1. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Chapter 16 Managing Bond Portfolios 16-1

2. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Outline Interest rate risk Duration Convexity Passive Bond Management –Bond index fund –Immunisation Active Bond Management –Horizontal analysis Interest rate swaps Financial engineering and interest rate derivatives 16-2

3. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Active strategy –Trade on interest rate predictions –Trade on market inefficiencies Passive strategy –Control risk –Balance risk and return Basic Strategies 16-3

4. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Inverse relationship between price and yield An increase in a bond’s yield to maturity results in a smaller price decline than the gain associated with a decrease in yield Long-term bonds tend to be more price sensitive than short-term bonds Bond Pricing Relationships 16-4

5. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh As maturity increases, price sensitivity increases at a decreasing rate Price sensitivity is inversely related to a bond’s coupon rate Price sensitivity is inversely related to the yield to maturity Bond Pricing Relationships (cont’d) 16-5

6. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh A measure of the effective maturity of a bond The weighted average of the times until each payment is received, with the weights proportional to the P.V. of the payment Duration is shorter than maturity for all bonds except zero coupon bonds Duration is equal to maturity for zero coupon bonds Duration 16-6

7. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Duration: Calculation 16-7

8. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh 8% Bond Time years PaymentPV of CF (10%) WeightC1 X C4.54038.095.0395.0197 14036.281.0376 1.5 2.0 40 1040 sum 34.553 855.611 964.540.0358.8871 1.000.0537 1.7742 1.8852 Duration Calculation: Spreadsheet 16.1 16-8

9. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Duration Is a simple statistic of the effective maturity of portfolio Is essential for immunisation Is a measure of the interest rate sensitivity of the portfolio 16-9

10. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Price change is proportional to duration and not to maturity  P/P = -D x [  (1+y) / (1+y)] D * = modified duration D * = D / (1+y)  P/P = - D * x  y Duration/Price Relationship 16-10

11. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Rules for Duration Rule 1: The duration of a zero-coupon bond equals its time to maturity Rule 2: Holding maturity constant, a bond’s duration is higher when the coupon rate is lower Rule 3: Holding the coupon rate constant, a bond’s duration generally increases with its time to maturity Rule 4: Holding other factors constant, the duration of a coupon bond is higher when the bond’s yield to maturity is lower 16-11

12. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Rules for Duration (cont’d) Rules 5: The duration of a level perpetuity is equal to: Rule 6: The duration of a level annuity is equal to: 16-12

13. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Rules for Duration (cont’d) Rule 7: The duration for a corporate bond is equal to: 16-13

14. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Yield Price Duration Pricing Error from convexity Duration and Convexity 16-14

15. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Why Convexity? Duration approximation understate the value of the bond –Underestimate the increase in bond price and overestimate the decrease in price The true price yield relationship has curvature called convexity Convexity improves the duration approximation 16-15

16. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Correction for Convexity Correction for Convexity: 16-16

17. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Duration and Convexity of Callable Bonds Negative convexity Price yield curve exhibits an unattractive asymmetry. Asymmetry due to the option to call back retained by the issuer Convexity prediction worse than the duration approximation Effective Duration: -(ΔP/P)/Δr 16-17

18. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Passive Management Bond-Indexing –Index may have a large number of securities –Thinly traded bonds –Rebalancing problem Cellular Approach: subclasses of bonds –On the basis of maturity and issuer –On the basis of the coupon rate and the credit risk 16-18

19. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Bond Index Funds 16-19

20. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Immunisation of interest rate risk: –Net worth immunisation Duration of assets = Duration of liabilities –Target date immunisation Holding Period matches Duration –Rebalancing Cash flow matching and dedication Passive Management 16-20

21. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Duration Matching Balances the difference between: -the reinvestment risk and price risk -Rebalancing required when interest rate and asset duration changes -Rebalancing is a continuous exercise even if interest rate is unchanged 16-21

22. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Why Active Management Duration matching immune portfolio only for parallel shift in the yield curve Immunisation is inappropriate goal in inflationary environment Need to characterise portfolio rebalancing activity through bond swaps 16-22

23. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Substitution swap Inter-market swap Rate anticipation swap Pure yield pickup Tax swap Active Management: Swapping Strategies 16-23

24. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Maturity Yield to Maturity % 3 mon 6 mon 9 mon 1.5 1.25.75 Yield Curve Ride 16-24

25. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Contingent Immunisation A combination of active and passive management The strategy involves active management with a floor rate of return As long as the rate earned exceeds the floor, the portfolio is actively managed Once the floor rate or trigger rate is reached, the portfolio is immunised 16-25

26. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Interest Rate Swaps Contract between two parties to exchange a series of cash flows One party pays a fixed rate and receives a variable rate One party pays a variable rate and receives a fixed rate Payments based on notional principal 16-26

27. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Swap Example Figure 16-11 Swap Dealer Company B Company A LIBOR 7% 6.95%7.05% 16-27

28. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Financial Engineering Inverse Floater –Performs poorly when interest rate rise and vice versa Created synthetically by allocating the cash flows from a fixed-rate security into two derivative securities 16-28

29. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Summary Default free bonds also have interest rate risk Life of the bond and sensitivity to interest rate changes are related Duration measures the average life of a bond Convexity is the curvature of the bond’s price-yield relationship 16-29

30. Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Investments, by Bodie, Ariff, da Silva Rosa, Kane & Marcus Slides prepared by Harminder Singh Summary Investors can immunise their portfolio against the interest rate changes Net-worth of a fixed-income portfolio can be immunised Duration of Assets = Duration of Liabilities Periodical rebalancing or cash flow matching Interest rate swap 16-30