1. FIXED INCOME PERFORMANCE ATTRIBUTION
A PRESENTATION TO THE EUROPEAN BOND COMMISSION
Wolfgang Marty
Portfolio Analytics CSAM Zürich

2. 1. INTRODUCTION
2. DECOMPOSING THE RETURN
3. FACTOR ANALYSIS
4. FIXED INCOME RISK MODELS
5. THE RISK MODELS OF WILSHIRE
6. EXAMPLES

3. 1. INTRODUCTION

4. INTRODUCTION THE INVESTMENT PROCESS
Target asset allocation
(Exante)
Forecasts (active)
Optimization
Re-balancing
Market movements
Performance evaluation
(Expost)

5. INTRODUCTION PERFORMANCE MONITORING PROCESS
Production / Reporting
Portfolio Analytics / Risk Control
(quantitative aspect)
(qualitative aspect)
Considering of output (ex-post) and input (ex ante)
Performance
Performance
Performance
Performance
Performance
Portfolio
Performance
measurement
accounting
Reporting
Analysis
Watch List
Analytics
Review
Feed Forward and Feed Back
Efficient monitoring of of Investment process

6. INTRODUCTION DEFINITION PORTFOLIO ANALYTICS
Portfolio analytics is concerned with quantifying the sources of the return and assessing the risk of a portfolio. It not only measures the evolution of the wealth over a certain time period but it provides a comprehensive discussion of the performance of specific portfolios.

7. INTRODUCTION RETURN MEASUREMENT
Different source of return (Currency return, local market return, return from high yield investment, etc.)
Computation ideally daily
Input data are critical
Return is measured either absolute or relative to a reference portfolio (Benchmark)
Return measurement is conceptually easier to understand than risk measurement

8. INTRODUCTION RISK ASSESSMENT
Different source of risk (Exchange rate risk, Interest rate risk, Credit risk, Sector risk, etc.)
Computation based on historical data (time series)
Updating once a month is sufficient
In portfolio analytics we mostly consider variance or covariance as risk measures
Differentiation between forward and backward looking risk
Computation of absolute and relative risk measures
Tracking Error is relative Risk Measure

9. DEFINITION PERFORMANCE ATTRIBUTION
INTRODUCTION
DEFINITION PERFORMANCE ATTRIBUTION
Return attribution mathematically: Decompose a real number into a sum
Risk attribution mathematically: Consider generalisation of theorem of Pythagoras b . a c

10. DEFINITION PERFORMANCE ATTRIBUTION
INTRODUCTION
DEFINITION PERFORMANCE ATTRIBUTION
More precisely: Analyse the portfolio performance and the relative performance in terms of the decisions that generate returns.
Conclusion: Need mapping from the decision making process to a performance attribution model.

11. 2. DECOMPOSING THE RETURN

12. THE WILSHIRE APPLICATION AXIOM RETURN OF A PORTFOLIO
(relative) return rp of a portfolio
The arithmetic (relative return) of a portfolio is the (relative) weighted average (wi), (wi - bi), of the arithmetic return (ri) of the individual securities.
On the right hand side and the left hand side is the same (no model)

13. THE WILSHIRE APPLICATION AXIOM ABSOLUTE DECOMPOSITION
Consider portfolio of 3 securities
Mac Donalds
IBM
CS Group
USA
Switzerland
Country
Portfolio return
w: weight
r: return
rP = w1 r w2 r w3 r3
Sector
Food
TMT
Bank

14. THE WILSHIRE APPLICATION AXIOM SLICING THE INVESTMENT UNIVERSE
Country (Subgroup)
Sector (Subgroup)
Multi step decision
Universe

15. THE WILSHIRE APPLICATION AXIOM CROSS PRODUCT
Interaction 4 2
Portfolio
Ending point y
Benchmark portfolio
Starting point 3 5

16. THE WILSHIRE APPLICATION AXIOM PROGRAM GLOBAL PERFORMANCE ATTRIBUTION
Universe: Bond Markets of JP Morgan Global Bond Index
The Application computes 3 different Model Returns (‘ Format ’) for 3 different return attribution
allows the measurement of 3 different investment processes
Model 1 and 2 are based on a form of the capital asset pricing model.
leverage factor is ratio of Bond duration and Benchmark Duration
Model 1 uses short term rate, Model 2 uses yield of a bond

17. THE WILSHIRE APPLICATION AXIOM PROGRAM GLOBAL PERFORMANCE ATTRIBUTION
Model computes the Model return of a Bond
The Application computes Buy and Hold return in USA Dollars:
Example: U.S. Treasury Bond
Price 07/01/2002: %
Price 07/31/2002: %
local return = ((end_price + end_accrued)/(begin_price + begin_accrued) -1)*100 = 3.29%

18. THE WILSHIRE APPLICATION AXIOM PROGRAM GLOBAL PERFORMANCE ATTRIBUTION
The difference between Model Return and Buy and Hold return is the selection effect.
Illustration: Return due to Market Movement versus Return calculated by duration times yield change.
Common in all Formats: Currency effect
The currency effect examines the impact of active currency exposure of the portfolio versus the benchmark
Return in Swiss Francs with currency return -0.47%: base currency return = ((1 + local_return/100) * ( currency_return/100) - 1)*100 = 2.80%

19. THE WILSHIRE APPLICATION AXIOM FORMAT 1: DURATION/COUNTRY
This format measures the following decisions:
Duration effect
Value added by being longer than the benchmark in a country where interest rate fell and shorter than benchmark in a country where interest rose.
It is only not zero if you have duration exposure in the benchmark and the portfolio.

20. THE WILSHIRE APPLICATION AXIOM FORMAT 1: DURATION/COUNTRY
Country effect
The country effect quantifies the effect of the managers active country bets on management performance by taking the difference between the portfolio weights and the benchmark weights for each country and then multiplying this bet by the relative return to that country (relative to the average local benchmark).
Asset allocation approach as it incorporates cross - country decisions

21. THE WILSHIRE APPLICATION AXIOM FORMAT 2: YIELD/EXPOSURE
This format measures the following decisions:
Yield effect
The yield component measures the return contribution in the portfolio relative to the benchmark by being invested in higher yielding securities (e.g. corporate bonds).

22. THE WILSHIRE APPLICATION AXIOM FORMAT 2: YIELD/EXPOSURE
Market effect
Is a combination of country-weighting and duration within country decisions. Thus a large country weighting offset by a short duration might result in a neutral or even negative net market exposure. In the duration/country format we would have a large country bet and a large negative duration bet.
Suited for investment process that centres around yield curve shifts

23. 3. FACTOR ANALYSIS

24. THE WILSHIRE APPLICATION AXIOM FORMAT 3: FACTOR EXPOSURE
The Format measures
the decomposition the returns in multi-currency portfolios in terms of different types of yield curve movements and currency changes.
Characteristics:
Measures investment process that makes bets on different sections of the yield curve
Consistent with Risk model
Best explanatory power of the three formats
It is regression based and represents a detailed description of returns in terms of a common set of risk factors

25. THE WILSHIRE APPLICATION AXIOM EFFECTIVE DURATION
shift(d1)
term structure
100bps
spot rate
shift(d1)
time

26. THE WILSHIRE APPLICATION AXIOM EFFECTIVE DURATION
Extension of flat yield concept
In Wilshire the spot rates are held in cubic spline forms
Takes shape of the spot rate curve into account
Effective duration and option adjusted duration is the same
Takes into account change of the bonds with different cash flows (callable bonds)
Defined as price sensitivity of bond to shift in actual yield curve

27. CHANGES OF THE YIELD CURVE WILSHIRE SHIFT SLOPE AND CURVATURE
term structure
spot rate
slope (d2)
curvature (d3)
shift(d1)
time

28. 4. FIXED INCOME RISK MODEL

29. FIXED INCOME RISK MODEL FACTOR ANALYSIS
Historical Data
Specify factors
Principal components analysis
Regression analysis
Problem: Interpretation of factors
Problem: Goodness of the fit

30. FIXED INCOME RISK MODEL COMPARISON
Barra
Shift
Twist
Butterfly
Wilshire Shift
Slope
Curvature
Prespecified by yield curve shapes with few parameters
Estimated by
historical data

31. FIXED INCOME RISK MODEL BARRA SHIFT TWIST AND BUTTERFLY

32. FIXED INCOME RISK MODEL BENCHMARK BOND EXPOSURES
Step 1: Compute by regression analysis the Risk Matrix given
the risk factors d1,d2,d3, country and currencies.
Different length of time periods (90, 180, 360 days,
exponential weightings)
Independent of Portfolio
Step 2: Compute the breakdown of the relative Risk (Tracking error)
given the Portfolio Holdings and the Benchmark holdings.

33. 5. THE RISK MODELS OF WILSHIRE

34. THE RISK MODELS OF WILSHIRE DIFFERENT MODELS
Wilshire Global Risk Model
Wilshire Global Credit Risk Model

35. THE RISK MODELS OF WILSHIRE SOME CHARACTERISTICS
Factors in Global Risk Model (based on 13 Countries of J.P. Morgan GBI, Total: 47 factors)
d1, d2, d3
Currency

36. THE RISK MODELS OF WILSHIRE CHARACTERISTICS
Factors in Credit Risk Model Total (16 countries, approx factor)
d1, d2, d3
Currency
Sectors
Quality Rating (Three Groups: Moody Aa, A, Baa)
Other spreads
Euro country spread
special Instrument in USA (e.g. GNMA prepay)

37. 6. EXAMPLES

38. EXAMPLE 1 ILLUSTRATION: BUCKETING APPROACH
Benchmark: JPM EMU Index
Portfolio: All Bonds with Duration > 8 Years (subset of Benchmark)

39. EXAMPLE 1 ILLUSTRATION: BUCKETING APPROACH
Benchmark: JPM EMU Index
Portfolio: All Bonds with Duration > 8 Years (subset of Benchmark)

40. EXAMPLE 1 ILLUSTRATION: DURATION /COUNTRY FORMAT

41. EXAMPLE 1 ILLUSTRATION: YIELD/EXPOSURE FORMAT

42. EXAMPLE 1 ILLUSTRATION: FACTOR FORMAT

43. EXAMPLE 2 SAMPLE REPORT

44. EXAMPLE 2 SAMPLE REPORT

45. EXAMPLE 2 SAMPLE REPORT

46. EXAMPLE 2 SAMPLE REPORT

47. EXAMPLE 2 SAMPLE REPORT

48. EXAMPLE 2 SAMPLE REPORT

49. EXAMPLE 2 SAMPLE REPORT

50. EXAMPLE 2 SAMPLE REPORT

51. EXAMPLE 2 SAMPLE REPORT