IIPC Illmer Consulting AG · IIPC Illmer Date: August 2012 - Slide 5 Investment Performance...
Transcript of IIPC Illmer Consulting AG · IIPC Illmer Date: August 2012 - Slide 5 Investment Performance...
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 0 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
IIPCIllmer
Investment Performance
Consulting AG
Holdings-Based Risk Attribution –
Background and Concept
Date: August 2012
Produced by: Dr. Stefan J. Illmer
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 1 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Agenda
Introductory thoughts
Monitoring risk from a top down perspective
Risk attribution – the big picture
Holdings-based risk attribution – an example
Decision-oriented risk attribution
Comments and questions
Contact details and disclaimer
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 2 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Introductory thoughts
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 3 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Introductory thoughts – the investment process (1/4)
Investment process Definition of benchmark
Definition of strategic asset allocation
Definition of tactical asset allocation
Implementation of tactical asset allocation
Investment reporting and controlling
Investment management process Tasks and duties of decision makers
Monitor target achievement.
Review circumstances and forecasts
relevant as input for decision-making
process.
Determine contributions to and drivers
for return and risk.
Systematic process evaluation and
constant process improvement.
Monitor compliance with laws and
regulations, policies and procedures as
well as investment restrictions.
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 4 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Ex-ante or forward looking
view
Overall absolute return equals
the sum of all return contributions which
are the result of
all risks taken based on decisions done by
decision makers
Introductory thoughts – return generation process (2/4)
3.52% p.a.
Ex-post or backward looking
view Monitoring of
results, forecasts and expectations
Multi-layer process
and multi-asset class portfolio
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 5 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Introductory thoughts – performance analysis overview (3/4)
Ex-post or
backward
looking
Industry
standard
Tailor-made
Ex-ante or
forward looking
Tailor-made
Industry
standard
Return
decomposition
Risk
decomposition
Current and future challenge
Complex
investment
processes
Tailor-made
Tailor-made
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 6 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Introductory thoughts – relevant questions (4a/4)
Ex-post or
backward
looking
Industry
standard
Tailor-made
Ex-ante or
forward looking
Tailor-made
Industry
standard
Return
decomposition
Risk
decomposition
Current and future challenge
Complex
investment
processes
Tailor-made
Tailor-made
Relevant questions to answer:
– What return measure(s)?
– What risk measure(s)?
– What methodology?
– ...
– ...
– What decisions to analyze?
– ...
– ...
– What are relevant risk drivers?
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 7 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Introductory thoughts – relevant questions (4b/4)
Future Past Today
How should it be done?
Is there any best practice?
How should it be done?
Is there any best practice?
Measure, analyze,
visualize, report, etc.
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 8 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Monitoring risk from a top down perspective
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 9 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Monitoring risk from a top down perspective (1/4)
What was the impact of
the investment committee
on the overall excess
risk?
Is the excess risk mainly
due to the asset allocation
decisions of the
investment committee?
Which asset class added
most to the overall
absolute risk?
What was the impact of the
stock picking decisions within
the equity portfolios on the
overall absolute risk?
What kind of investment
decision added most to the
overall excess risk?
Did the index choice of
the equity portfolios lower
or increase the excess
risk?
… ?
What is the impact of the
proposed rebalancing on
the risk profile of the total
assets?
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 10 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Investment process
Benchmark
SAA
TAA
Stock picking
Monitoring risk from a top down perspective (2/4)
Performance
decomposition
Performance contribution Performance attribution
Contributions to return and risk
(absolute or relative)
Equities Bonds Etc.
USA Europe Etc.
Financials Telecom Etc.
AAA AA Etc.
USD JPY Etc.
Asset
allocation
Stock picking Etc.
Benchmark
SAA
TAA
Stock picking
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 11 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Performance attribution
Sector / instruments e.g. countries, industries,
sectors, stocks, etc.
Factors e.g. fundamental, stock
specific, etc.
Decision makers e.g. client, consultants,
portfolio manager, etc.
Investment activities e.g. benchmark, strategic
and tactical asset allocation,
etc.
Contributions
absolute relative
Portfolio Benchmark
Return Risk
ex-post ex-ante
Monitoring risk from a top down perspective (3/4)
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 12 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Monitoring risk from a top down perspective (4/4)
Investment process Definition of benchmark
Definition of strategic asset allocation
Definition of tactical asset allocation
Implementation of tactical asset allocation
Investment reporting and controlling
Investment management process Relevant aspects to consider:
• Focus on all asset classes and the total
portfolio and less – in isolation – on specific
asset classes or carve-outs of the total
portfolio.
• Focus more on the amount of risk and less on
the kinds of risk.
• Focus on total risk of asset classes and
portfolios and less on their risk characteristics
or the individual investments.
• Focus on the overall result but also on the
impact of individual decisions and decision
makers.
• Focus on the intended and less on the actual
consequences of investment decision – except
for the last sub-process implementation.
• Focus on the total investment process and
less on the individual sub-processes.
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 13 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Risk attribution – the big picture
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 14 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Risk attribution
Ex-post analysis Ex-ante analysis
Absolute risk
Decomposition of volatility
Excess risk
Decomposition of excess volatility and
tracking error
Absolute risk attribution Excess risk attribution
Remark: Lot of other (statistical) risk measures can be considered. In the following we focus on
variance and volatility.
Risk attribution – the big picture (1/3)
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 15 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Risk attribution – the big picture (2/3)
Risk attribution
Single factor based attribution Multi factor based attribution
Holdings-based risk attribution
Weights and covariances of segments
=> Factor may be the market, the benchmark
or the portfolio
=> More for risk analytics on an aggregated
level
=> Focus is the amount of risk
Factor exposures and factor covariances
=> Factors may be for example the region,
the country, the currency, the sector
or some fundamental factors
=> More for detailed risk analytics on an
instrument level
=> Focus are the kinds of risk
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 16 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
How much risk is coming from each factor?
Risk Model: Global Portfolio Benchmark
Number of Securities 67 1'550
Number of Currencies 8 0
Portfolio Value
Total Risk (ex-ante) 18.81% 18.21%
- Factor Specific Risk 18.66% 18.18%
- Stock Specific Risk 2.39% 1.02%
Tracking Error (ex-ante) 2.57%
Relative Value at Risk
R-squared 0.98
Beta-adjusted Risk 18.64% 18.21%
Predicted Beta 1.02
Predicted Dividend Yield 1.86 2.01
P/ E Ratio (E: 12 months) 28.39 26.00
P/ B Ratio (B: year-end) 2.58 2.56
3'570'469 0.52%
2.08%
9.35%
2.39% Stock Specific Risk
- Covariance (+/ -)
Explication of risk model: Factor risk is a standard deviation that is
measured by multiplying the 5-year exposure of the components of a portfolio
to each risk factor and by multiplying these figures by the externally determined
risk of each factor. The Tracking Error is measured similarly except that it is the
difference between portfolio and benchmark exposure that is multiplied.
Specific Risk is the standard deviation that measures the volatility of the risk not
captured by the factor model. The model consists of 3 regional, 21 country, 38
industry and 8 fundamental factors (market cap, 4-year E/P growth, E/P, B/P, 5-
year yield, long term debt, 5-year ROE variablity and 5-year earnings variability).
Tracking Error
2.57%
1.50%
0.18%
0.83%
0.77%
0.78%
0.27%
Portfolio
18.81%
18.66%
11.50%
6.98%
2.64%
1.44%
8.42%
- Country
- Industry
- Fundamental
- Currency
84'334'091
Risk Model: Global
Total Risk (ex-ante)
Factor Specific Risk
- Region
Decomposition of the ex-ante absolute and
relative excess risk of an equity portfolio.
How much risk is coming from each asset
class, each decision and each decision maker?
Weights Volatilities p.a.Contribution to
Variance in %
Cash 5.00% 0.86% -0.07%
Domestic Bonds 13.00% 2.88% 1.83%
Foreign Bonds 13.00% 8.41% 10.16%
Domestic Equities 21.00% 17.37% 42.04%
Foreign Equities 15.00% 17.83% 32.22%
Alternative Investments 7.00% 17.59% 13.48%
Real Estate 15.00% 1.27% 0.41%
Mortages 11.00% 0.38% -0.07%
Total 100.00% 7.83% 100.00%
Decomposition of the ex-ante (systematic)
absolute risk of an multi asset class portfolio.
Risk attribution – the big picture (3/3)
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 17 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Holdings-based risk attribution – an example
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 18 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Inputs and assumptions
Single factor based risk attribution using the investment portfolio as the
explaining factor. Here we estimate and decompose the portfolio absolute risk
by using the weighted risk characteristics of the asset classes the portfolio is
invested in. For the estimation and the decomposition of the portfolio risk we
need the following input data:
Weights of the different asset classes for the investment portfolio for the
relevant period.
Estimated covariances between asset classes for the investment portfolio for
the relevant period.
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 19 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Some formulas (1/3)
Since covariances are additive the risk of a portfolio can easily be decomposed.
𝑅𝑃 = 𝑤𝑖𝑃 × 𝑅𝑖
𝑃
𝑛
𝑖=1
⇒
𝜎2 𝑅𝑃 = 𝑤𝑖𝑃 × 𝑤𝑗
𝑃 × 𝐶𝑜𝑣 𝑅𝑖𝑃, 𝑅𝑗𝑃 ⇒
𝑛
𝑗=1
𝑛
𝑖=1
𝜎2 𝑅𝑃 = 𝑤𝑖𝑃 2
𝑛
𝑖=1
× 𝜎2 𝑅𝑖𝑃 + 𝑤𝑖
𝑃 ×𝑤𝑗𝑃 × 𝐶𝑜𝑣 𝑅𝑖
𝑃, 𝑅𝑗𝑃 ⇒
𝑛
𝑗=1𝑖≠𝑗
𝑛
𝑖=1
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 20 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Some formulas (2/3)
Risk contributions can easily be calculated using the part of the portfolio risk
based on the weighted variances of the individual asset classes. It is more
difficult for the part of the portfolio risk based on the weighted covariances
between the different asset classes – assuming correlated returns of the asset
classes.
The weighted covariances between the different asset classes can be presented
separate or can be assigned to the different asset classes by using a specific
smoothing algorithm – where here we use the split 50/50.
𝜎2 𝑅𝑃 = 𝑤𝑖𝑃 2
𝑛
𝑖=1
× 𝜎2 𝑅𝑖𝑃 + 𝑤𝑖
𝑃 × 𝑤𝑗𝑃 × 𝐶𝑜𝑟𝑟𝑒𝑙 𝑅𝑖
𝑃, 𝑅𝑗𝑃 × 𝜎 𝑅𝑖
𝑃 × 𝜎 𝑅𝑗𝑃
𝑛
𝑗=1𝑖≠𝑗
𝑛
𝑖=1
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 21 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Some formulas (3/3)
𝜎2 𝑅𝑃 = 𝑤𝑖𝑃 2
𝑚
𝑖=1
× 𝜎2 𝑅𝑖𝑃 + 𝑤𝑖
𝑃 ×𝑤𝑗𝑃 × 𝐶𝑜𝑣 𝑅𝑖
𝑃, 𝑅𝑗𝑃
𝑛
𝑗=1, 𝑗≠𝑖
𝑚
𝑖=1
𝜎2 𝑅𝑖𝑃 = 𝑤𝑖
𝑃 2 × 𝜎2 𝑅𝑖𝑃 + 𝑤𝑖
𝑃 × 𝑤𝑗𝑃 × 𝐶𝑜𝑣 𝑅𝑖
𝑃, 𝑅𝑗𝑃
𝑛
𝑗=1, 𝑗≠𝑖
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 22 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Weights Volatilities p.a.
Cash 5.00% 0.30%
Domestic Bonds 7.00% 3.47%
Foreign Bonds hedged 5.00% 3.08%
Foreign Bonds unhedged 18.00% 6.79%
Mortages 25.00% 1.08%
Domestic Equities 30.00% 17.42%
Foreign Equities 5.00% 18.92%
Domestic Real Estate 5.00% 6.91%
Total 100.00%
Starting point
𝜎2 𝑅𝑃 =𝑤1𝑃
⋮𝑤𝑛𝑃
𝑇
×𝜎2 𝑅1
𝑃 ⋯ 𝐶𝑜𝑣 𝑅1𝑃, 𝑅𝑛𝑃
⋮ ⋱ ⋮𝐶𝑜𝑣 𝑅𝑛
𝑃, 𝑅1𝑃 ⋯ 𝜎2 𝑅𝑛
𝑃×𝑤1𝑃
⋮𝑤𝑛𝑃
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 23 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Calculations (1/2)
Covariance Matrix p.a. CashDomestic
Bonds
Foreign Bonds
hedged
Foreign Bonds
unhedgedMortages
Domestic
Equities
Foreign
Equities
Domestic Real
Estate
Cash 0.00001 0.00002 0.00002 0.00000 0.00001 -0.00003 -0.00007 0.00000
Domestic Bonds 0.00002 0.00120 0.00063 0.00006 0.00024 -0.00089 -0.00169 -0.00005
Foreign Bonds hedged 0.00002 0.00063 0.00095 0.00068 0.00018 -0.00098 -0.00117 -0.00012
Foreign Bonds unhedged 0.00000 0.00006 0.00068 0.00461 0.00005 0.00390 0.00785 0.00023
Mortages 0.00001 0.00024 0.00018 0.00005 0.00012 -0.00041 -0.00056 0.00000
Domestic Equities -0.00003 -0.00089 -0.00098 0.00390 -0.00041 0.03036 0.02564 0.00084
Foreign Equities -0.00007 -0.00169 -0.00117 0.00785 -0.00056 0.02564 0.03581 0.00085
Domestic Real Estate 0.00000 -0.00005 -0.00012 0.00023 0.00000 0.00084 0.00085 0.00478
Weight Matrix CashDomestic
Bonds
Foreign Bonds
hedged
Foreign Bonds
unhedgedMortages
Domestic
Equities
Foreign
Equities
Domestic Real
Estate
Cash 0.25% 0.35% 0.25% 0.90% 1.25% 1.50% 0.25% 0.25%
Domestic Bonds 0.35% 0.49% 0.35% 1.26% 1.75% 2.10% 0.35% 0.35%
Foreign Bonds hedged 0.25% 0.35% 0.25% 0.90% 1.25% 1.50% 0.25% 0.25%
Foreign Bonds unhedged 0.90% 1.26% 0.90% 3.24% 4.50% 5.40% 0.90% 0.90%
Mortages 1.25% 1.75% 1.25% 4.50% 6.25% 7.50% 1.25% 1.25%
Domestic Equities 1.50% 2.10% 1.50% 5.40% 7.50% 9.00% 1.50% 1.50%
Foreign Equities 0.25% 0.35% 0.25% 0.90% 1.25% 1.50% 0.25% 0.25%
Domestic Real Estate 0.25% 0.35% 0.25% 0.90% 1.25% 1.50% 0.25% 0.25%
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 24 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Calculations (2/2)
Contribution to Covariance CashDomestic
Bonds
Foreign Bonds
hedged
Foreign Bonds
unhedgedMortages
Domestic
Equities
Foreign
Equities
Domestic Real
Estate
Cash 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
Domestic Bonds 0.00000 0.00001 0.00000 0.00000 0.00000 -0.00002 -0.00001 0.00000
Foreign Bonds hedged 0.00000 0.00000 0.00000 0.00001 0.00000 -0.00001 0.00000 0.00000
Foreign Bonds unhedged 0.00000 0.00000 0.00001 0.00015 0.00000 0.00021 0.00007 0.00000
Mortages 0.00000 0.00000 0.00000 0.00000 0.00001 -0.00003 -0.00001 0.00000
Domestic Equities 0.00000 -0.00002 -0.00001 0.00021 -0.00003 0.00273 0.00038 0.00001
Foreign Equities 0.00000 -0.00001 0.00000 0.00007 -0.00001 0.00038 0.00009 0.00000
Domestic Real Estate 0.00000 0.00000 0.00000 0.00000 0.00000 0.00001 0.00000 0.00001
Contribution to
VarianceNot smoothed Smoothed
Cash 0.00000 0.00000
Domestic Bonds 0.00001 -0.00001
Foreign Bonds hedged 0.00000 0.00000
Foreign Bonds unhedged 0.00015 0.00044
Mortages 0.00001 -0.00002
Domestic Equities 0.00273 0.00328
Foreign Equities 0.00009 0.00053
Domestic Real Estate 0.00001 0.00003
Covarianz 0.00124
Total 0.00424 0.00424
Contribution to
Variance in %Not smoothed Smoothed
Cash 0.00% -0.01%
Domestic Bonds 0.14% -0.28%
Foreign Bonds hedged 0.06% -0.12%
Foreign Bonds unhedged 3.52% 10.42%
Mortages 0.17% -0.51%
Domestic Equities 64.48% 77.29%
Foreign Equities 2.11% 12.53%
Domestic Real Estate 0.28% 0.66%
Covarianz 29.24% 0.00%
Total Variance 100.00% 100.00%
Total Volatility 6.51%
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 25 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Weights Volatilities p.a.Contribution to
Variance in %
Contribution to
Variance
Contribution to
Volatility
Cash 5.00% 0.30% -0.01% 0.00000 0.00%
Domestic Bonds 7.00% 3.47% -0.28% -0.00001 -0.02%
Foreign Bonds hedged 5.00% 3.08% -0.12% 0.00000 -0.01%
Foreign Bonds unhedged 18.00% 6.79% 10.42% 0.00044 0.68%
Mortages 25.00% 1.08% -0.51% -0.00002 -0.03%
Domestic Equities 30.00% 17.42% 77.29% 0.00328 5.03%
Foreign Equities 5.00% 18.92% 12.53% 0.00053 0.82%
Domestic Real Estate 5.00% 6.91% 0.66% 0.00003 0.04%
Total 100.00% 6.51% 100.00% 0.00424 6.51%
Results
Remark: Contribution to volatility are approximated by the relative weights of the contributions of the variances multiplied with the
portfolio volatility.
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 26 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Decision-oriented risk attribution
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 27 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Definition – Decision-oriented risk attribution
Definition of benchmark
Definition of strategic asset allocation
Definition of tactical asset allocation
Implementation of tactical asset allocation
Investment reporting and controlling
Investment management process Decision-oriented risk attribution is
the decomposition of the (absolute
or excess) risk of an investment
portfolio according to specific
investment decisions done by
specific decision makers.
The decomposition approach is
difficult to standardize and therefore
normally tailor-made as the relevant
investment management processes
differ – sometimes substantially.
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 28 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Generic decomposition approach (1/2)
Decision-oriented decomposition of the absolute
(excess) risk allows to quantify the risk contribution or
the value added of the individual decision makers and
is based on the following steps:
Step 1: Identify the circumstances, the investment
management setup, and derive relevant
assumptions for calculation.
Step 2: Mirror the specific investment decisions
into (absolute) asset allocations.
Step 3: Calculate the corresponding risk figures.
Step 4: Assign the absolute risk as well as the risk
differences to the investment decisions
and to the relevant decision makers.
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 29 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Mirror investment decisions
Weights BenchmarkStrategic asset
allocation
Tactical asset
allocation
Portfolio
strategies
allocation
Actual portfolio
allocation
Domestic bonds 10.00% 10.00% 10.00% 10.00% 12.00%
Foreign bonds 20.00% 10.00% 25.00% 25.00% 23.00%
Domestic equities 30.00% 35.00% 55.00% 55.00% 55.00%
Foreign equities 40.00% 45.00% 10.00% 10.00% 10.00%
Total assets 100.00% 100.00% 100.00% 100.00% 100.00%
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 30 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Calculation of risk figures (1/6)
Target risk
Benchmark risk
SAA risk
TAA risk
Portfolio index risk
Portfolio actual risk
Benchmark weights
and indices
Investment target and risk profile
Definition of benchmark
Definition of strategic asset allocation
Definition of tactical asset allocation
Definition of portfolio strategies
Implementation of portfolio strategies
SAA weights
TAA weights
Portfolio indices
Portfolio weights and
stock weights
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 31 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Calculation of risk figures (2/6)
Target risk
Benchmark risk
SAA risk
TAA risk
Portfolio index risk
Portfolio actual risk
Excess = Risk contribution due to the definition of the benchmark
Excess = Risk contribution due to the definition of the strategic asset allocation
Excess = Risk contribution due to the definition of the tactical asset allocation
Excess = Risk contribution due to the definition of the portfolio strategies
Excess = Risk contribution due to the implementation of the portfolio strategies
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 32 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Calculation of risk figures (3/6)
Target risk
Benchmark risk
SAA risk
TAA risk
Portfolio index risk
Portfolio actual risk
E.g. weight of domestic equities and choice of respective benchmark index
E.g. difference in weight of domestic equities
E.g. difference in weight of domestic equities
E.g. choice of respective portfolio index
E.g. difference in weight of domestic equities, stock picking and rest
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 33 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Calculation of risk figures (4/6)
Target risk
Benchmark risk
SAA risk
TAA risk
Portfolio index risk
Portfolio actual risk
Remark: Here we decompose the absolute excess risk – means the difference in total risk.
𝐴𝐸𝑅 = 𝑤𝑖𝐵 × 𝑤𝑗
𝐵 × 𝐶𝑜𝑣 𝑅𝑖𝐵 , 𝑅𝑗𝐵
𝑛
𝑗=1, 𝑗≠𝑖
𝑚
𝑖=1
− 𝑇𝑎𝑟𝑔𝑒𝑡 𝑟𝑖𝑠𝑘
𝐴𝐸𝑅 = 𝑤𝑖𝑆𝐴𝐴 × 𝑤𝑗
𝑆𝐴𝐴 × 𝐶𝑜𝑣 𝑅𝑖𝐵 , 𝑅𝑗𝐵
𝑛
𝑗=1, 𝑗≠𝑖
𝑚
𝑖=1
− 𝑤𝑖𝐵 × 𝑤𝑗
𝐵 × 𝐶𝑜𝑣 𝑅𝑖𝐵 , 𝑅𝑗𝐵
𝑛
𝑗=1, 𝑗≠𝑖
𝑚
𝑖=1
𝐴𝐸𝑅 = 𝑤𝑖𝑇𝐴𝐴 × 𝑤𝑗
𝑇𝐴𝐴 × 𝐶𝑜𝑣 𝑅𝑖𝐵 , 𝑅𝑗𝐵
𝑛
𝑗=1, 𝑗≠𝑖
𝑚
𝑖=1
− 𝑤𝑖𝑆𝐴𝐴 ×𝑤𝑗
𝑆𝐴𝐴 × 𝐶𝑜𝑣 𝑅𝑖𝐵 , 𝑅𝑗𝐵
𝑛
𝑗=1, 𝑗≠𝑖
𝑚
𝑖=1
𝐴𝐸𝑅 = 𝑤𝑖𝑇𝐴𝐴 × 𝑤𝑗
𝑇𝐴𝐴 × 𝐶𝑜𝑣 𝑅𝑖𝑃𝐼 , 𝑅𝑗𝑃𝐼
𝑛
𝑗=1, 𝑗≠𝑖
𝑚
𝑖=1
− 𝑤𝑖𝑇𝐴𝐴 × 𝑤𝑗
𝑇𝐴𝐴 × 𝐶𝑜𝑣 𝑅𝑖𝐵 , 𝑅𝑗𝐵
𝑛
𝑗=1, 𝑗≠𝑖
𝑚
𝑖=1
𝐴𝐸𝑅 = 𝑤𝑖𝑃𝐴 ×𝑤𝑗
𝑃𝐴 × 𝐶𝑜𝑣 𝑅𝑖𝑃𝐴 , 𝑅𝑗
𝑃𝐴
𝑛
𝑗=1, 𝑗≠𝑖
𝑚
𝑖=1
− 𝑤𝑖𝑇𝐴𝐴 × 𝑤𝑗
𝑇𝐴𝐴 × 𝐶𝑜𝑣 𝑅𝑖𝑃𝐼 , 𝑅𝑗𝑃𝐼
𝑛
𝑗=1, 𝑗≠𝑖
𝑚
𝑖=1
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 34 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Calculation of risk figures (5/6)
Weights BenchmarkStrategic asset
allocation
Tactical asset
allocation
Portfolio
strategiesImplementation
Domestic Bonds 1 5.00% 5.00% 5.00% 5.00% 5.00%
Domestic Bonds 2 5.00% 5.00% 5.00% 5.00% 7.00%
Foreign Bonds 1 4.00% 2.00% 5.00% 5.00% 5.00%
Foreign Bonds 2 16.00% 8.00% 20.00% 20.00% 18.00%
Domestic Equities 1 13.64% 15.91% 25.00% 25.00% 25.00%
Domestic Equities 2 16.36% 19.09% 30.00% 30.00% 30.00%
Foreign Equities 1 20.00% 22.50% 5.00% 5.00% 5.00%
Foreign Equities 2 20.00% 22.50% 5.00% 5.00% 5.00%
Total 100.00% 100.00% 100.00% 100.00% 100.00%
Volatilities BenchmarkStrategic asset
allocation
Tactical asset
allocation
Portfolio
strategiesImplementation
Domestic Bonds 1 0.30% 0.30% 0.30% 0.31% 0.35%
Domestic Bonds 2 3.47% 3.47% 3.47% 2.99% 2.57%
Foreign Bonds 1 3.08% 3.08% 3.08% 3.02% 3.21%
Foreign Bonds 2 6.79% 6.79% 6.79% 6.34% 6.00%
Domestic Equities 1 1.08% 1.08% 1.08% 0.87% 0.78%
Domestic Equities 2 17.42% 17.42% 17.42% 17.58% 17.76%
Foreign Equities 1 18.92% 18.92% 18.92% 18.78% 18.69%
Foreign Equities 2 6.91% 6.91% 6.91% 3.37% 1.21%
Total 7.05% 7.64% 6.59% 6.55% 6.47%
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 35 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Calculation of risk figures (6/6)
Target risk
7.50%
Portfolio actual risk
6.47%
Surplus risk for the investment portfolio => - 1.03%
Risk contribution due to benchmark definition => - 0.45%
Risk contribution due to strategic asset allocation => + 0.59%
Risk contribution due to tactical asset allocation => -1.05%
Risk contribution due to portfolio strategies => - 0.04%
-
=
+
Risk contribution due to implementation => - 0.08%
+
+
+
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 36 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
-1.5%
-1.0%
-0.5%
0.0%
0.5%
1.0%
Domestic Bonds Foreign Bonds Domestic Equities Foreign Equities Total assets
Assigning of absolute excess risk figures (1/5)
Including the
added risk
due to the
definition of
benchmark
versus the
target risk
Remark: Contribution to volatility are approximated by the relative weights of the contributions of the variances multiplied with the
portfolio volatility.
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 37 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Assigning of absolute excess risk figures (2/5)
Decomposition of
the absolute
excess risk if not
reflecting the
investment
management
process
-1.5%
-1.0%
-0.5%
0.0%
0.5%
1.0%
Asset allocation effect Stock picking effect Interactioneffect
Total effects
Remark: Contribution to volatility are approximated by the relative weights of the contributions of the variances multiplied with the
portfolio volatility.
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 38 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Assigning of absolute excess risk figures (3/5)
Decomposition of
the absolute
excess risk
reflecting the
actual investment
management
process
-1.5%
-1.0%
-0.5%
0.0%
0.5%
1.0%
Definition ofbenchmark
Definition ofstrategic asset
allocation
Definition oftactical asset
allocation
Definition ofportfolio
strategies
Implementationof portfoliostrategies
Totalmanagement
effect
Remark: Contribution to volatility are approximated by the relative weights of the contributions of the variances multiplied with the
portfolio volatility.
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 39 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Assigning of absolute excess risk figures (4/5)
Management effects to excess riskAsset allocation
effect
Stock picking
effect
Interaction
effectTotal effects
Domestic Bonds 0.00% 0.01% 0.00% 0.00%
Foreign Bonds -0.10% -0.07% 0.01% -0.09%
Domestic Equities -0.76% -0.02% 0.07% -0.82%
Foreign Equities -0.13% -0.28% 0.24% -0.13%
Total assets -0.99% -0.36% 0.32% -1.03%
Management effects to excess riskBoard of
directors
Investment
committee
Portfolio
managerTotal effects
Domestic Bonds 0.00% 0.01% 0.00% 0.00%
Foreign Bonds -0.04% -0.02% -0.07% -0.09%
Domestic Equities -0.16% 1.15% 0.01% -0.82%
Foreign Equities -0.25% -1.64% -0.02% -0.13%
Total assets -0.45% -0.50% -0.08% -1.03%
Remark: Contribution to volatility are approximated by the relative weights of the contributions of the variances multiplied with the
portfolio volatility.
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 40 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Assigning of absolute excess risk figures (5/5)
Effective
portfolio
weights and
stock picking
Remarks: Decomposition might change depending on the investment management process. Contribution to volatility are
approximated by the relative weights of the contributions of the variances multiplied with the portfolio volatility.
!
Management effects to excess riskBoard of
directors
Investment
committee
Portfolio
managerTotal effects
Domestic Equities -0.16% 1.15% 0.01% -0.82%
SAA and
TAA weights
and choice of
portfolio
index
Definition of
benchmark
versus target
risk
Management effects to excess riskAsset allocation
effect
Stock picking
effect
Interaction
effectTotal effects
Domestic Equities -0.76% -0.02% 0.07% -0.82%
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 41 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Comments and questions
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 42 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Holdings-Based Risk Attribution – Background and Concept
Comments and questions
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 43 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Contact details and disclaimer
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 44 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Contact details
Illmer Investment Performance Consulting AG
Weinbergstrasse 28
CH - 8200 Schaffhausen
Switzerland
www.iipc-ag.com
Dr. Stefan Joachim Illmer
Tel. +41 / 79 / 962 20 37
Email: [email protected]
Produced by: Dr. Stefan J. Illmer Date: August 2012 - Slide 45 IIPC
Illmer
Investment Performance
Consulting AG Success through excellence!
Disclaimer
This document was produced by Illmer Investment Performance Consulting AG (hereafter "IIPC-
AG") with the greatest of care and to the best of its knowledge and belief. However, IIPC-AG
provides no guarantee with regard to its content and completeness and does not accept any liability
for losses which might arise from making use of this information. This document is provided for
information purposes only and is for the exclusive use of the recipient. It does not constitute an offer
or a recommendation to buy or sell financial instruments or banking services.
It is expressly not intended for persons who, due to their nationality or place of residence, are not
permitted access to such information under local law.