Higher convexity refers to higher curvature in the price-yield relationship. – The convexity of noncallable bonds are usually positive. – The slope of the cuve that shows the price-yield relation increases at higher yields.

Convexity

1 P (1 y ) 2

n t 1

CFt (t 2 t ) (1 y )t
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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.
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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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