16-1

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

16-2

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.

16-3

Interest Rate Risk (Continued)

16-4

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 inversely related. – An increase in a bond’s YTM results in a smaller price change than a decrease in yield of equal magnitude. – Prices of long-term bonds tend to be more sensitive to interest rate changes than prices of short-term bonds.

16-5

Interest Rate Risk (Continued)

– The sensitivity of bond prices to changes in yields increases at a decreasing rate as maturity increases. – Interest rate risk is inversely related to the bond’s coupon rate.

• Homer and Liebowitz’s (1972) bond-pricing relationship – The sensitivity of a bond’s price to change in its yield is inversely related to the YTM at which the bond currently is selling. 16-6

Interest Rate Risk (Continued)

• Why and how different bond characteristics affect interest rate sensitivity?

16-7

Interest Rate Risk (Continued)

• Duration

– Macaulay’s duration: the weighted average of the times to each coupon or principal payment made by the bond. • Weight applied to each payment is the present value of the payment divided by the bond price.

wt D

CFt /(1 y ) t , Bondprice

T

T

wt

t 1

1

t * wt

t 1

16-8

Interest Rate Risk (Continued)

• Example:

16-9

Interest Rate Risk (Continued)

– Duration is shorter...

(1)