1. 1 Fixed-Income Portfolio Management

2. 2 Portfolio Management Process Four steps: 1.Setting the objectives (return, risk, and constraints) 2.Developing a portfolio strategy 3.Implementing the chosen strategy 4.Monitoring and adjusting the portfolio

3. 3 Investment Objectives Broadly, there are two types of investors based on investment objectives. 1.The first type of investor does not have liability matching as a specific objective. 2.The second type of investor has a liability that needs to be met.

4. 4 Classification of Strategies The following five types of strategies based on a scale that ranges from totally passive to full-blown active management. Pure bond indexing Enhanced indexing by matching primary risk factors Enhanced indexing by small risk factor mismatches Active management by larger risk factor mismatches Full-blown active management

5. 5 Bond Indexing Reasons for bond indexing: 1.Indexed portfolios have lower fees than actively managed accounts. 2.Outperforming a broadly based market index on a consistent basis is a difficult task. 3.Broadly based ond index portfolios provide excellent diversification.

6. 6 Selection of a Benchmark Bond Index The choice depends heavily on 1. Market value risk As the maturity and duration of a portfolio increase, the market risk increases. For investors who are risk averse, the short-term or intermediate- term index may be more appropriate as a benchmark index than the long index. 2. Income risk If stability and dependability of income are the primary needs of the investor, then the long portfolio is the least risky and the short portfolio is the most risky.

7. 7 Selection of a Benchmark Bond Index (continued) 3. Credit risk The average credit risk of the benchmark index should be appropriate for the indexed portfolio’s role in the investor’s overall portfolio and satisfy any constraints placed. 4. Liability framework risk This risk should be minimized. In general, it is prudent to match the investment characteristics (e.g., duration) of assets and liabilities.

8. 8 Type of Risk and its Measure Type of Risk Measure Interest rate risk- Portfolio duration Yield curve risk -Key rate durations, and -Distribution of the PV of the cash flows Spread risk- Spread duration Credit risk-Contribution to duration by credit rating Optionality risk- Delta of the portfolio

9. 9 Tracking Risk Tracking risk, also known as tracking error, is a measure of the variability with which a portfolio’s return tracks the return of a benchmark index. Tracking risk is defined as the standard deviation of the portfolio’s active return. Active return = portfolio’s return – benchmark index’s return Tracking risk = standard deviation of the active returns

10. 10 Calculation of Tracking Error for Two Hypothetical Portfolios: Benchmark Is the Lehman U.S. Aggregate Index (Portfolio A) Observation period = January 2007–December 2007; Benchmark index = Lehman U.S. Aggregate Index Portfolio A Month in 2007 Portfolio Return (%) Benchmark Index Return (%) Active Return (%) January-0.02-0.040.02 February1.581.540.04 March-0.040.00-0.04 April0.610.540.07 May-0.71-0.760.05 June-0.27-0.300.03 July0.910.830.08 August1.261.230.03 September0.690.76-0.07 October0.950.900.05 November1.081.040.04 December0.020.28-0.26 Sum0.041 Mean0.0034 Variance0.0086 Standard Deviation = Tracking error0.0930 Tracking error (in basis points)9.30

11. 11 Calculation of Tracking Error for Two Hypothetical Portfolios: Benchmark Is the Lehman U.S. Aggregate Index (Portfolio B) Observation period = January 2007–December 2007; Benchmark index = Lehman U.S. Aggregate Index Portfolio B Month in 2007 Portfolio Return (%) Benchmark Index Return (%) Active Return (%) January-1.05-0.04-1.01 February2.131.540.59 March0.370.000.37 April1.010.540.47 May-1.44-0.76-0.68 June-0.57-0.30-0.27 July1.950.831.12 August1.261.230.03 September2.170.761.41 October1.800.90 November2.131.041.09 December-0.320.28-0.60 Sum3.42 Mean 0.2850 Variance 0.6262 Standard Deviation = Tracking error 0.7913 Tracking error (in basis points) 79.13

12. 12 Tracking Risk Tracking risk arises primarily from mismatches between a portfolio’s risk profile and the benchmark’s risk profile. For example, 1.Portfolio duration 2.Key rate duration and present value distribution of cash flows 3.Sector and quality percent 4.Sector duration contribution 5.Quality spread duration contribution

13. 13 Enhanced Indexing Strategies The bond manager may seek to reduce the transaction costs and enhance the portfolio’s return by the following ways. 1.Lower cost enhancements. The managers can increase the portfolio’s net return by simply maintaining tight controls on trading costs and management fees. 2. Issue selection enhancements The manager may identify and select securities that are undervalued in the marketplace or will soon be upgraded. 3. Yield curve positioning Some maturities along the yield curve tend to remain consistently overvalued or undervalued. By overweighting the undervalued areas of the cure and underweighting the overvalued areas, the manager may be able to enhance the portfolio’s return.

14. 14 Enhanced Indexing Strategies (Continued) 4. Sector and quality position -Experience has shown that the best yield spread per unit of duration risk is usually available in corporate securities with less than five years to maturity. A manager can increase the return on the portfolio without a commensurate increase in risk by tilting the portfolio toward these securities. -Periodic over- or underweighting of sectors or qualities. Conducted on a small scale, the manager may overweight Treasuries when spreads are expected to widen and underweight then when spreads are expected to narrow. 5. Call exposure positioning For example, a decline in yields will lead to underperformance relative to the effective duration model’s prediction. This underperformance creates an opportunity for the portfolio manager to underweight these issues under these conditions.

15. 15 Active Strategies In contract to indexers and enhanced indexers, an active manager is quite willing to accept a large tracking risk, with a large positive active return. By carefully applying his or her superior forecasting or analytical skills, the active manager hopes to be able to generate a portfolio return that is considerably higher than the benchmark return.

16. 16 Extra Activities Required for the Active Manager The active manager will 1.Identify which index mismatches are to be exploited 2.Extrapolate the market’s expectations (or inputs) from the market data 3.Independently forecast the necessary inputs and compare these with the market’s expectations 4.Estimate the relative values of securities in order to identify areas of under-or overvaluation

17. 17 Active Portfolio Strategies Interest-Rate Expectations Strategies A money manager who believes that he or she can accurately forecast the future level of interest rates will alter the portfolio’s sensitivity to interest- rate changes. A portfolio’s duration may be altered by swapping (or exchanging) bonds in the portfolio for new bonds that will achieve the target portfolio duration. Such swaps are commonly referred to as rate anticipation swaps. Although a manager may not pursue an active strategy based strictly on future interest-rate movements, there can be a tendency to make an interest- rate bet to cover inferior performance relative to a benchmark index. There are other active strategies that rely on forecasts of future interest-rate levels.

18. 18 Active Portfolio Strategies (continued) Yield Curve Strategies Yield curve strategies involve positioning a portfolio to capitalize on expected changes in the shape of the Treasury yield curve. A shift in the yield curve refers to the relative change in the yield for each Treasury maturity. A parallel shift in the yield curve is a shift in which the change in the yield on all maturities is the same. A nonparallel shift in the yield curve indicates that the yield for maturities does not change by the same number of basis points.

19. 19 Combinations of Yield Curve Shifts Yield Maturity Positive Butterfly Flattening Parallel Upward Shift/Flattening/Positive Butterfly

20. 20 Combinations of Yield Curve Shifts Yield Maturity Negative Butterfly Steepening Parallel Downward Shift/Steepening/Negative Butterfly

21. 21 Active Portfolio Strategies (continued)  Yield Curve Strategies  In portfolio strategies that seek to capitalize on expectations based on short- term movements in yields, the dominant source of return is the impact on the price of the securities in the portfolio. The key point is that for short-term investment horizons, the spacing of the maturity of bonds in the portfolio will have a significant impact on the total return.  In a bullet strategy, the portfolio is constructed so that the maturities of the securities in the portfolio are highly concentrated at one point on the yield curve.  In a barbell strategy, the maturities of the securities in the portfolio are concentrated at two extreme maturities.  In a ladder strategy the portfolio is constructed to have approximately equal amounts of each maturity.

22. 22 Active Portfolio Strategies (continued) Yield Spread Strategies  Yield spread strategies involve positioning a portfolio to capitalize on expected changes in yield spreads between sectors of the bond market.  Swapping (or exchanging) one bond for another when the manager believes that the prevailing yield spread between the two bonds in the market is out of line with their historical yield spread, and that the yield spread will realign by the end of the investment horizon, are called intermarket spread swaps.  Credit or quality spreads change because of expected changes in economic prospects. Credit spreads between Treasury and non-Treasury issues widen in a declining or contracting economy and narrow during economic expansion.  Spreads attributable to differences in callable and noncallable bonds and differences in coupons of callable bonds will change as a result of expected changes in (1) the direction of the change in interest rates, and (2) interest- rate volatility.

23. 23 Active Portfolio Strategies (continued) Individual Security Selection Strategies  There are several active strategies that money managers pursue to identify mispriced securities  The most common strategy identifies an issue as undervalued because either i.its yield is higher than that of comparably rated issues, or ii.its yield is expected to decline (and price therefore rise) because credit analysis indicates that its rating will improve.  A swap in which a money manager exchanges one bond for another bond that is similar in terms of coupon, maturity, and credit quality, but offers a higher yield, is called a substitution swap.

24. 24 Total Return Analysis and Scenario Analysis Before executing a trade, an active manager needs to analyze the impact that the trade will have on the portfolio’s return. The two primary tools are total return analysis and scenario analysis.

25. 25 Total Return Analysis Total return analysis involves assessing the expected effect of a trade on the portfolio’s total return given an interest rate forecast. The total return on a bond is the rate of return that equates the future value of the bond’s cash flows with the full price of the bond. Semiannual total return = (total future dollars/full price of the bond) 1/n -1 where n is the number of periods in the investment horizon

26. 26 Scenario Analysis The total return number does very little to help the manager assess the risk that he faces. A prudent manager will repeat the calculation of total return for different sets of assumptions or scenarios. The purpose of conducting a scenario analysis is to gain a better understanding of the risk and return characteristics of the portfolio before trades are undertaken.

27. 27 Scenario Analysis (continued) Scenario analysis is useful in a variety of ways: 1.The manager is able to assess the distribution of possible outcomes. 2.The analysis can be reversed, beginning with a range o acceptable outcomes, then calculating the range of interest movements that would result in a desirable outcome. 3.The contribution of the individual components (inputs) to the total return may be evaluated. 4.The process can be broadened to evaluate the relative merits of entire trading strategies.

28. 28 Classes of Liabilities Type of LiabilityAmount of Liability Timing of Liability Example IKnowKnownA principal repayment IIKnowUnknownA life insurance payout IIIUnknownKnownA floating rate annuity payout IVunknown Post-retirement health care benefits

29. 29 Liquidity Concerns uncertainty about the timing and/or the amount of the cash outlays the entity that holds the obligation against the institution may have the right to change the nature of the obligation the potential for the depositor or policyholder to withdraw cash early or borrow against a policy the possibility of reduction in cash inflows (this means the inability to obtain deposits)

30. 30 Surplus Management Define the economic surplus of the portfolio as economic surplus = market value of assets – present value of liabilities Assume that a company’s assets and liabilities have the characteristics shown below. This economic surplus of the company has increased (decreased) as rates rise (fall). The increase (decrease) is a result of the mismatch in duration between the assets and liabilities.

31. 31 Balance Sheet Characteristics of a Company Market ValuePresent ValueEconomic Surplus Duration Assets$500--$1004 Liabilities--$400--7

32. 32 Interest Rate Scenarios Market ValuePresent ValueEconomic Surplus A. Increase by 100 bps Assets$480--$108 Liabilities--$372-- B. Decrease by 100 bps Assets$520--$92 Liabilities--$428

33. 33 Dedication Strategies Dedication strategies are specialized fixed-income strategies that are designed to accommodate specific funding needs of the investor. They generally are classified as passive in nature. Two important types of dedication strategies: - immunization strategies - cash flow matching strategies

34. 34 Assumptions of Immunization Classical immunization theory is based on several assumptions: 1.Any changes in the yield curve are parallel changes. 2.The portfolio is valued at a fixed horizon date, and there are no interim cash flows. 3.The target value of the investment is defined as the portfolio value at the horizon date if the interest rate structure does not change. If the assumptions of classical theory hold, immunization provides a minimum-risk strategy.

35. 35 Immunization Strategies The purpose of immunization is to identify the portfolio for which the change in price is exactly equal to the change in reinvestment income at the time horizon of interest. If the manager can construct such a portfolio, an assured rate of return over that horizon is locked in. The implementation of an immunization strategy depends on the type of liabilities that the manager is trying to meet - a single liability - multiple liabilities - general cash flows

36. 36 Immunization of a Portfolio to Satisfy a Single Liability Suppose that a life insurance company sells a GIC that guarantees an interest rate of 6.25% every six months (12.5% on a bond-equivalent yield basis) for 5.5 years (11 six-month periods). Also suppose that the payment made by the policyholder is $8,820,262. Then, the value that the life insurance company has guaranteed the policyholder 5.5 years from now is $8,820,2621(1.06252) 11 = $17,183,033 When investing the $8,820,262, the target accumulated value for the portfolio manager of the life insurance company is $17,183,033 after 5.5 years, which is the same as a target yield of 12.5% on a bond-equivalent basis.

37. 37 Immunization of a Portfolio to Satisfy a Single Liability (continued) Suppose that the portfolio manager buys $8,820,262 par value of a bond selling at par with a 12.5% yield to maturity that matures in 5.5 years. The portfolio manager will realize a 12.5% yield only if the coupon interest payments can be reinvested at 6.25% every six months. That is, the accumulated value will depend on the reinvestment rate.

38. 38 Immunization of a Portfolio to Satisfy a Single Liability (continued) If yields do not change and the coupon payments can be reinvested at the initial YTM (12.5%), the portfolio manager will achieve the target value. If market yields rise, an accumulated value (total return) higher than the target value (target yield) will be achieved. In contrast, the market value (total return) is then less than the target value, if the market yield declines. Therefore, investing in a coupon bond with a yield to maturity equal to the target yield and a maturity equal to the investment horizon does not assure that the target value will be achieved.

39. 39 Exhibit 25-3 Accumulated Value and Total Return After 5.5 Years: 5.5-Year 12.5% Bond Selling to Yield 12.5% Investment horizon (years): 5.5; Coupon rate: 0.125; Maturity (years): 5.5; Yield to maturity: 0.125; Price: 100; Par value purchased: $8,820,262; Purchase price: $8,820,262; Target accumulated value: $17,183,033 After 5.5 years New Yield a Coupon Interest Interest on Interest Price of Bond b Accumulated Value Total Return 0.160$6,063,930$3,112,167$8,820,262$17,996,3600.1340 0.1556,063,9302,990,7168,820,26217,874,9080.1326 0.1456,063,9302,753,1778,820,26217,637,3690.1300 0.1406,063,9302,647,0378,820,26217,521,2300.1288 …. 0.0656,063,9301,088,0038,820,26215,972,1950.1109 0.0606,063,930996,5778,820,26215,880,7690.1098 0.0556,063,930906,5118,820,26215,790,7030.1087 0.0506,063,930817,7858,820,26215,701,9770.1077 a Immediate change in yield. b Maturity value.

40. 40 Immunization of a Portfolio to Satisfy a Single Liability (continued) Suppose that instead of investing in a bond maturing in 5.5 years the portfolio manager invests in a 15-year bond with a coupon rate of 12.5% that is selling at par to yield 12.5%.

41. 41 Exhibit 25-4 Accumulated Value and Total Return After 5.5 Years: 15-Year 12.5% Bond Selling to Yield 12.5% Investment horizon (years): 5.5; Coupon rate: 0.125; Maturity (years): 15; Yield to maturity: 0.125; Price: 100; Par value purchased: $8,820,262; Purchase price: $8,820,262; Target accumulated value: $17,183,033 After 5.5 years New Yield a Coupon Interest Interest on Interest Price of Bond Accumulated Value Total Return 0.160$6,063,930$3,112,167$7,337,902$16,513,9990.1173 0.1556,063,9302,990,7167,526,48816,581,1340.1181 0.1456,063,9302,753,1777,925,48116,742,5880.1200 0.1406,063,9302,637,0378,136,54216,837,5090.1211 …. 0.0656,063,9301,088,00312,527,91419,679,8470.1514 0.0606,063,930996,57712,926,30119,986,8080.1544 0.0556,063,930906,51113,341,61720,312,0580.1576 0.0506,063,930817,78513,774,67720,656,3920.1609 a Immediate change in yield.

42. 42 Immunization of a Portfolio to Satisfy a Single Liability (continued) The equality of the duration of the asset and the duration of the liability is the key to immunization. To immunize a portfolio’s target accumulated value (target yield), a portfolio manager must construct a bond portfolio such that 1.the duration of the portfolio is equal to the duration of the liability 2.the present value of the cash flow from the portfolio equals to the present value of the future liability.

43. 43 Rebalancing an Immunized Portfolio He duration of the portfolio will change as the market yield changes. The duration will also change simply because of the passage of time. How often should a portfolio be rebalanced to adjust its duration? The answer involves balancing the costs and benefits of rebalancing. Methods for rebalancing include 1.Investing new funds 2.Changing the weight of a particular security to adjust the dollar duration 3.Using derivatives

44. 44 Time Horizon The immunized time horizon is equal to the portfolio duration. Duration is equal to a weighted average of the individual security durations. Securities in the portfolio should be limited to high-quality, very liquid instruments.

45. 45 Dollar Duration Dollar duration is a measure of the change in portfolio value for a 100 bps change in market yields Dollar duration = Duration * Portfolio value * 0.01 The investor’s goal is to reestablish the dollar duration of a portfolio to a desired level.

46. 46 Initial Durations of a Three-Bond Portfolio SecurityPriceMarket ValueDurationDollar Duration Bond #1104.0131,065,6135.02553,548 Bond #296.089978.3761.23212,054 Bond #3103.0631,034,6931.47946,343 Dollar duration$111,945

47. 47 Rebalancing Based on the Dollar Duration The portfolio dollar duration has changed from $111,945 to $82,579. Our requirement is to maintain the portfolio dollar duration at the initial level. The rebalancing ratio is $111,945.$82,579 = 1.356 Rebalancing requires each position to e increased by 35.6 percent. The cash required for this rebalancing is Cash required = 0.356*(1,023,704+1,004,770+1,002,045)=$1,079,012

48. 48 Duration of a Three-Bond Portfolio after One Year SecurityPriceMarket ValueDurationDollar Duration Bond #199.8221,023,7044.24643,466 Bond #298.7281,004,7700.3053,065 Bond #399.8401,002,4583.59636,048 Dollar duration$82,579

49. 49 Immunization Risk The sufficient condition for the immunization of a single liability is that the duration of the portfolio be equal to the duration of the liability. However, a portfolio will be immunized against interest-rate changes only if the yield curve is flat and any changes in the yield curve are parallel changes (i.e., interest rates move either up or down by the same number of basis points for all maturities). Immunization risk is the risk of reinvestment. The portfolio that has the least reinvestment risk will have the least immunization risk.

50. 50 Extensions of Classical Immunization Thoery A natural extension of classical immunization theory is to extend the theory to the case of nonparallel shifts in interest rates. 1. The first extension is multifunctional duration, also known as functional duration or key rate duration. 2. The second extension is to overcome the limitations of a fixed horizon. 3. The third extension is to analyze the risk and return trade-off for immunized portfolios. 4. The fourth extension is to integrate immunization strategies with elements of active bond portfolio management strategies.

51. 51 Contingent Immunization (the fourth extension) Contingent immunization provides a degree of flexibility in pursuing active strategies while ensuring a certain minimum return in the case of a parallel rate shift. In contingent immunization, immunization serves as a fall- back strategy if the actively managed portfolio does not grow at a certain rate. Contingent immunization is possible when the prevailing available immunized rate of return is greater than the required rate of return.

52. 52 Contingent Immunization EXAMPLE. To illustrate the contingent immunization strategy, suppose that a client investing $50 million is willing to accept a 10% rate of return over a four-year investment horizon at a time when a possible immunized rate of return is 12%. What is the safety net return and the safety cushion? The 10% return is called the safety net return. The difference between the immunized return and the safety net return is called the safety cushion. In our example, the safety cushion is 200 basis points (e.g., 12% minus 10% = 2% or 200 basis points).

53. 53 Structuring a Portfolio to Satisfy Multiple Liabilities For pension funds, there are multiple liabilities that must be satisfied ─ payments to the beneficiaries of the pension fund. A stream of liabilities must also be satisfied for a life insurance company that sells an insurance policy requiring multiple payments to policyholders, such as an annuity policy. There are two strategies that can be used to satisfy a liability stream: i.multiperiod immunization ii.cash flow matching

54. 54 Multiple Liability Immunization Multiperiod immunization is a portfolio strategy in which a portfolio is created that will be capable of satisfying more than one predetermined future liability regardless if interest rates change. Even if there is a parallel shift in the yield curve, it has been demonstrated that matching the duration of the portfolio to the duration of the liabilities is not a sufficient condition to immunize a portfolio seeking to satisfy a liability stream. Instead, it is necessary to decompose the portfolio payment stream in such a way that each liability is immunized by one of the component streams. There may be no actual bonds that would give the component payment stream.

55. 55 Multiple Liability Immunization The necessary and sufficient conditions that must be satisfied to assure multiple liability immunizations are: 1.The (composite) duration of the portfolio must equal the (composite) duration of the liabilities. 2.The distribution of duration of individual portfolio assets must have a wider range than the distribution of the liabilities. The two conditions for multiple liability immunization assure immunization against parallel rate shifts only.

56. 56 Cash Flow Matching Strategies This approach, also referred to as dedicating a portfolio, can be summarized as follows. A bond is selected with a maturity that matches the last liability stream. An amount of principal plus final coupon equal to the amount of the last liability stream is then invested in this bond. The remaining elements of the liability stream are then reduced by the coupon payments on this bond, and another bond is chosen for the new, reduced amount of the next-to-last liability. Going backward in time, this cash flow matching process is continued until all liabilities have been matched by the payment of the securities in the portfolio.

57. 57 Cash Flow Matching vs. Multiple Liability Immunization Multiple liability immunization is superior to cash flow matching approach. Reasons 1.Multiple liability immunization require les money to fund liabilities. 2.Cash flow matching requires a relatively conservative rate of return assumption for short-term cash. 3.Funds from a cash flow-matched portfolio must be available when each liability is due.

58. 58 Extensions of Liability-Driven Strategies Deterministic models assume that the cash flows from assets and liabilities are known with certainty. However, most non- Treasury securities have embedded options that permit the borrower or the investor to alter the cash flows. A number of models have been developed to handle real-world situations in which liability payments and/or asset cash flows are uncertain. Such models are called stochastic models. Such models require that the portfolio manager incorporate an interest-rate model, that is, a model that describes the probability distribution for interest rates.

59. 59 Extensions of Liability Driven Strategies (continued) Optimal portfolios then are solved for using a mathematical programming technique known as stochastic programming. The complexity of stochastic models, however, has limited their application in practice. Nevertheless, they are gaining in popularity as more portfolio managers become comfortable with their sophistication. There is increasing awareness that stochastic models reduce the likelihood that the liability objective will not be satisfied and that transactions costs can be reduced through less frequent rebalancing of a portfolio derived from these models.