1. Bond Portfolio Management: Extra b How can you tell bond yields of different maturities are mis-aligned? Maturity T 1 yr. 5 yrs10 yrs30 yrs Yield

2. Example: Cox-Ingersoll-Ross Model b The price of a T-yr zero-coupon bond should be:

3. T-yr Yield according to CIR b T-yr yield and short-term rate must be related to each other according to

4. Example b Parameter values: k = 0.5 r = 0.02 v = 3%k = 0.5 r = 0.02 v = 3% Today’s short-term rate: R = 4.6% 1-yr yield = 5.2% 5-yr yield = 5.7% 10-yr yield = 5.9%30-yr yield = 6.05%Today’s short-term rate: R = 4.6% 1-yr yield = 5.2% 5-yr yield = 5.7% 10-yr yield = 5.9%30-yr yield = 6.05%

5. Example continued b According to the CIR: the yields should be as follows:

6. Example continued b 30-yr

7. Strategy Implications b From chart, The diff. between actual and CIR yields is larger for 10- yr than for 30-yr !The diff. between actual and CIR yields is larger for 10- yr than for 30-yr ! b If CIR curve is true, then Short the 30-yr bondsShort the 30-yr bonds Long the 10-yr bondsLong the 10-yr bonds b counting on an eventual convergence between actual and CIR curves!

8. Risks in Strategy b Interest-Rate risk: Duration-matching will take care of some.Duration-matching will take care of some. b Model risk: What if the model is wrong?What if the model is wrong?