Fixed Income Performance Attribution
Asset Management
What is Performance Attribution?
1
Uses of Performance Attribution
2
Content
3
Drivers of Return in Fixed Income
Returns Based Attribution
4
Factor Based Attribution
5
Successive Revaluation
What Is Performance Attribution?
1
A framework for understanding the results of a portfolio manager’s investment decisions on a portfolio’s relative return vs. a benchmark
Framework Decision support Relative
Imposes simplifying principles Evaluates and provides feedback
What is Performance Attribution?
1
Uses of Performance Attribution
2
Content
3
Drivers of Return in Fixed Income
Returns Based Attribution
4
Factor Based Attribution
5
Successive Revaluation
Uses of Performance Attribution
2
Provide feedback for decisions within an investment process Framework should mirror investment process
Provide feedback about a selected investment process
Framework should be more general than investment process Provide feedback within a risk budgeting process
What is Performance Attribution?
1
Uses of Performance Attribution
2
Content
3
Drivers of Return in Fixed Income
Returns Based Attribution
4
Factor Based Attribution
5
Successive Revaluation
Drivers of Fixed Income Return
3
Price
Sum of all discounted cash flows
Return
Received cash flows plus change in price Discount rate
Government interest rate: term structure of rates Spread
– Systematic: swap spreads, industry spreads, rating spread
– Issuer/Security specific: supply/demand, issuer specific news
Cash flows: accrued income/coupon payments, prepayments, sinking funds
Change in price
– Change in expected cash flows (e.g. prepayments, optionality)
– Change in discount rate (government rate or spreads)
The Continuum of Performance Attribution Methodologies
3
Returns based (Brinson Facher) Duration modified returns basedFactor based with observed shifts
Factor based with estimated shifts (Regression)
Successive revaluation
An Example for Comparison
3
Period: September 2011
Portfolio: USD Treasury barbell portfolio (with 6 securities) vs. the JPM Traded USD Index
Long and short buckets are separated at the 10 years to maturity point
Coupon % of Description Rate Maturity Port
<10 Years to Maturity USA TREASURY NTS 1.5 1.5 31.12.2013 14.40 USA TREASURY NTS 0.7 0.75 15.12.2013 17.41 USA TREASURY BDS 2% 2 30.11.2013 17.95 Subtotal 49.76 >10 Years to Maturity US 6.750% 30YR BOND 6.75 15.08.2026 14.07 US 6.500% 30YR BOND 6.5 15.11.2026 17.09 US 6.000% 30YR BOND 6 15.02.2026 19.08 Subtotal 50.24 0 1 2 3 4 0.25 0.5 1 2 3 4 5 7 10 15 20 25 30 Spot Yi eld ( %) Years to Maturity
Yield Curves
31.08.2011 Yield (%) 30.09.2011 Yield (%) Yield CurvesWhat is Performance Attribution?
1
Uses of Performance Attribution
2
Content
3
Drivers of Return in Fixed Income
Returns Based Attribution
4
Factor Based Attribution
5
Successive Revaluation
Returns Based Attribution
An Introduction
4
Seeks to explain return differences between the portfolio and benchmark (Rportfolio – Rbenchmark)
Algebraic breakdown using only returns and weights of portfolio and benchmark
Flexible groupings
Allocates by weighting and selection decisions
Often representative of the investment process
Returns Based Attribution
Example
4
Allocation: Use benchmark to judge good/bad groups
Selection: compares portfolio and benchmark return within group Characteristics:
– Easily customizable to any investment process that concentrates on allocation to groups and selection within groups
– Easy to understand and interpret
– Relatively low data requirements Results are easily distorted when the investment process is
multi-dimensional
– e.g. currency, sector and rating Difficult to apply to most fixed income investment processes – Duration
Portfolio A Benchmark A Relative Return
Group Begin Base Begin Base Allocation Selection Total
Weight Rtn (%) Weight Rtn (%) Effect Effect
<10 Years to Maturity 49.76 -0.19 85.31 0.33 0.46 -0.26 0.20 >10 Years to Maturity 50.24 4.53 14.69 9.16 2.68 -2.33 0.35 Total 100.00 2.18 100.00 1.63 3.14 -2.58 0.55
What story does it tell?
Allocation effect shows that weighting decisions between the buckets were good due to the overweight of the better performing long bonds Selection effect was negative, especially in the long bonds bucket, but no clarity of cause
Can Returns Based Models Be Applied to Fixed Income?
4
The methodology can be extended to account for duration choices
What story does it tell?
Allocation effect remains unchanged — long bonds outperformed short bonds
In both categories, the portfolio had a shorter duration than the benchmark, giving a negative impact as the return per unit duration is positive
About half of the long bucket “selection” effect comes from duration positioning within the bucket
Portfolio A Benchmark A Relative Return
Group Begin Duration Base Begin Duration Base Duration
Effect
Allocation Selection Total
Weight Rtn (%) Weight Rtn (%) Effect Effect
<10 Years to Maturity 49.76 2.25 -0.19 85.31 4.10 0.33 -0.07 0.46 -0.18 0.20 >10 Years to Maturity 50.24 10.25 4.53 14.69 13.58 9.16 -1.13 2.68 -1.20 0.35 Total 100.00 6.27 2.18 100.00 5.49 1.63 -1.20 3.14 -1.38 0.55 Benchmark Excess
Group Base Duration Rtn (%)
Rtn (%) Duration <10 Years to Maturity 0.33 4.10 0.08 >10 Years to Maturity 9.16 13.58 0.67 Total 1.63 5.49 0.30
What is Performance Attribution?
1
Uses of Performance Attribution
2
Content
3
Drivers of Return in Fixed Income
Returns Based Attribution
4
Factor Based Attribution
5
Successive Revaluation
Returns Based Attribution
An Introduction
5
Seeks to explain return differences between the portfolio and benchmark (Rportfolio – Rbenchmark) as well as portfolio and benchmark returns individually
Breakdown of returns based on systematic factors, which are obtained during model creation
Regression analysis often used to determine returns or exposures to factors
Modeled returns, for portfolio, benchmark and differences, determined based on factor returns and exposures to factors
Factor Attribution and Fixed Income
5
Because of the strong mathematical relationship between changes in interest rates and price changes, fixed income is particularly well analyzed with this approach
Standard measures of mathematical sensitivity: duration, spread duration, convexity, etc.
R2 for government bonds tends to be above 95%
compared to 40% to 50% for equity regression For bonds, factor models help minimize the number dimensions necessary to explain yield curve shifts
Designing a Factor Model
5
General model description: Security returns can be expressed as a linear combination of sensitivities to systematic factors and the returns associated with those systematic factors
s i factors i i s
s
income
return
Exposure
R
#
,
*
_
Fixed Income Factors
Durations/interest shifts: three factor representation, key rate representation Spread durations/spread shift: flexible granularity
Other impacts: prepayments, optionality, etc.
A simple factor model for fixed income:
ss s
s
income
return
duration
yield
curve
shift
0.02 0.04 0.04 0.1 0.11 0.06 0.01 -0.11 -0.36 -0.49 -0.61 -0.78 -0.89 -0.9 -0.75 -0.6 -0.45 -0.3 -0.15 0 0.15 0.25 0.5 1 2 3 4 5 7 10 15 20 25 30 Yield Change (%)
Measuring the Yield Curve Shift
5
Observed shifts
Estimates of underlying curves are made and then shifts are observed/measured
The goal is still to break down the observed shift into component parts (our example: a parallel shift)
Since underlying curve estimates are easily available, the data requirements are low
Estimated shifts
The effects of the underlying curve shifts are determined via regression analysis
Can account for imperfect responses to expected sensitivities and/or interaction between different kind of shifts
Requires a universe of data for regression estimates
t t t i i t i s t s
e
E
D
r
,
, ,
,
Returns to Shifts Estimated Security Returns and
Exposures (Duration) Measured
Observed Shifts
Which Shift to Take?
5
Observed shifts
Given the observed yield curve, which point best proxies the parallel shift of the yield curve?
– Average: -0.22%
– 6-year point (~portfolio duration): -0.05%
– A split: 2-year point (+0.10%) for short and 15-year point (-0.49%) for long (not really parallel)
Average 6 Years Split
Coupon Maturity % of Carry Duration Residual Duration Residual Duration Residual Description Rate Maturity Port Effect Effect Effect Effect Effect Effect Effect
<10 USA TREASURY NTS 1.5 1.5 31.12.2013 14.40 0.12 0.50 -0.79 0.11 -0.40 -0.23 -0.06 USA TREASURY NTS 0.7 0.75 15.12.2013 17.41 0.06 0.50 -0.76 0.11 -0.37 -0.23 -0.03 USA TREASURY BDS 2% 2 30.11.2013 17.95 0.16 0.48 -0.84 0.11 -0.47 -0.22 -0.14 Subtotal 1.411 49.76 0.06 0.25 -0.40 0.06 -0.21 -0.11 -0.04 >10 US 6.750% 30YR BOND 6.75 15.08.2026 14.07 0.37 2.25 1.89 0.51 3.63 5.01 -0.87 US 6.500% 30YR BOND 6.5 15.11.2026 17.09 0.36 2.27 1.96 0.52 3.72 5.05 -0.82
Comparing the Results
Observed Shifts
5
For a neutral analysis, we take the “average” shift (-0.22%) What story does it tell us?
The portfolio has lower yielding securities in the short bucket and higher yielding securities in the long bucket Duration impact includes both weight and duration: with an underexposure in the short bucket of -2.4 years and an overexposure in the long bucket of 3.2 years, the duration effect is slightly positive
Selection impact is due to weighting: the benchmark had more negative selection in the short bucket and less positive selection in the long bucket
Portfolio A Benchmark A Relative Return
Group Begin Duration Base Begin Duration Base Carry
Effect
Duration Selection Total
Weight Rtn (%) Weight Rtn (%) Effect Effect
<10 Years
to Maturity 49.76 2.25 -0.19 85.31 4.10 0.33 -0.11 -0.52 0.26 -0.37 >10 Years
to Maturity 50.24 10.25 4.53 14.69 13.58 9.16 0.13 0.69 0.10 0.93
Comparing the Results
Estimated Shifts
5
Regression analysis gives a parallel shift of -0.44% What story does it tell us?
The portfolio has lower yielding securities in the short bucket and higher yielding securities in the long bucket Duration impact includes both weight and duration: with an underexposure in the short bucket of -2.4 years and an overexposure in the long bucket of 3.2 years, the duration effect is positive
Selection impact in short bucket is due to weighting: in the long bucket, the portfolio securities
underperformed the duration expectation, whereas the benchmark securities outperformed it
Portfolio A Benchmark A Relative Return
Group Begin Duration Base Begin Duration Base Carry
Effect
Duration Selection Total
Weight Rtn (%) Weight Rtn (%) Effect Effect
<10 Years
to Maturity 49.76 2.25 -0.19 85.31 4.10 0.33 -0.11 -1.04 0.78 -0.37 >10 Years
to Maturity 50.24 10.25 4.53 14.69 13.58 9.16 0.13 1.38 -0.58 0.93
What is Performance Attribution?
1
Uses of Performance Attribution
2
Content
3
Drivers of Return in Fixed Income
Returns Based Attribution
4
Factor Based Attribution
5
Successive Revaluation
Successive Revaluation
6
Successive revaluation involves shifting the curve and repricing all of the bonds: Only one “factor shift” is applied during each revaluation
Shifts can be attained by any of the foregoing methodologies Is a data and calculation intensive attribution methodology
Contacts
Do you have questions?
We look forward to hearing from you
Mary Cait McCarthy, CFA, FRM
Head Investment Reporting Credit Suisse
Zurich: +41 44 332 95 02
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