1. comm 324 --- W. Suo Slide 1

2. comm 324 --- W. Suo Slide 2  Active strategy Trade on interest rate predictions Trade on market inefficiencies  Passive strategy Control risk Balance risk and return Managing Fixed Income Securities: Basic Strategies

3. comm 324 --- W. Suo Slide 3 Managing interest rate risk  Bond price risk  Coupon reinvestment rate risk  Matching maturities to needs  The concept of duration Duration-based strategies  Controlling interest rate risk with derivatives

4. comm 324 --- W. Suo Slide 4  Design a bond portfolio so that its performance will match that of some bond index Performance is measured through its total return over some investment horizon  Motivation: low advisory fee, and the overall poor performance of active bond managers  Critics: it does not necessarily give optimal performance, or satisfies a clients’ objective; it also excludes opportunities in instruments not in the index portfolio (e.g., CMOs)  Indexation requires: Choice of a specific index Performance period Flexibility level: frequency of transaction, derivatives transaction, repo, etc  Bond-Index Funds Indexation: how does it work? Passive Management Bond Indexing

5. comm 324 --- W. Suo Slide 5 Liability Funding Strategies  Classification of liabilities Type I liabilities: both amount and timing are known E.g., GICs II: amount is known, timing is known E,g., Life insurance policy III: timing is known, but amount is unknown IV: both timing and amount are known Insurance policies Pension funds  Different types of liabilities needs different investment strategies

6. comm 324 --- W. Suo Slide 6 Passive Bond Portfolio Strategies  Cash flow matching and dedication  Immunization of interest rate risk Net worth immunization Duration of assets = Duration of liabilities Target date immunization Holding Period matches Duration

7. comm 324 --- W. Suo Slide 7 Cash Flow Matching  Also called dedicating a portfolio: a bond is selected with a maturity that matches the last liability stream: the amount of coupon + principal equal to the last liability stream. The reminding elements of the liability stream are then reduced by the coupon payment on this bond, and then another bond is chosen for the new, reduced amount of the next-to-last liability. Going back in time, this cash flow matching process is continued until all liabilities have been matched.  Difference form immunization: no duration requirement no rebalance required no risk that liabilities won’t be satisfied  Disadvantage?

8. comm 324 --- W. Suo Slide 8 Cash flow matching and dedication example  Consider the problem of funding a stream of pension liabilities consisting of $100 million at the end of each for the next three years.  Assume that the following securities are available for investment (annual coupon) SecuritiesP0CF1CF2CF3 1100.000101100 295.00088108 3105.00012 112 494.339610000 585.733901000 675.131500100

9. comm 324 --- W. Suo Slide 9 How to set up portfolio?  One way is to use strips Total cost: 94.3396+ 85.7339+ 75.1315=255.20 Can you do better?  Can also achieve the goal by  Cost: 251.49  With reinvestment (see spreadsheet example) 123456 0.81170.000.89290.81170.00

10. comm 324 --- W. Suo Slide 10 Immunization  Consider the following case: a life insurance company sells a GIC that guarantees an interest of 6.25% every 6 months for 5.5 years. Suppose the payment made by the policy holder is $8,820.262. An amount of $ 8,820.262*(1+0.0625)^11 = $17,183,033 has been guaranteed after 5.5 years. suppose that the portfolio manager buys $ 8,820.262 par value of a bond selling at par with a 12.5% yield and matures in 5.5 years, what will happen?

11. comm 324 --- W. Suo Slide 11 Immunization  PV of asset must equal the PV of liabilities  Duration of the assets must match the duration of liabilities Why match duration?  The assets must have a dominance patter over the liabilities for prescribed yield changes (e.g., higher convexity)  Immunization provides a hedge for the portfolio’s value, but not its cash flow

12. comm 324 --- W. Suo Slide 12 Example  Three strips with maturity T=1, 2 and 3, and YTM of 6%, 8% & 10%, respectively  Liability 100 million at the end of each year Duration when market yields are at 10%: D=1.937  Use strip 3 to immunize the liability To get n3=-2.14

13. comm 324 --- W. Suo Slide 13 Notes on duration of bond portfolios  The duration of a bond portfolio is equal to the weighted average of the durations of the bonds in the portfolio  The portfolio duration, however, does not change linearly with time. The portfolio needs, therefore, to be rebalanced periodically to maintain target date immunization  Immunization risk non-parallel shift in the yield curve credit risk, and call risk  Why not just use the ZCB?  The immunization technique can be generalized to satisfy multi-period liabilities

14. comm 324 --- W. Suo Slide 14 Contingent Immunization  Identifying both the available immunization target rate a lower safety net level return with which the investor would be minimally satisfied Example: suppose that a client investing $50m is willing to accept a 10% rate of return over 4 years at a time when a possible immunized return is 12%. The 10% is called safety net return, the difference (200bp) is called the safety cushion minimum acceptable return after 4 years: $5m * (1.05)^8=$73,872,772 which can be achieved by $43,348,691 at the possible 12%. The dollar safety margin is $6,651,309 initially, the manager pursue an active portfolio strategy, e.g., he put all the funds into a 20Y 12% coupon bond selling at par

15. comm 324 --- W. Suo Slide 15 Contingent Immunization …  What happens after 6 months? if the market yield falls to 9%, then the value of the 19.5Y 12% will be $63.67m, and the coupon amount is $3m. Total is $66.67m at 9%, $54,283,888 will be need to achieve the minimum amount $73,872,772 dollar safety margin is positive so the manager can still be actively manager if the market yield falls to 14.26%, the market value of the bond decline to $42,615,776, total value of the investment $45,615,776. However, $45,614,893 is need to achieve the minimum amount $73,872,772 manager is required to Immunize the the portfolio to achieve the minimum target value over the investment horizon