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Calgary CFA Wealth Management Conference: g y gOpportunities in the Next Investment Frontier

Exploiting the Volatility Anomaly Exploiting the Volatility Anomaly in Financial Markets

Harin de Silva CFAHarin de Silva, CFA

555 West Fifth Street, 50th Floor Los Angeles, California 90013 213.688.3015 www.aninvestor.com

Outline

I. Low Volatility Anomaly

Performance of High vs. Low Risk Stocks

Global and Non-US Markets

II Using VMS as a Style or FactorII. Using VMS as a Style or Factor

III. Minimum Variance Applications

IV. Implementation

I Low Volatility AnomalyI. Low Volatility Anomaly

Typical Risk and Return Relationship in Asset Markets (1979-2009)

16%

U.S. Small Cap U.S. Large Cap

World Stocks

U.S. Bonds

12%

Int'l Stocks

T-Bills

8%

Ret

urn

T Bills

4%

0%

0% 5% 10% 15% 20%

Risk

4

Source: Analytic Investors, LLC

What is the Low Volatility Anomaly?

4 R h f f h h k l b l 4 Research from a variety of sources shows that investors mis-price risk in global equity markets

– Black, F., Jensen, M.C. and Scholes, M, “The Capital Asset Pricing Model: Some Empirical Tests”, St di i th Th f C it l M k t P P bli hi N Y k 79 121 (1972)Studies in the Theory of Capital Markets, Praeger Publishing, New York, pp.79-121 (1972)

– Fama, French. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics, 33 (1993)

– Ang, Hodrick, Xing, Zhang. “The Cross-Section of Volatility and Expected Returns.” The Journal of Finance, 61 (2006)

– Ang, Hodrick, Xing, Zhang. “High Idiosyncratic Volatility and Low Returns, International and Further US Evidence”, NBER Working Paper (2008)

4 Our research1 shows that this systematic mis-pricing can be used to build portfolios that have has better risk/return characteristics than the market portfoliothat have has better risk/return characteristics than the market portfolio

– The unconstrained portfolio not only generated excess return versus a broad market index, but also generated roughly 25-30% less risk (for the US equity market)

5

1 Clarke, de Silva, Thorley. “Minimum-Variance Portfolios in the U.S. Equity Market.” The Journal of Portfolio Management, Fall 2006

Testing the Low Volatility Anomaly

4 Monthly U.S. stock returns from 1968 – 2005 (1000 largest capitalization in the CRSP database)(1000 largest capitalization in the CRSP database)

4 Separate stocks into volatility quintiles each month based on previous 5-year volatility

4 Calculate capitalization-weighted returns each month for each quintile

6

No Penalty for Lower Volatility Quintile Portfolio

1968 - 2005

1 1%1.1%

1.2% 12.0%

8.8%

7.1%

1.1%

1.0%1.0%

1.0%

0 9%

1.0%

1.1%

8.0%

10.0%

3.7%

4.6%

5.7%

0.8%

0.8%

0.9%

4.0%

6.0%

0.6%

0.7%

2.0%

0.5%

Volatility Quintile 1 (Low Volatility)

Quintile 2 Quintile 3 Quintile 4 Volatility Quintile 5 (High Volatility)

0.0%

Monthly Standard Deviation (Risk) Average Monthly Return

7

Source: Clarke, de Silva and Thorley (2006)


Volatility Anomaly Not Dependent on the Economic Cycle1968 - 2005

Volatility During NBER Contractions (70 Months)0.8% 14.0%

1968-2005

7.9%

9.2%

11.7%

6 %

0.0%

0.5%

0.0%

0.2%

0.4%

0.6%

8.0%

10.0%

12.0%Monthly Standard Deviation (Risk) Average Monthly Return

5.2%6.2%

-0.4%

-0.1%-0.2%

-0 8%

-0.6%

-0.4%

-0.2%

0 0%

2.0%

4.0%

6.0%

1968 - 2005

0.8%Volatility Quintile 1

(Low Volatility)Quintile 2 Quintile 3 Quintile 4 Volatility Quintile 5

(High Volatility)

0.0%

Volatility During NBER Expansions (386 Months)

1.4% 10.0%

5.2%

8.2%

6.6%

1.2%

1.3%

1.2%

1.1%

1.2%

6.0%

8.0%


4.2%

3.4%1.0%

1.1%

0.8%

1.0%

2.0%

4.0%

8

Source: Clarke, de Silva and Thorley (2006)

0.6%Volatility Quintile 1

(Low Volatility)Quintile 2 Quintile 3 Quintile 4 Volatility Quintile 5

(High Volatility)

0.0%

Beta and Idiosyncratic Risk

60%

65%

Low Beta/ High Idiosyncratic

50%

55%

ic R

isk

40%

45%

Idio

sync

rati

25%

30%

35%

High Beta/ Low Idiosyncratic

25%

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

Market Beta

9

Source: BARRA for stocks in MSCI World.

Overall Performance of Beta Quintiles – Average Return and RiskJanuary 1997 – July 2011

Q411%

12%

urn

MSCI USA

Q1Q2 Q3

Q4

9%

10%

11%

urn

MSCI World

Q1

Q2

Q3

Q5

9%

10%

Ave

rage

Ret

u

Q57%

8%

9%

Ave

rage

Ret

Q2

8%

11% 13% 15% 17% 19% 21% 23% 25% 27% 29% 31% 33% 35% 37%Risk

7%MSCI Japan

18%

MSCI Australia

6%

10% 15% 20% 25% 30% 35%Risk

Q1 Q2Q4

5%

6%

7%

age

Ret

urn

Q1

Q4Q514%

15%

16%

17%

18%

age

Ret

urn

Q3

Q5

3%

4%

15% 20% 25% 30% 35%

Ave

ra

Q2

Q3

Q4

10%

11%

12%

13%

15% 20% 25% 30% 35%

Ave

ra

15% 20% 25% 30% 35%

Risk

15% 20% 25% 30% 35%Risk

Source: Compustat and BARRA. Portfolios formed monthly based on BARRA beta forecast.

10

Impact of Volatility on Compounded Return

4 Most academic studies use average return as a measure of portfolio performance4 Investor wealth is tied to geometric return4 Relationship between geometric return(g), arithmetic return (μ), and standard deviation

(σ)is approximated by the following:

11

Overall Performance of Beta Quintiles – Geometric Return and RiskJanuary 1997 – July 2011

Q1Q2

Q3Q48%

9%

10%

11%

etur

n

MSCI World

Q1

Q2

Q3

Q4

8%

9%

10%

etur

n

MSCI USA

3%

4%

5%

6%

7%

Geo

met

ric

Re

Q54%

5%

6%

7%

Geo

met

ric

Re

Q52%

11% 14% 17% 20% 23% 26% 29% 32%

Risk

3%

11% 13% 15% 17% 19% 21% 23% 25% 27% 29% 31% 33% 35% 37%

Risk

MSCI Japan18%

MSCI Australia

Q1Q2

Q3 Q4

2%

3%

4%

5%

Ret

urn

Q1

13%

14%

15%

16%

17%

18%

ic R

etur

n

Q5-1%

0%

1%

15% 20% 25% 30% 35%

Geo

met

ric

Q2

Q3

Q4

Q58%

9%

10%

11%

12%

13%

Geo

met

r

-2%Risk 15% 20% 25% 30% 35%

Risk


12

Why Does the Low Volatility Equity Anomaly Exist?

4 Market portfolio is inefficient

Investors focus on pricing of individual securities and treat securities within an asset class the

Explanations include…

– Investors focus on pricing of individual securities and treat securities within an asset class the

same (for example, large cap stocks), not the pricing of total portfolios

4 “Lottery effect” associated with high volatility stocks

44 Limits to Borrowing create “overpricing” of high volatility stocks

But exclude…But exclude…

4 Transaction Costs

4 Analysts Coverage

4 Institutional Ownership

4 Trading Activity

4 E V l M S ll C A l

13

4 Exposure to Value, Momentum or Small Cap Anomaly

Limits to Borrowing Create Overpricing of High Beta Stocks

Aggressive investors

Leverage constrained hi h b t i t

Conservative investors

high beta investor

pect

ed R

etur

n

Market Portfolio(Beta=1)

Rf

Ex (Beta=1)

Risk (Beta)

14

Risk (Beta)

II Using VMS as a Style or FactorII. Using VMS as a Style or Factor

Using Volatility as a Style (Factors)

4 Styles or factors are useful because they tell us what kind of “themes” or exposures a portfolio has and whether those exposures are being rewarded.

C N D fi i iCommon Name Definition

Small-Cap Factor (Small-Cap) Return on Small minus Big stocks

Value Factor (Value)Return on High minus Low book-to-market ratio stocks

Momentum Factor (Momentum)Return on High past return stocks minus Low past return stockspast return stocks

Specific Risk Factor (Specific Risk) Return on Volatile minus Stable stocks (VMS)

tyFa

ctor

s

Beta Factor (Beta) Return on High Beta stocks minus Low Beta stocksVo

lati

lit

16

A New Dimension of Style?

17

Source: A New Dimension of Style, Russell Investments

Cumulative Monthly Factor Returns (1968-2009)

4 Over the long run, there has been no extra reward for choosing volatile stocks over stable stocks.

Market Small-Cap Value Momentum Specific Risk Beta(Vol minus Stable) (High Beta minus Low Beta)

400

500

)

(Vol minus Stable) (High Beta minus Low Beta)

200

300

etic

Ret

urn

(%

0

100

mul

ativ

e A

rith

m

-100

Cum

18

-200

1967

1970

1973

1976

1979

1982

1985

1988

1991

1994

1997

2000

2003

2006

2009

Factor Exposures in Mutual Fund Portfolios

4 Specific risk factor exposures are as large as momentum factor exposures.

Large Cap Value Large Cap Growth

0.94 0.95

0.8

1.0

0.22

0.4

0.6

Exp

osur

e

-0.03

0.

0 09 0 080 08

0.070.12

0.0

0.2

Fact

or

-0.09 -0.08-0.08

-0.18

-0.4

-0.2

Market Small-Cap Value Momentum Specific Risk

19

Source: Morningstar (1983 – 2008); Clarke, R., H. de Silva, and S. Thorley. “Know Your VMS Exposure.” Journal of Portfolio Management, (Winter 2010)

Recent Performance of Beta Quintiles in MSCI World

120Performance in 2011

105

110

115

f a D

olla

r

95

100

mul

ativ

e G

row

th o

f

80

85

90Cum Quintile 1 (Low Beta)

Quintile 2Quintile 3Quintile 4Quintile 5 (High Beta)

80

Dec

-10 Ja

n-11 Feb

-11

Mar

-11 Apr

-11

May

-11 Ju

n-11

Jul-

11

Aug

-11


20

III Minimum Variance ApplicationsIII. Minimum Variance Applications

Building Low Risk Portfolios

Market Portfolio

Possible?

8

10

Rat

e (%

)

Capital Market Line

Possible?

4

6er

Ris

k Fr

ee R

Theoretical Minimum Variance Portfolio0

2

0 10 20 30

Ret

urn

ove

0 10 20 30

Standard Deviation (%)

4 Th ffi i f i h f f li h h h i f 4 The efficient frontier represents the set of portfolios that have the maximum rate of return for every given level of risk

4 The market portfolio should outperform the minimum variance portfolio

22

4 What if the minimum variance portfolio outperformed the market with less risk?

Data and Methodology

4 At the beginning of each month from January 1968 to December 2005 (456 months) we complete five steps and then roll the process forward:

1) Select the largest 1000 securities with sufficient historical data, including one year of prior 1) Select the largest 1000 securities with sufficient historical data, including one year of prior

monthly returns (or one year of “high frequency” daily return data) and ex-ante factor

exposures.

2) Calculate the sample covariance matrix based on historical returns for each of the 1000 2) Calculate the sample covariance matrix based on historical returns for each of the 1000

securities.

3) Structure the sample covariance using Bayesian Shrinkage or Principal Components.

4) F d th ti t d i t i i t th ti i d d t i ti l tf li 4) Feed the estimated covariance matrix into the optimizer and determine optimal portfolio

weights for the minimum variance portfolio under various constraints.

5) Use the realized security returns in the current month to track the performance of the

i i d d k f li optimized and market portfolios.

23


Simulation Results (US Market, 1968-2005)

10) Minimum Variance Portfolio(6.5%, 11.7%)

Market Portfolio

Constrained Minimum Variance Portfolio1

(5 6% 11 9%)6

8

ree

Rat

e (%

)

(5.6%, 15.4%)(5.6%, 11.9%)

2

4

n ov

er R

isk

F

0

2

0 10 20 30

Standard Deviation (%)

Ret

ur

Standard Deviation (%)Source: Clarke, de Silva, Thorley. “Minimum-Variance Portfolios in the U.S. Equity Market.” The

Journal of Portfolio Management, Fall 2006

24

1 Constrained for size, style and momentum factors.

*Reliance on hypothetical performance has inherent limitations.

Active Industry Biases Are Not Constant in the Unconstrained Minimum Variance Portfolio (U.S. Market)

December 1985 December 1995 December 2005

Basic Materials 0.6 6.8 0.7

Energy -3.1 0.1 -5.4

Consumer Non-Cyclical 5.6 -1.3 7.9

Consumer Cyclical -9.0 -1.9 -1.8

Consumer Services -1.7 -2.7 2.0

Industries -4.1 -2.3 -2.2

Utilities 28.1 28.4 5.0

Transportation -1.3 -0.7 -0.8

Health Care -4.8 -6.7 6.8

T h l 11 6 8 0 9 4Technology -11.6 -8.0 -9.4

Telecommunications 1.0 -4.0 -1.2

Commercial Services -1.4 -1.1 -1.8

25

Financials 1.7 -6.1 -9.7

Source: Analytic Investors, LLC

Realized Portfolio Risk (Trailing 60 Months) in U.S. MarketMin Var Market Tracking Error

16%

18%

20%

12%

14%

16%

8%

10%

4%

6%

0%

2%

26


Long Term Results in U.S. Market Show Similar Effect

Rolling 12 Month Returns

100%

Rolling 12-Month Returns

US Low Vol S&P 500Mean Return 9.8% 9.2%

Std. Dev. 15.7% 19.6%

Sharpe 0.38 0.27

Beta 0.74 1.00

50%

Volatility Reduction 20.0% -

Tracking Error 7.68% -

0%

-50%

U.S. Low Vol S&P 500

-100%

Feb

-30

Feb

-32

Feb

-34

Feb

-36

Feb

-38

Feb

-40

Feb

-42

Feb

-44

Feb

-46

Feb

-48

Feb

-50

Feb

-52

Feb

-54

Feb

-56

Feb

-58

Feb

-60

Feb

-62

Feb

-64

Feb

-66

Feb

-68

Feb

-70

Feb

-72

Feb

-74

Feb

-76

Feb

-78

Feb

-80

Feb

-82

Feb

-84

Feb

-86

Feb

-88

Feb

-90

Feb

-92

Feb

-94

Feb

-96

Feb

-98

Feb

-00

Feb

-02

US Min Var S&P 500

27

Based on CRSP data. Portfolios constructed as described in Clarke, de Silva, Thorley. “Minimum-Variance Portfolios in the U.S. Equity Market.” The Journal of Portfolio Management, Fall 2006

Minimum Variance Performance Across Regions

Sh R ti *Sharpe Ratios*(1991-2004)

0.851.0 Minimum Variance

0.60

0.85

0.520.60

0.31

0.480.43

0.4

0.6

0.8

Rati

o

MSCI Cap Weighted Benchmark

0.20

0 2

0.0

0.2

Sharp

e R

-0.15-0.19

-0.4

-0.2

Gl b l N th A i J P ifi E J EGlobal North America Japan Pacific Ex-Japan Europe

28

Portfolios constructed as described in Clarke, de Silva, Thorley. “Minimum-Variance Portfolios in the U.S. Equity Market.” The Journal of Portfolio Management, Fall 2006

Minimum Variance Rolling 12-Month Returns

20%

40%

60%

80%

20%

40%

60%

Europe Pacific ex-JapanVolatility Reduction = 27%Tracking Error = 9.1%Positive Excess Return

Volatility Reduction = 40%Tracking Error = 12.8%Positive Excess Return

-60%

-40%

-20%

0%

%

-20%

0%

20%

60%80%

-80%

Oct

-92

Jul-

93

Apr

-94

Jan-

95

Oct

-95

Jul-

96

Apr

-97

Jan-

98

Oct

-98

Jul-

99

Apr

-00

Jan-

01

Oct

-01

Jul-

02

Apr

-03

Jan-

04

Oct

-04

MinVar Pac ExJap MSCI Pac ExJap

-40%

Oct

-92

Jul-

93

Apr

-94

Jan-

95

Oct

-95

Jul-

96

Apr

-97

Jan-

98

Oct

-98

Jul-

99

Apr

-00

Jan-

01

Oct

-01

Jul-

02

Apr

-03

Jan-

04

Oct

-04

Europe MV MSCI Europe

Japan Volatility Reduction = 25%Tracking Error = 13.1%

GlobalVolatility Reduction = 35%

20%

40%

0%

20%

40%

60%

gPositive Excess Return Tracking Error = 9.5%

Positive Excess Return

-40%

-20%

0%2 3 4 5 5 6 7 8 8 9 00 1 1 2 3 4 4

-60%

-40%

-20%

0%

-92

-93

-94

-95

-95

-96

-97

-98

-98

-99

-00

-01

-01

-02

-03

-04

t-04

29

Oct

-9

Jul-

93

Apr

-9

Jan-

9

Oct

-9

Jul-

9

Apr

-9

Jan-

9

Oct

-9

Jul-

9 9

Apr

-0

Jan-

0

Oct

-0

Jul-

0

Apr

-0

Jan-

0

Oct

-0

Global Min Var MSCI World

Oct

Jul-

Apr

-

Jan-

Oct

Jul-

Apr

-

Jan-

Oct

Jul -

Apr

-

Jan-

Oct

Jul -

Apr

-

Jan-

Oct

JapanMV MSCI Japan

Performance After Market Declines

Average Standard 1 Year After Market Decline*

80%

100%

120%

140%

160%Average

PerformanceStandard Deviation

Minimum Variance 36.9% 14.6%S&P 500 41.8% 17.7%Difference -4.9%

1 Year After Market Decline

U.S. Minimum Variance

S&P 500

0%

20%

40%

60%

80%

Jun-

32

Mar

-35

Apr

-38

Apr

-42

Jun-

49

Sep

-53

Dec

-57

Oct

-60

Oct

-62

Oct

-66

May

-70

Sep

-74

Mar

-78

Jul-

82

Jul-

84

Dec

-87

Oct

-90

Oct

-02

Average Performance

Standard Deviation3 Years After Market Decline*

30.0%

40.0% Minimum Variance 19.5% 13.3%S&P 500 19.8% 16.3%Difference -0.3%

U.S. Minimum Variance

S&P 500

0 0%

10.0%

20.0%

30

* Period defined as the 12 and 36 months following a bear market decline of 10% or more..

0.0%

Jun-

32

Mar

-35

Apr

-38

Apr

-42

Jun-

49

Sep

-53

Dec

-57

Oct

-60

Oct

-62

Oct

-66

May

-70

Sep

-74

Mar

-78

Jul-

82

Jul-

84

Dec

-87

Oct

-90

Oct

-02

III ImplementationIII. Implementation

Increasing Diversification – The Portfolio Context

MSCI World MSCIDow

Jones HFRI Fund

of Funds Barclays

Low Volatility Correlations*(06/30/95– 06/30/10)

MSCI World Minimum Volatility

MSCIWorld Index

Russell 1000

Jones Emerging

Markets

of Funds Composite

Index

Barclays Capital U.S.

Aggregate

MSCI World Minimum Volatility 1.00

MSCI World Index 0.92 1.00

Russell 1000 0.86 0.96 1.00

Dow Jones Emerging Markets 0.72 0.80 0.73 1.00

HFRI Fund of Funds Composite Index 0.57 0.66 0.61 0.69 1.00

l C i l S ABarclays Capital U.S. Aggregate 0.13 0.02 0.02 -0.03 0.02 1.00

32

Investing in Low Beta/Volatility Strategies

4 Minimum Variance Portfolios– MSCI/BARRA Minimum Variance Indices (not available as ETF as yet)

4 Active Low Volatility Equity Strategies– SEI Investments

– Other Active Managers

4 “Single Factor” ApproachesRussell 1000 Low Volatility ETF (LVOL)– Russell 1000 Low Volatility ETF (LVOL)

– Russell 1000 Low Beta ETF (LBTA)

– S&P500 Low Volatility Portfolio ETF (SPLV)

44 Potential Shorts…or Hedging Tools?– S&P500 High Beta Portfolio ETF (SPHB)

– Russell 1000 High Beta ETF (HBTA)

– Russell 1000 High Volatility ETF (HVOL)

33

Performance of S&P ETFs

34

Concluding Thoughts….

4 Volatility or Beta anomaly is widely documented

4 Requires longer run horizon to exploit the benefits of

compounding – so likely more persistent than other more

publicized anomalies (small cap, value etc)

4 Best exploited as part of a integrated asset allocation strategy

35

References

Clarke, de Silva and Thorley (2006), “Minimum-Variance Portfolios in the U.S. Equity Market”, Journal of Portfolio Management, Fall.

Clarke, de Silva and Thorley (2010), “Know Your VMS Exposure”, Journal of Portfolio Management, Fall.

Clarke, de Silva and Thorley (2011), “Minimum-Variance Portfolio Composition” , Journal of Portfolio , y , p ,Management, Winter.

Fama and French (1993), “Common Risk Factors in the Returns on Stocks and Bonds,” Journal of Financial Economics”, 33.

Haugen and Baker (1991), “The Efficient Market Inefficiency of Capitalization-Weighted Stock Portfolios”, Journal of Portfolio Management, Spring.

Russell Investments (2011), The Third Dimension of Style.

36