Fixed Income Portfolios

1. Fixed Income Portfolios

2. Overview • Setting Investment Objectives • Establishing investment policy • Selecting a portfolio strategy • Selecting assets • Measuring and Evaluating performance

3. Setting Investment Objectives • Varies with type of financial institution • pension fund -- generate cash flow sufficient to cover obligations • life insurance -- meet obligations in insurance (long term) and generate profit • banks earn spread over short term deposits, timing of liabilities

4. Establishing Investment Objectives • Asset allocation • Match assets and liabilities based on goals of the financial institution • Client and Regulatory constraints • limits on credit ratings • Tax and Financial Reporting implications • mutual funds are tax exempt so munis are not attractive

5. Selecting a Portfolio Strategy • Active vs. passive strategies • Active - Attempts to forecast and exploit changes in future rates and macro economic variables. Change portfolio composition often in response to expectations. • Passive - Closer to buy and hold. Goal is to replicate or benchmark for example to an index. • Combinations of both

6. Selecting a Strategy • Structured portfolio strategies • goal is to achieve a predetermined benchmark or goal such as matching the timing of future liabilities. • Immunization - eliminating the impact of interest rate changes in the cash flows received • Cash flow matching or horizon matching • Often include low risk active strategies within a passive strategy

7. What Determines Strategy Choice? • Efficiency of market • If market is efficient, you cannot beat the market return consistently. This implies indexing as the strategy. • Liabilities • Must be able to meet future obligations of the firm (think about a bank, pension fund or insurance firm)

8. Selecting Assets • Identifying individual securities (identifying mispriced securities if not indexing or matching cash flows • Identifying cash flow characteristics

9. Measuring and Evaluating Performance • Measuring against a benchmark • Meeting liability constraints

10. Sources of Active Portfolio Returns • Changes in the level of Interest Rates • Changes in the shape of the Yield Curve • Changes in the yield spreads among bond sectors • Changes in the option adjusted spread • Changes in the yield spread of a particular bond • Changes in asset allocation within bond sector

11. Manager Expectations vs.Market Consensus • The market consensus should be reflected in the current market prices and yields. • This may or may not agree with the manager expectations.

12. Interest rate expectations • Expected change in interest rates will often force manager to make a change in strategy. • This may not include actually changing the underlying assets for example swaps may be used to shorten or lengthen the duration of a portfolio. • Problem – No reason to believe that you can forecast accurately

13. Yield Curve Strategies • Positioning your portfolio to capitalize on expected changes in the shape of the Treasury Yield Curve

14. Parallel Shifts Short Intermediate Long Maturity Short Intermediate Long Maturity

15. Twists Flattening Twist Short Intermediate Long Maturity Steepening Twist Short Intermediate Long Maturity

16. Butterfly Shifts Positive Butterfly Short Intermediate Long Maturity NegativeButterfly Short Intermediate Long Maturity

17. Common Shifts • Most common shifts are combinations of the types above • Downward shift combined with steepening • More likely to also be combined with a negative butterfly • Upward shift combined with flattening • More likely to be combined with a positive butterfly

18. Portfolio Strategies • Need to consider the timing of the cash flows and therefore the duration of the portfolio and / or maturity. • Look at expectations of future yield curve shifts • Match liabilities

19. Ladder or Spaced Maturity • Maturity is capped and then the portfolio is spread out evenly across the range of maturities • Assume 5 year cap – then 20% of portfolio is in each year. 20% 20% 20% 20% 20% 1 2 5 3 4

20. Ladder or Spaced • Once a year matures it is assumed to be reinvested in new 5 year bonds. Therefore the trend continues • Advantages • Reduces Investment income fluctuations • Requires little investment expertise • Since it continues to roll over into cash it provides flexibility

21. Front End Load (bullet) Strategy • Place all of securities in a short period of time 20% 80% 1 5 2 3 4

22. Front End Load • Uses the portfolio as a source of liquidity since it is so short term • Advantages • Avoids large capital losses if rates increase since short run securities are less sensitive to interest rate changes.

23. Back End (bullet) Strategy • Places all of portfolio at the upper end of the maturity 60% 20% 20% 9 10 1 2 3 4 5 6 7 8

24. Back End Strategy • Stresses Investment income instead of liquidity • Advantages • Increases gain if interest rates decrease since long term bonds are more sensitive to rate changes (but also larger decline in value if rates increase) • Forces institution to depend upon money market for short term returns.

25. Barbell Strategy • Combination of front end and back end load. The goal is to balance the desire for liquidity and income. 25% 25% 15% 15% 10% 10% 9 10 1 2 3 4 5 6 7 8

26. Barbell • Combines both goals of liquidity and income • Advantages • Not as responsive to interest rates (either increase or decrease) as back end load, more responsive than front end load.

27. Rate Expectations • Aggressive strategy based on expected rates Shift if rates are expected to decrease Shift if rates are expected to increase 9 10 1 2 3 4 5 6 7 8

28. Rate Expectations • Very aggressive, attempts to match portfolio to rate expectations. • Advantages • If successful, capital gains will be increased and capital losses will be decreased.

29. Analysis of the portfolios • How the portfolios actually respond will be dependent upon changes in the yield curve (steepening etc.) Not just a static measure of interest rates. • Given the duration of portfolio, and estimating the value change is implicitly assuming that the the yield on each of the assets in the portfolio changes by the same amount.

30. Want to look at total return • The best way to compare across portfolios is to compare total return if a shift actually occurs.

31. Compare two portfolios • Bullet: 100% in Bond C • $ duration = 6.434 • $ convexity = 55.4506 • YTM 9.25% • Barbell: 50.2% in bond A and 49.8% in bond B • $ duration = (0.502)(4.005)+(.498)(8.882) = 6.434 • $ convexity = (0.502)(19.8164)+(.498)(124.17) =71.7846 • YTM = .502(.0850)+.498(.0950) = 8.998%

32. Cost of Convexity • The barbell has a higher convexity but a lower yield. The bullet has a yield 25.5 basis points higher than the barbell. This is the cost of convexity. • Which portfolio does better for a yield change? It depends on the yield shift (parallel or twist etc)

33. Key Point • Looking at just the duration, convexity, YTM etc. does not provide a good indication of which portfolio is “better.”

34. Measuring Yield Curve Risk • Key Rate Duration, Calculating the change in value for a security or portfolio after changing one key interest rate keeping other rates constant. • Each point on the spot yield curve has a separate duration associated with it. • If you allowed all rates to change by the same amount, you could measure the response to the security or portfolio to a parallel shift in the yield curve.

35. Key Rates and Portfolios • By focusing on a group of key rates it is possible to investigate the impact of changes in the shape of the yield curve on specific parts of a portfolio, we will cover this in more detail in the portfolio section of the course.

36. Using Key Rate Durations* • Assume you have three key rtes 2 years, 16 years and 30 years. Assume that you are investing in zero coupon instruments at each maturity (the duration will be equal to the maturity). • Therefore each bond will respond to changes in its portion of the yield curve. From Fabozzi Fixed Income for the CFA p310 - 312

37. Consider 3 portfolios • Portfolio 1 (Barbell) • $50 in the 2 year, 0 in the 16 year, and $50 in the 30 year • Portfolio 2 (Bullet) • 0 in the 2 year, $100 in the 16 year, and 0 in the 30 year • Portfolio 3 (Spread) • $33.33 in each of the possible bonds.

38. Portfolio Duration • The weighted average of the key rate durations similarly the effective duration will be the weighted average of the durations of the securities in the portfolio.

39. Key Rate Duration • For each maturity (key rate) we need to find the key rate duration. • Let D(1) be the duration for the 2 year part of the curve • Let D(2) be the duration for the 16 year part of the curve • Let D(3) be the duration for the 30 year part of the curve • Portfolio 1 • For portfolio 1 the only portion of the portfolio that is sensitive to a change in the 2 year rate is the two year security, the similar result happens for each of the other maturities.

40. Portfolio Key Rate Durations • Portfolio 1 • D(1)=(50/100)2+(0/100)0+(50/100)0=1 • D(2)=(50/100)0+(0/100)0+(50/100)0=0 • D(3)=(50/100)0+(0/100)0+(50/100)30=15 • Portfolio 1 • D(1)=(0/100)0+(100/100)0+(0/100)0=0 • D(2)=(0/100)0+(100/100)16+(0/100)0=16 • D(3)=(0/100)0+(100/100)0+(0/100)30=0 • Portfolio 1 • D(1)=(33.3/100)2+(33.3/100)0+(33.3/100)0=.6666 • D(2)=(33.3/100)0+(33.3/100)16+(33.3/100)0=5.333 • D(3)=(33.3/100)0+(33.3/100)0+(33.3/100)30=10

41. Effective Duration • The effective duration of each portfolio would be the weighted average of the securities durations • Portfolio 1 (50/100)2+(0/100)16+(50/100)30 = 16 • Portfolio 2 (0/100)2+(100/100)16+(0/100)30 = 16 • Portfolio 3 (33.3/100)2+(33.3/100)16+(33.3/100)30 = 16

42. A parallel shift in the yield curve • Assume that all spot decrease by 10% • Given the key rate durations for portfolio 1 • D(1)=1, D(2)=0, D(3)=15 • For a 100 Bp decrease in the 2 year rate, the portfolio should see a 1% increase in price, for a 10 Bp decrease price should increase by .1% • Similarly a 10 Bp decrease in the 30 year rate should increase price by 1.5% • The total change in price is then .1%+ 1.5%

43. Three possible yield curve shifts • Now lets consider the impact of three different possible shifts in the yield curve on each of the three portfolios • Scenario 1 Parallel Downward Shift All maturities decrease by 10 Bp • Scenario 2 2-yr rate shifts up 10 Bp, 30-yr rate shifts down by 10Bp • Scenario 3 2-yr rate shifts down 10 Bp, 30-yr rate shifts up by 10Bp

44. Comparison of shifts

45. Yield Spread Strategies • Positioning a portfolio to capitalized on expected changes in yield spreads. • Intermarket Spread Swaps – exchanging one bond for another between sectors of the bond market based on the yield spread

46. Credit Spreads • Credit spreads (Spread between treasury and similar maturity non treasury) generally widen in a declining economy and narrow during expansion. • Yield Ratios vs. Spreads. As the level of rates change so should the absolute spread.

47. Yield Spread Strategies • Positioning a portfolio to take advantage of changes in the spread between two classifications of bonds. • One example would be an intermarket spread swap. • May recognize differences in credit spreads, or embedded options.

48. 10% BBB rated Corp, 5 yrs to mat, YTM = .10 8% Treasury, 5 yrs to Mat, YTM = .09072458 Example: Credit Spreads Expected to Widen Yield Spread = .10-.090724 = .009275742 (92.75742Bp) What strategy should you undertake? Purchase the Treasury and Short the Corp 1) Treasury yield falls - price of treasury increases 2) Corp. yield increases - price of corp decreases

49. Corp Time 0 Receive $100 Next Day Pay $100 Total = $100 Treasury Time 0 Buy 1.044 of Treas =$100 Next Day Sell 1.044 @ 97.21 Total = 101.50635 Example continued Assume that you hold the positions for 1day. At that time the treasury yield has decreased to 8.70%

50. Importance of Duration • When comparing spreads it is imperative to look at positions that have the same duration. • If the duration of the new and old position are not the same then you are accepting risk associated with a change in the level of rates as well as a change in the spread.