Enhancing Risk/Return Attribution with Sector Equity Models · Return Attribution of ZSample [...

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Enhancing Risk/Return Attribution with Sector Equity Models Stanislav Radchenko

March 25, 2014


Return Attribution of ‘Sample’ Portfolio (2001)

A sector model improves return attribution results

-4.42% asset selection vs. -2.01% asset selection contribution

What is ‘Sample’ Portfolio?

Total Market Return Sector Model (IT) Return

Total -32.07% Total -32.07%

Benchmark -27.10% Benchmark -27.10%

Active -4.97% Active -4.97%

+ Risk Indices -0.49% + Risk Indices -2.90%

Momentum -1.45% Momentum -3.85%

+ Industries -0.06% + Industries -0.06%

+Market Equity 0.00% +Market Equity 0.00%

+Asset Selection -4.42% +Asset Selection -2.01%


Sample Style Tilt Portfolio Analysis: What is It?

Benchmark: Market Cap Sector IT

Portfolio: Optimized portfolio with Momentum = b+0.3

All other styles = b

Dates: Optimized on Dec 29, 2000 using USE4L

Monthly performance Attribution for 2001 without rebalancing

Buy and hold the optimal portfolio from 2000/12/29


Risk Attribution of Sample Portfolios (2000/12/29)

A sector model improves risk attribution results

40.7% asset selection vs. 26.1% asset selection contribution

Significant difference in active risk

3.7% vs. 4.8% active risk

Portfolio is down -4.97% (1.35 vs. 1.03 std. deviation move)

Total Market St Dev %CR Sector Model (IT) St Dev %CR

Total 51.9% Total 53.9%

Benchmark 51.7% Benchmark 53.1%

Active 3.7% Active 4.8%

+ Risk Indices 2.9% 63.3% + Risk Indices 4.3% 79.1%

+ Industries 0.6% 3.1% + Industries 0.6% 1.6%

+Market Equity 0.3% 0.8% +Market Equity 0.3% 0.5%

+Covariances - -7.9% +Covariances - -7.2%

+Asset Selection 2.4% 40.7% +Asset Selection 2.4% 26.1%


Outline

Risk/return attribution results for sector style tilt portfolios

Why do sector model improve risk/return attribution results?

Observations for 2013


Long/Short Sector Style Tilt Portfolios

Benchmark: Market Cap Weighted Sector Benchmark

Style tilt portfolio

TOP: Go long top 20% of names

BOTTOM: go long bottom 20% of names

Risk/return attribution results for long/short (active) style tilt portfolios

Monthly rebalancing


Example of Active Style Tilt Portfolio Return Attribution

1996 1998 2000 2002 2004 2006 2008 2010 2012 2014-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Style Tilt Portfolio: LEVERAGE in Utilities

Active

Sect

USE4L

Utilities style tilt portfolio: Long firms with high Leverage in Utilities,

short firms with low Leverage in Utilities

Factor Return Contribution to Active Style Tilt Portfolio Return


Sector Models Improve Risk/Return Attribution Results

Return/risk attribution results improve for sector style tilt portfolios

Table 5.1: Improvements in Return Attribution and Risk Decomposition of sector style tilt portfolios with Sector Models

Mean change |specific returns|

Mean change in std(specific

returns)

Ex Post Variance Decomposition

Total Market

Sector Model Diff

Energy -27% -26% 55% 70% 31%

Materials -30% -30% 41% 67% 73%

Industrials -10% -12% 50% 66% 39%

Consumer Disc. -23% -25% 43% 68% 68%

Consumer Staples -25% -25% 36% 57% 70%

Health Care -20% -19% 56% 71% 36%

Financials -21% -20% 52% 72% 49%

IT -19% -18% 39% 64% 78%

Telecoms -10% -10% 37% 41% 14%

Utilities -39% -40% 31% 66% 128%

Average -22% -22% 44% 64% 59%

Better 10 10

10

Worse 0 0 0

Table 5.2: Improvements in Return Attribution and Risk Decomposition of total market style tilt portfolios with Sector Models



returns)


Total Market

Sector Model Diff

Energy -31% -29% 64% 73% 15%

Materials -28% -28% 51% 70% 39%

Industrials -11% -12% 58% 65% 15%

Consumer Disc. -22% -23% 56% 69% 24%


Health Care -22% -21% 67% 77% 16%

Financials -21% -20% 61% 71% 17%

IT -19% -19% 49% 64% 39%

Telecoms -8% -7% 40% 43% 8%

Utilities -42% -42% 39% 66% 70%

Average -23% -23% 53% 65% 29%

Better 10 10

10

Worse 0 0 0

Sector Model Styles

Size

Beta

Residual Volatility

Liquidity

Leverage

Growth

Momentum

Industry Momentum*

Short-Term Reversal*

Long-Term Reversal*

Seasonality*

Prospect*

Sentiment*

Asset Turnover*

Earnings Quality*

Profitability*

Value*New SES Factors


Sector Models Improve Risk/Return Attribution Results

Return/risk attribution results improve for sector style tilt portfolios

Table 5.1: Improvements in Return Attribution and Risk Decomposition of sector style tilt portfolios with Sector Models



returns)


Total Market

Sector Model Diff

Energy -27% -26% 55% 70% 31%

Materials -30% -30% 41% 67% 73%

Industrials -10% -12% 50% 66% 39%

Consumer Disc. -23% -25% 43% 68% 68%


Health Care -20% -19% 56% 71% 36%

Financials -21% -20% 52% 72% 49%

IT -19% -18% 39% 64% 78%

Telecoms -10% -10% 37% 41% 14%

Utilities -39% -40% 31% 66% 128%

Average -22% -22% 44% 64% 59%

Better 10 10

10

Worse 0 0 0

Table 5.2: Improvements in Return Attribution and Risk Decomposition of total market style tilt portfolios with Sector Models



returns)


Total Market

Sector Model Diff

Energy -31% -29% 64% 73% 15%

Materials -28% -28% 51% 70% 39%

Industrials -11% -12% 58% 65% 15%

Consumer Disc. -22% -23% 56% 69% 24%


Health Care -22% -21% 67% 77% 16%

Financials -21% -20% 61% 71% 17%

IT -19% -19% 49% 64% 39%

Telecoms -8% -7% 40% 43% 8%

Utilities -42% -42% 39% 66% 70%

Average -23% -23% 53% 65% 29%

Better 10 10

10

Worse 0 0 0

Total Market Styles

Size

Beta

Residual Volatility

Liquidity

Leverage

Growth

Non-Linear Size*

Non-Linear Beta*

Momentum

Book-to-Price*

Dividend Yield*

Earnings Yield*

* Not in Sector model


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Why Do Sector Models Improve Results?


Significant Factor Differences Across Sectors Total market and Sector models:

𝑅𝑡 = 𝐵𝑡−1𝑓𝑡 + 𝑒𝑡

𝑅𝑠,𝑡 = 𝐵𝑠,𝑡−1𝑓𝑠,𝑡 + 𝑒𝑠,𝑡 , 𝑠 = 1,2, … .10

Rt, Rst are N by 1 and Ns by 1 vector of stock returns

𝑓 ~𝑁 𝑓0, 𝜎2 𝐵𝑇𝑊𝐵 −1

𝑓𝑠 ~𝑁(𝑓𝑠,0, 𝜎𝑠

2 𝐵𝑠𝑇𝑊𝑠𝐵𝑠

−1)

Non-linearity: 𝒇𝟎 ≠ 𝒇𝐬,𝟎

Total Market:

Sector:


Significant Differences in Factor Performance: 𝒇𝟎 ≠ 𝒇𝐬,𝟎

For 47 factors out of 170 (28%), sector factor returns are different from the total market factor returns at 10% significance level

Energy Materials Industrials ConsDisc ConsStap

Health

Care Financials

Inform.

Tech Telecoms Utilities 10% Sig

Size 0.49 0.10 0.96 0.08 0.93 0.16 0.98 0.03 0.62 0.35 3

Liquidity 0.19 0.26 0.01 0.43 0.98 0.94 0.36 0.01 0.17 0.12 2

Beta 0.45 0.94 0.67 0.09 0.94 0.82 0.18 0.58 0.22 0.80 1

Momentum 0.57 0.84 0.05 0.33 0.02 0.22 0.39 0.35 0.00 0.13 3

Leverage 0.83 0.93 0.13 0.24 0.82 0.27 0.61 0.88 0.20 0.06 1

Growth 0.08 0.26 0.04 0.79 0.36 0.87 0.15 0.00 0.85 0.04 4

Asset Turnover 0.45 0.78 0.17 0.70 0.91 0.00 0.97 0.27 0.49 0.01 2

Earnings Quality 0.37 0.00 0.38 0.08 0.09 0.51 0.05 0.04 0.21 0.05 6

Sentiment 0.43 0.02 0.72 0.22 0.44 0.30 0.54 0.45 0.95 0.75 1

Profitability 0.92 0.34 0.22 0.31 0.69 0.23 0.00 0.01 0.88 0.22 2

Long Term Reversal 0.07 0.03 0.73 0.92 0.28 0.31 0.01 0.12 0.41 0.33 3

Prospect 0.39 0.94 0.14 0.41 0.06 0.85 0.33 0.56 0.03 0.21 2

Value 0.80 0.97 0.09 0.92 0.93 0.14 0.03 0.79 0.87 0.52 2

Residual Volatil ity 0.26 0.25 0.47 0.74 0.92 0.20 0.19 0.26 0.38 0.02 1

Seasonality 0.55 0.29 0.05 0.07 0.62 0.52 0.06 0.16 0.10 0.06 4

Short Term Reversal 0.02 0.00 0.18 0.09 0.08 0.00 0.16 0.12 0.36 0.00 6

Industry Momentum 0.02 0.98 0.51 0.50 0.15 0.09 0.08 0.94 0.01 0.49 4

F-test, All Factors 0.09 0.00 0.01 0.18 0.29 0.00 0.00 0.00 0.01 0.00

10% Significance 4 5 5 5 4 3 6 5 3 7 47


Sector Models Improve Factor Explanatory Power

Sector models have higher adjusted R2

1998 2000 2002 2004 2006 2008 2010 20120

10

20

30

40

50

60

Year

Trai

ling

12m

Adj

uste

d R

2 (P

erce

nt)

TotMkt

Sector


Pricing of Leverage Factor by Selected Sectors

Significant differences in factor performance over time

Long firms with high leverage, short firms with low leverage (US)

-25%

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

LeverageCumulative Performance by Selected Sectors

Utilities

Financials

Total Market


Integrated Sector Model Overview

Integrated Sector model is for ALL stocks in the universe

Individual sectors are on the main diagonal of the factor covariance matrix

Off-diagonal elements of the covariance matrix need to be calculated

Specific risk estimates are consistent with sector specific risk estimates

Integrated Sector Model: Factor Covariance Matrix Diagram

Sector 1

Sector 2

Sector 3


Integrated Sector Model Methodology: Overview

Integrated sector covariance is built using a factor model for sector returns

Factor model for sector factors links sector and total-market factor returns and covariances

g : total market model factor returns

X : sensitivity (exposure) of sector factors to total market factors (‘Sector-Total Market’ sensitivity map)

Factor covariances across sectors are built on factor covariances of total market model

Stock Returns

Equity Factor Model: R stocks = B∙F + E

Stock Variance Covariance Matrix

Sector Factor Returns

Sector Factor Return Factor Model: R factor = X∙g + U

Cross Sector Factor Covariance Matrix

Step 1

Step 2

Step 3


Bayesian Shrinkage of Sector Factor Returns

PRIOR: Total Market model

Shrinkage depends on sector breadth

Shrinkage varies over time

Financials over 2008-2009

Utilities in 2002 (Enron)

Shrinkage is factor specific

2000 2010

10

20

30

%

Prior Weights (10, 50, 90 quantiles): ENERGY

10P

50P

90P

2000 2010

10

20

30

%

Prior Weights (10, 50, 90 quantiles): MATERIALS

2000 2010

4

6

8

10

12

%

Prior Weights (10, 50, 90 quantiles): INDUSTRIALS

2000 2010

5

10

15

%

Prior Weights (10, 50, 90 quantiles): Cons. Discs

2000 2010

10

20

30

%

Prior Weights (10, 50, 90 quantiles): Conss Stap.

2000 2010

5

10

15

20

25

%

Prior Weights (10, 50, 90 quantiles): Health Care

2000 2010

2468

101214

%

Prior Weights (10, 50, 90 quantiles): FINANCIALS

2000 2010

5

10

15

20

25

%

Prior Weights (10, 50, 90 quantiles): Inform. Tech.

2000 2010

20

40

60

80

%

Prior Weights (10, 50, 90 quantiles): TELECOM

2000 2010

20

40

%

Prior Weights (10, 50, 90 quantiles): UTILILITY

𝑓𝑝𝑜𝑠𝑡,𝑖 = (1 − 𝑤𝑖)𝑓𝑠𝑒𝑐𝑡,𝑖

+ 𝑤𝑖𝑓𝑡𝑜𝑡𝑚𝑘𝑡,𝑖


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Looking at 2013 using US Sector Equity Models


Factor Performance in 2013: A Few Observations

QE Tapering and Financial Regulation Uncertainty

Poor performance of Value factor in Financials in 2013

Poor performance of Value factor during crisis periods

Health Care Reform

Poor performance of Profitability factor in Health Care sector (expected profit margin squeeze)

Strong performance of Growth factor in Health Care sector (expected increase in demand)

Continued Economic Recovery

Poor performance of all Quality factors (ATO, Quality, Profitability) because of improvements in consumer confidence

Strong performance of Momentum in Energy and Materials sectors

Value Sentiment

ATO QUALITY PROFIT VALUE MOMENT INDMOM SEASON STR LTR PROSPECT SENTIM

Energy 4.2% 7.7% -1.1% -1.7% 5.4% 0.8% -1.4% -1.6% -4.3% 3.3% 0.5%

Materials 3.4% 2.0% 1.0% 4.3% 6.0% 4.2% -1.3% -2.7% 6.4% 0.0% -0.7%

Industrials 1.4% 4.0% 1.1% 0.8% 2.7% 0.0% 2.0% 1.0% -0.5% 0.4% 0.8%

Cons. Discsretionary -0.3% -2.5% -4.8% 0.7% 0.5% 1.8% 0.6% 1.5% 0.5% -0.1% 0.6%

Cons. Staples -3.4% 0.8% 6.4% 6.0% 0.3% -2.1% 0.1% -1.0% 0.2% 2.2% 2.6%

Health Care 3.2% 3.0% -6.1% 5.6% 6.8% 0.6% 5.2% -1.1% 0.9% 1.7% -0.3%

Financials 0.5% 1.8% -0.5% -4.1% -1.2% 2.3% 0.4% 1.6% -0.8% 0.7% 0.4%

Info Tech -1.8% 3.2% -1.8% 4.6% 2.7% -3.4% -1.2% -0.4% 5.0% 0.3% -1.6%

Telecomuncations 5.0% 2.5% -3.9% 5.4% 5.6% 0.6% -3.1% -1.2% -3.2% -2.0% 1.2%

Utility -0.1% -0.3% 0.0% 0.8% 2.3% 0.2% -1.6% 2.7% -0.9% 0.4% 0.8%

Total Mkt 1.9% 2.9% -0.8% 0.8% 2.2% 0.2% 0.3% -0.6% 1.5% 0.6% 0.2%

Factor Performance in 2013

Qualty Momentum


Factor Performance in 2013: A Few Observations

Poor performance of Value factor in 2013 and during crisis periods in general

Strong performance of Growth factor in Health Care sector in 2013

GROWTH RESVOL SIZE LIQUIDITY BETA LEVERAGE

Energy 3.9% -6.7% -5.4% 3.1% -6.8% 0.4%

Materials -3.2% -10.3% -3.7% -0.3% 0.8% 1.2%

Industrials -2.7% 4.0% -0.1% -0.6% 2.7% 0.6%

Cons. Discsretionary -0.2% 3.8% -0.5% 1.8% 1.8% 1.4%

Cons. Staples 2.1% 3.3% -3.8% 5.2% 4.5% 0.3%

Health Care 11.3% -5.7% -4.5% -1.2% 2.0% 4.5%

Financials 0.3% 1.5% -2.7% 4.6% 4.6% -2.0%

Info Tech 2.8% 0.8% -3.2% 3.5% -1.6% -0.3%

Telecomuncations 0.5% 0.7% -3.4% -4.6% -1.6% 6.0%

Utility 1.7% 0.1% 0.4% 0.4% 6.0% 2.1%

Total Mkt 2.1% 0.2% -2.4% 1.7% 1.9% 1.0%

Risk Factors

Factor Performance in 2013

-5%

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

93 95 97 99 01 03 05 07 09 11 13

Cumulative Factor Performance: Value in Financials

-15%

-10%

-5%

0%

5%

10%

15%

20%

25%

30%

93 95 97 99 01 03 05 07 09 11 13

Cumulative Factor Performance: Growth in Health Care


Conclusions

Sector models offer granular look into sources of portfolio risk and returns

Sector models offer economic insights that traditional regional risk models do not have


22 msci.com

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Enhancing Risk/Return Attribution with Sector Equity Models · Return Attribution of ZSample [...

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