1. FIXED INCOME SECURITIES
LECTURE 7
Managing Bond portfolios

2. Managing Fixed Income Securities: Basic Strategies
Active strategy
Trade on interest rate predictions
Trade on market inefficiencies
Passive strategy
Control risk
Attempts to control risk of the portfolio
Balance risk and return
Not trying to “beat the market”

3. BOND PORTOLIOS METHODS OF MANAGMENT Passive
rests on the belief that bond markets are semi-strong efficient
current bond prices viewed as accurately reflecting all publicly available information

4. BOND PORTOLIOS METHODS OF MANAGMENT Active
rests on the belief that the market is not so efficient
some investors have the opportunity to earn above-average returns

5. Passive Management Bond-Index Funds Immunization of interest rate risk
Net worth immunization
Target date immunization
Holding period matches Duration
Cash flow matching and dedication

6. Fixed Income Portfolio Management - Passive
Indexation
Build a portfolio that replicates an observable index
High-grade: Salomon Brothers, Lehman Brothers
High-yield: Credit Suisse First Boston
Problems: Numerous index components, liquidity is low for many, bonds mature
Solution: Cell approach

7. Liability Management: Indexing (1)
Bond Indexing is constructing a bond portfolio whose returns over time replicate the returns of a bond index.The replicating portfolio is formed by:
Using all the bonds in the index (costly)
Use a sample of bonds:
Form a bond portfolio which is highly correlated.
Cell matching strategy

8. Liability Management: Indexing (2)
Cell Matching Strategy:
The bond index is decomposed into cells.
Each cell defines a different mix of features (duration, credit, ratings, etc.)
Example:
Bond Index: Two Durations (D > 5, D < 5), two sectors (Corporate, Treasury), and two quality ratings (AA, A). With these feature, eight cells can be formed.

9. Liability Management: Indexing (3)
Cell Matching
Example:
The index fund is constructed by selecting bonds to match each cell and then allocating funds to each type of bond based on each cell’s allocation.

10. Cell approach

11. net worth Immunization :
How Does net worth Immunization Work? For net worth immunization, if
Duration of assets = Duration of liabilities
i.e., both sides of the balance sheet have the same sensitivity to interest rate changes

12. Net worth immunization
DURgap=DURa-（L/A*DURL） %ΔNW≈-DURgapⅹΔi/（1+i）
Immunization requires DURgap=0, If assets and liabilities are not equal,then immunization requires that A*DURa=L*DURL

13. Target Date Immunization
Construct a bond or bond portfolio with a duration equal to the duration of your liabilities.
Seeks to ensure that a predetermined sum of money is available at a specific time in the future regardless of interest rate movements

14. How Does target date Immunization Work?
If horizon = duration of portfolio, then bond price risk offsets reinvestment risk exactly

15. Target Date Immunization example
Suppose an insurance company issues a GIC,for $10000.If the GIC has a five-year maturity and a guaranteed interest rate of 8% ,the insurance company is obligated to pay $10000*(1.08)5= in five years.
The insurance company chooses to fund its obligation with $10000 of 8% annual coupon bonds, selling at par value, with six years to maturity.
The duration of the six-year maturity bonds used to fund the GIC is five years.

16. Target Date Immunization ex:
Terminal Value of a bond portfolio after 5 years
Time
Cash Flow
@8%
@7%
@9% 1
800 2
800
980.03 3
800
933.12
915.92
950.48 4
800
864.00
856.00
872.00
800 5
800
800
800
5 Sale of bond
10800/1+r
10000

17. Strategies for Multiple Liabilities:
Matching or Focused Strategy: Match the duration of each liability with a bond with that duration. For example, if you had CFs of $1M in each of years 4, 5, and 6, you could buy three bonds (or portfolios) with respective durations of 4, 5, and 6.
Portfolio or Barbell Strategy: Construct a portfolio with a portfolio duration equal to the average duration of your liabilities:. In the above example, you would form a portfolio with a duration of 5:
Note: Empirical Studies support matching as being more effective.

18. Immunization: Problems
Immunization based on duration matching will only work well for small interest rate changes
Problem: convexity
Portfolio duration does not decrease linearly with the passage of time
Duration generally decreases less rapidly than maturity
Portfolios need to be rebalanced periodically to maintain immunization
Analysis more complicated if yield curve is not flat

19. Rebalancing
Over time, the duration of the bond and the duration of the liability change.
As interest rates change, the duration of the bond and the duration of the liability change.
Position may lose its immunization.
Rebalancing refers to changing the bond position to regain immunization.
Strategies: Sell bond and buy new one; add a bond to change Dp; reinvest CF differently; use futures or options.; set up combination matching (CF matching for early liabilities and immunization for longer-term liabilities.

20. Cash Flow Matching and Dedication
Cash Flow Matching: cash flow from the bond exactly offsets the liability
Dedication strategy (cash flow matching on a multiperiod basis)
zero-coupon bonds
coupon bonds

21. Fixed Income Portfolio Management - Active
Active management presumes that the manager can generate a positive a (or provide a positive risk-adjusted return)
sources of potential profit
Trade on interest rate predictions
Trade on market inefficiencies:
identification of relative mispricing within the fixed-income markets.

22. Active Bond Management: Swapping Strategies
Swaps:Exchanging one bond for another in anticipation of a change in the relative prices of the bonds
Substitution swap
Intermarket spread swap
Rate anticipation swap
Pure yield pickup swap
Tax swap

23. Fixed Income Portfolio Management - Active
Substitution swap: exchanging one bond for another to exploit pricing discrepancies
Inter-market spread swap: yield spread between 2 market segments is too wide or too narrow
Rate anticipation swap: move toward higher/lower D portfolio depending on i-rate forecasts
Pure yield pickup swap: buy higher yield bonds and sell lower yield bonds (increase in risk)
Tax swap: refers to a swap to exploit some tax advantage.

24. Rate Anticipation Swap1
Strategy of buying bonds with high or low durations based on the expectation of an upward or downward parallel shift in the yield curve. It is a type of yield curve shift strategy.
Strategy:

25. Rate Anticipation Swap2
D = HD => immunized
then price risk and reinvestment risk offset one another
D > HD => net price effect
D < HD => net reinvestment rate risk

26. Rate Anticipation Swap2
Consider a bond with 10 years to maturity, 8% coupon (paid annually), priced at $ Current interest rates = 10%
Duration = 7.04
Suppose your HD = 4 years
You expect interest rates will decline
Since D > HD => net price risk

27. Rate Anticipation Swap2
Future Value(CF)
Time
Cash Flow
@10%
@8%
@12% 1 80
106.48
100.78
112.39 80 2
96.80
93.31
100.35 3 80
88.00
86.40
89.60 4 80
80.00
80.00
80.00
Price
912.89
835.54
Interest on interest
51.28
40.49
62.35
Change:
Price
87.11
-77.35
Interest
-10.79
11.07
Net Price Effect
76.32
-66.28

28. Rate Anticipation Swap3: Relative Return Value Analysis
We can calculate the overall expected return for each bond in our scenario (expected return under each interest rate scenario weighted by the probability of that scenario occurring) and the current duration of each bond in our portfolio and graph the relationship. Those bonds falling above a regression line (showing the general relationship) would be doing ok!

29. Rate Anticipation Swap4: Strategic Frontier Analysis
We can graph the bonds in our portfolio with the best case scenario (an interest rate decrease) on the vertical axis and the worst case scenario on the horizontal axis, as shown below:

30.                                                                                                 
Those securities which fall into Quadrant I represent aggressive securities

31. Quality Swap
Strategy of buying bonds with high or low quality rating based on the expectation of a change in economic states.
Strategy:

32. Yield Pick-Up Swap
Strategy of identifying bonds which are identical but do not yield the same rates. The assumption is that the returns on the bonds will eventually converge.
Strategy:

33. Active Bond Management: horizon analysis(期限分析)
horizon analysis is one form of interest rate forecasting.
Selects a particular holding period and predicts the yield curve at the end of that period.
Calculates expected total return
Repeat above procedure for many bonds and selects the ones promising superior holding-period returns for the portfolio.

34. Expected total return
Expected total return =（expected terminal wealth-initial wealth）/initial wealth
Expected terminal wealth=total coupon interest payments+interest on interest+projected price at the end of the planned investment horizon。

35. a particular version of horizon analysis: Riding the Yield Curve
Yield to Maturity %
Maturity
3 mon 6 mon mon

36. Riding yield curve 9-month bill 3 month bill => earn .75%
Price today = $100/(1.015)3 = $95.63
Price in 3 months = $100/(1.0125)2 = $97.55
Holding period return = ( )/95.63 = 2%
3 month bill => earn .75%

37. Yield Curve Strategies
Yield Curve Strategies: Forecast a yield curve shift and then devise an appropriate strategy to profit from the forecast.
Common Types of YC Shifts
Yield Curve Strategies

38. Yield Curve Strategies (2)
Types of YC Shifts:
Parallel Shifts: Rates on all maturities change by the same number of basis points (or by the same percentage).
Twisting:
Flattening:
Steepening:

39. Yield Curve Strategies (3)
Humpedness:
Positive Butterfly: ST and LT rates change more than intermediate.
Negative Butterfly: Intermediate rates change more than ST and LT.

40. Yield Curve Strategies (4)
Types of Yield Curve Strategies:
Bullet Strategy: Portfolio of bonds concentrated in one maturity area.
Barbell Strategy: Portfolio concentrated in each extreme.
Ladder Strategy: Equal allocation in each maturity.

41. Yield curve strategies
bullet strategy = concentrated durations
barbell strategy = two extreme maturities
ladder strategy = uniform distribution

42. Yield curve strategies
If interest rates change by the same amount for all terms of bonds, the yield curve is said to have had a "parallel shift". This almost never happens. When the difference between short- and long-term interest rates increases, the yield curve is said to "steepen"; when the difference between short- and long-term rates decreases, the yield curve is said to "flatten".
Flatten--"barbell" portfolio better?
Steepening yield curve—bullet portfolio better?

43. Yield curve strategies
Every strategy performance depends on the magnitude of the change in yields and how the yield curve shifts
It is imperative to perform total return analysis

44. Yield Curve Strategies: Total Return Analysis
Total Return Analysis: The correct YC strategy depends on your expectations. One approach to use in identifying the appropriate strategy is Total Return Analysis.
Total Return analysis involves determining the possible returns from different YC strategies given different YC shifts.

45. Contingent Immunization
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 immunized.

46. Contingent Immunization (1)
Contingent Immunization can be described as both an active and passive strategy.
Bond manager pursues an active bond strategy until an agreed-upon minimum rate is reached; when that occurs the manager immunizes the position.

47. Contingent Immunization (2)
Example:
Suppose an Investment Company offers a contingent immunization strategy for investors with HD = 3.5 years based on a current 4-year, 9% annual coupon bond trading at a YTM of 10% (assume flat YC at 10%). The bond has a duration of 3.5 years and an immunization rate of 10%.

48. Contingent Immunization (3)
The contingent immunization strategy calls for an active strategy to be pushed until the minimum target rate of 8% is reached; at that time, the investment will be immunized. The minimum target rate is reached when the investment’s safety margin is zero:

49. Contingent Immunization (4)
Suppose the investment company has a client with $1M to invest and HD = 3.5 years.
Client’s Initial Safety Margin (SM):

50. Contingent Immunization (5)
As part of its active strategy, suppose the investment company invest the client’s funds in a 10-year, 10% annual coupon bond trading at par.
Scenario 1: One year later the YC shifts down to 8%
Client’s Safety Margin (SM):

51. Contingent Immunization (6)
With a positive SM, the company could maintain its current investment, pursue a different active strategy, or it could immunized the position.
If the company immunizes, it would liquidate the original 10-year bond and purchase a bond with HD = 2.5 years yielding 8% (assume flat YC at 8%). If it did this, it would be able to provide the client with a 11.96% rate for the 3.5 year period:

52. Contingent Immunization (7)
Scenario 2: One year after investing in the 10-year bond, the YC shifts up to 12.25%.
Client’s Safety Margin (SM):

53. Contingent Immunization (8)
With the SM approximately zero, the company would immunized the position.
The company would liquidate the original 10-year bond and purchase a bond with HD = 2.5 years, yielding 12.25% (assume flat YC at 12.25%). For the 3.5 year period the rate would be the minimum target rate of 8%: