What Solutions Are Possible to the Free Rider Problem, Both Inside and Outside of Government
CHAPTER 16 MANAGING BOND PORTFOLIOS
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 than maturity for all bonds except zero coupon bonds. – Duration
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 than maturity for all bonds except zero coupon bonds. – Duration