The Missing Risk Premium: - PowerPoint Presentation

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The Missing Risk Premium: - PPT Presentation

Why Low Volatility Investing Works Eric Falkenstein 2013 Copyright 2013 Eric G Falkenstein 1 Who am I Im an economics PhD who has worked as a quant risk manager and portfolio manager See more at the following websites ID: 482952

2013 eric copyright falkenstein eric 2013 falkenstein copyright risk return returns premium utility equity relative volatility expected theory beta

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Slide1

The Missing Risk Premium:Why Low Volatility Investing Works

Eric Falkenstein2013

1Slide2

Who am I

I’m an economics PhD who has worked as a quant, risk manager, and portfolio

manager. See more at the following websites

www.betaarbitrage.com

Falkenblog

www.efalken.com

Old Book Finding Alpha (2009)New Book The Missing Risk Premium, out this spring

My 1994 dissertation, first 3 sentences:“This paper documents two new facts. First, over the past 30 years variance has been negatively correlated with expected return for NYSE&AMEX stocks and this relationship is not accounted for by several well-known

prespecified factors (e.g., the price-to-book ratio or size). More volatile stocks have lower returns, other things equal

.”So, risk premiums and low-

vol

have been a

bit of a hobby-horse

The Stakes

“It is impossible to appreciate how the financial system works without understanding risk.” Stephen Cecchetti

"Risk is not an add-on … it permeates the whole body of thought.“ Robert C. Merton

4Slide5

“most returns and price variation come from variation in risk

premia

”

John Campbell

Risk free rate

Risk premium

Big Idea: this is the Risk-Return Trade-off

In general, in practice: risk is not positively related to return

Risk and Return

Risk aversion like aversion to smellinessThe logic applied to this idea, via a utility function that has decreasing marginal returns, generates many mathematically consistent results that seem highly plausible

Standard Theory is

Intuitive

Leveraged Firms

B vs. BBB rated Bonds

Out-of-the-money options vs. at-the-money optionsS and C corps vs. equity indexes

Highest volatility vs. modest

vol

stocks

R rated movies vs. G rated moviesLotto vs. ‘quick pick’ lotteries50-1 horses vs. 3-1 horses Mutual funds, currencies, futures, countries, yield curve

…And Wrong

Finance Misleading

Most practical finance is about generating expected values Finding c

ovariances to generate different discount rates is a massive waste of time, pure rationalization in practice

10Slide11

Conspiracy?

Economists find standard utility functions much more productive (in theory)Asset managers can justify anything via ‘risk’, which is omnipresent and as yet unmeasurable

Amenable to rigorous sequence of lectures

11Slide12

Standard Theory

12Slide13

St. Petersburg Paradox (1738): what is value of $1 paid if you get a head in a coin flip, where the payoff is (number of times coin flipped)^2?

Should be infinity

Why not? Diminishing marginal returns

Marginal UtilitySlide14

Fundamental to economic reasoningMarginal Revolution transformed economics in 1860sWalras

, Jevons, MengerPre 1860s ‘classical’ economists: Marx, Smith, Ricardo, MillTransformed Theory of Value

Basic Idea of Utility

14Slide15

Global concavity of utility is the

necessary and sufficient

condition for the existence of a risk premium

Where does Risk Premium Come From?

Utility not applied between goods, but to everythingVon-Neumann-Morgenstern (1944)

Utility Theory and Risk Aversion

16Slide17

Iso

-Utility Curves for Return and VolatilitySlide18

Standard Deviation

Expected Return

100% investment in security

with highest E(R)

100% investment in minimum

variance portfolio

No points plot above

the

red line

All portfolios

on the

red line

are efficient

Why we like efficient portfoliosSlide19

Exp

Return

Volatility

Tobin: Two-Fund Separation Theorem

Port-1

Port-2

Port-3

U4Slide20

Always hold some cash: liquidity preference

Standard Deviation

Expected Return

CSlide21

Regardless of risk preference, everyone uses same risky

portfolioSlide22

How to

Derive

The

Capital Asset Pricing ModelSlide23

CAPM is the Security Market Line (SML)

Beta

Expected Return

Market Portfolio

1.0

E(R)Slide24

General Equilibrium aka Stochastic Discount Factor  CAPMSlide25

Asset Pricing Theory Was Always Treated Well

1971 Institutional Investor

:“The Beta Cult: The New Way to Measure Risk.”Contrast with almost constantly ridiculed Efficient Markets

Hypothesis, which is much more successful (

, it’s hard to outperform the indices)

linear in risk factors, covariances with something

include something very like the stock market as one of the prominent factors

Hope for Final TheorySlide27

Empirical Evidence

27Slide28

Return

Volatility

Small Stocks

17.30%

33.4%

Stocks

13%

20.2%

Corporate Bonds

6.0%

8.7%

Government Bonds

5.70%

9.4%

T-bills

3.90%

3.2%

Volatility Often Used as a Risk Shorthand

Brealey

and Myers Investments Book

From Cam Harvey (editor of Journal of Finance) website

If only this worked in more places…

29Slide30

The Risk Premium Problem

After 45 years, there are no measure of risk that are generally positively correlated with returns

Fama

and French 1992

From Campbell 2000

Fama-French (1992)

Show beta is just a size effectFounding father (

Fama) admits CAPM is ‘incomplete’, and beta itself useless

31Slide32

Theory:

Longer hair people are short

Omitted variable: gender

Theory:

high beta firms have high returns

Omitted variable: size

Example of how small firm effect showed up in beta tests Slide33

CAPM Recognized as Empirical Failure

“More empirical effort may have been put into testing the CAPM equation than any other result in finance. The results are quite mixed and in many ways discouraging.”Mark Rubinstein

“empirically vacuous,” Fama and French“having a low, middle or high beta does not matter; the expected return is the same.

Stephen Ross

33Slide34

A Survey of Empirical Anomalies to the Standard Model

The standard theory involves a specific metric of covariance, and so it could be, we simply haven’t found the right oneAs a ‘framework’, not a theory, it is non-falsifiable

However, it’s hard to conceive of one not correlated with total volatility

34Slide35

My Dissertation (1994) page 53

Total Volatility and Returns

35Slide36

Cross-Sectional Annual Returns Sorted by Idiosyncratic and Total Volatility

Ang,,

Hodrick, Xing and Zhang (JoF 2006)

Beta and Returns: 1962-2011

Beta-Low

Beta0.5

Beta1.0

Beta1.5

Beta-High

AnnRet

10.8%

11.4%

8.2%

4.5%

AnnStdev

13.1%

11.6%

17.4%

26.2%

33.9%

Beta

0.57

1.04

1.44

1.78

37Slide38

Low Rated Equities also have lower returns

Equities and bond ratings (Distress)

StockReturns

AAA 12.4% AA 13.9% A 14.3% BBB 14.2% BB 15.0% B 8.6% C -12.7%

Leverage and Equity Returns

Penman, Richardson, and Tuna. 2007

Equity Returns Practice Theory

Volume($)>

2,000

50,000

500,000

Price>

0.01

0.1

0.01

0.1

0.01

0.1

Count

7372

6685

6423

5757

4603

3939

AnnReturn

-29.1%

-35.4%

-9.1%

-13.5%

-34.2%

-41.0%

Penny Stocks:

Eraker

and Ready (2009)

Call Options

Sophie Ni (2007)Should amplify the equity risk premium the greater the out-of-the-money

IPO has a lot of UncertaintyJay Ritter (see his website). 1970-2011.

8k observationsInitial Public Offerings (IPOs)

Deither, Malloy, and

Scherbina (2002). Table 2. Data from 1983-2000.Analyst Disagreement

Steve Sharpe and Gene Amromin

(2005). People have higher expected returns when they have lower expected volatilities

Total Volatility over Time

Contemporaneous Correlation Clearly Negative

Total Volatility over Time

45Slide46

SPY Total Return to Overnight vs. Daily Return Periods

Moskowitz, and Vissing-Jorgensen (2002)

Small Business Returns

Currencies: Uncovered Interest Rate Parity

Sharpe 0.99 from 1976-2008 in Burnside et al (2009)

Here’s Long AUD, Short JPY

48Slide49

Merrill High Yield Master II (HOAO) Merrill BBB-AA Index (COCO)Indices here overstate realized returns

Corporate Bonds

Dimson, Marsh, Staunton (2005)

17 Countries, 1900-2005, Annual Data

World Country Returns

Emerging market Returns

51Slide52

1% premium from 0.25 to 3 yearsNo premium from 5 to 30 yearsVolatility, Covariance, increasing linearly

Treasury Yield Curve

52Slide53

1% premium from 0.25 to 3 yearsNo premium from 5 to 30 yearsVolatility, Covariance, increasing linearly

Treasury Yield Curve

53Slide54

Futures return from rollHarvey and

Erb (2007) copper, heating oil, and live cattle were on average in backwardization,

corn, wheat, silver, gold, and coffee were in contangoIt isn’t clear what covariance, volatility has to do with this

Futures

54Slide55

Devany and Walls (1999), 2015 movies from 1984-96

Movie Returns by Rating

Snowberg and Wolfers

(2009)Sports Books:

Longshot Bias

IPO has a lot of UncertaintyJay Ritter (see his website). 1980-2008.IPO Returns -3.7% annually below size-matched firms for first 5 years

Initial Public Offerings (IPOs)

57Slide58

Trading VolumeTurnover of stock a proxy for disagreement

Highly correlated with beta

58Slide59

Equity Risk Premium

Top line return is not the same as average or marginal return

59Slide60

What is the Equity Risk Premium?

The most important constant in finance

Lorie and Fisher (1964): 9.0% raw return (no bond return)Ibbotson and

Sinquefield (1976): 10.9%Mehra and Prescott (1986): 6.2%

1999 Barclays and CSFB estimated 8.8%Ibbotson (1926-97): 8.9%Finance Texts (1998): 8.5%Ivo Welch Survey (1998): 8.5%

Crash!

AIMR estimate (2002): 3.0%

WSJ survey (2005): 2.0%

1 to 2 to 1 has a total return of 0%100%, -50% return has average of 25%Arithmetic returns useful if you rebalance, as opposed to invest all your money at inception

Stock returns have volatility around 20%, for the indices, which implied a 2% adjustment

Geometric vs. Arithmetic Averages

62Slide63

Dichev (2005)1, 2, 1

 return 0% if cf is {-1,0,+1}

 return -17.7%

is {-1,-1,+1.5}

Total return different than Internal Rate of Return based on timing of investmentsDistributions  Dividends-New MoneyCorr(Distributionst,Returnt+1)= +33%Corr

(Distributionst+1,Returnt)= -27% bad timing

Bad Market Timing

63Slide64

Commissions, 8.5% load through 1970’s to buy a mutual fundbid-ask cross

Stocks quoted at 8 ¾ - 9 in the 1990sbuy at 9, sell at 8 ¾, lose 2.78%Phantom cost: most investors don’t know real time prices

Stoll and Whaley (1983) 1.78% comm+bid-askBhardwaj and Brooks (1992): 4.4% total

Currently very low if you are smart (0.2%)

Transaction Costs

64Slide65

USA primary data point in World Value Weighted IndexCoincidentally, 2-0 in World Wars

Never went communistBrown, Goetzmann, and Ross (1995)

Czechoslovakia, Hungary, Poland, Russia, and China all zeroed outJorion and Goetzmann (1999)

US real return 350 basis points above median for 39 countries in 20

century

Peso-Dollar FX rate fixed from 1954-76Higher interest rate in PesoPeso ‘floated’ in 1976: lost 45%

Peso devalued by 82% in 1982Small probability, big loss, explains interest rate premiumRobert Barro

(2006) argues a correct probability of a significant catastrophe explains much of the equity premium, about 300 basis points2% change of a 15% to 45% GDP decline

Peso Problem

66Slide67

10% stock return: 6% post tax with a 40% tax rateGannon and

Blume (2006) apply this to S&P500 assuming 20% turnover from 1961-2005, using actual capital gains, dividend top-tier tax rates

Cap gain avg: 26%

Top tax rate

avg

; 49% (includes 6% state tax)

67Slide68

Beardstown Ladies investment club1983-94 return 23.4%Best selling authors

Audited financials: 9.1%, below 14.9% for marketFailed to include contributions

68Slide69

Investors Don’t Match Indices

Dalbar study from the Investment Company Institute:1990-2010 Annual ReturnsS&P500 return: 9.1%

69Slide70

Returns not Like in Representative Agent Model

Equity Return Uncorrelated with GDP growth over a Century

70Slide71

Hedge Fund Money Goes to Insiders

From Simon Lack

71Slide72

Geometric vs. Arithmetic Averaging 1.0

%Survivorship Bias 1.0%

Peso Problems 1.0%Taxes

1.0

Adverse Market Timing

1.0%Transaction Costs 1.0%Sum 6.0%Most estimates around 3.5% for equity premium. With these additions, the Marginal Investor clearly could be seeing a 0% equity premium.Equity Premium Subtractions

Scope of the Risk Premium Failure

Positive Risk

Premium (3)

Zero Risk

Premium (14)

Negative Risk

Premium (12)

Short End of Yield Curve

BBB-AAA Corporate Spread

Efficient Equity Investor

Long-End of Yield Curve

B to BBB Bond

Futures

Private Investments

Movies

Mutual

Funds

VIX

and Equity

World Equity

Emerging Markets

Hedge Funds

Real Estate

CTAs

Private Equity

Intraday Stock Return

Average Equity Investor

Betas

Volatility

Financial Distress

Trading Volume

Analyst Disagreement

Equity Options

Lotteries

Sports

Betting

Currencies

IPO equity

Returns

MVPs

New Theory

In general, risk and return are uncorrelated because risk is a deviation from the consensusThis makes risk symmetric, too much or too little exposure generates similar risk Thus, volatile assets don’t need extra return to be held…

74Slide75

Basic Idea of Relative Risk and no Premium

Total Return

Avg.

Relative Return

State 1

-10

–5

State 2

–5

Taking the first order condition, we haveSince each agent is identical, in equilibrium each agent holds the same amount

SoWhich means, the expected return on risky assets is te risk free rate

Utility Proof

76Slide77

Taking the first order condition in the standard model we have

This is the standard result, that higher volatility generates a higher return, linear in the variance, adjusted by the coefficient of risk aversionBecause the exponential utility is CARA, not CRRA, higher

amount in the risky asset generates a higher risk premium

Utility Proof Benchmark

77Slide78

See how relative utility model explainsWhy when investors take risks, they expect above average returns

Returns are relative to the risk free rateDon’t short assets with expected return<Rf

Relative Utility and Different Beliefs

78Slide79

Abel (1990): Gali (1995):

DeMarzo,, Kandiel, Kremer (2003):

Roussanov (2010):

Relative Risk in academia

Outside the Box Evidence

80Slide81

Within a society, rich people tend to be much happier than poor people.But, rich societies tend not to be happier than poor societies (or not by much).

As countries get richer, they do not get happier.Easterlin’s Paradox (1974)

81Slide82

Progress and Happiness a PuzzleGregg Easterbrook’s The Progress Paradox,

David Myers’s The American Paradox, and

Barry Schwartz’s The Paradox of ChoiceJapan: between 1958-1987 per capita income rose 500%

No change in subjective well-being

Knight and Song (2006): Chinese villagers more affected by relative than absolute wealth, compared to their villages

Choose between

82Slide83

Half of all stocks have expected returns below the marketZero recommendations for firms with expected returns below the market

returnBuy Recommendations exclude low risk firms

Risk

Expected Return

Buy!

Who cares?

83Slide84

Should invest in world portfolioChan, Covrig, and Ng (2005): Everyone is investing mainly in domestic portfolio

Avoiding easy way to diversify riskLow covariance with risks from home economy

Home Bias

84Slide85

“I want a product to be defined relative to a benchmark”

Bill Sharpe‘Risk, see Benchmarking’Kenneth Fisher’s

Only Three Questions that Count“small stocks were in a depression” in the 1980’s

Eugene

Fama

, Merton Miller

Everyone Benchmarks

“…rank among our equals, is, perhaps, the strongest of all our desires.” Adam Smith

“Men do not desire merely to be rich, but to be richer than other men.” John Stuart Mill“any individual or group of individuals, who consent to a reduction of money-wages relatively to others, will suffer a relative reduction in real wages, which is sufficient justification for them to resist it”

JM Keynes“The motive is emulation–the stimulus of an invidious comparison... especially in any community in which class distinctions are quite vague”

Thorsten Veblen

Our wants and pleasures have their origin in society; we therefore measure them in relation to society; we do not measure them in relation to the objects which serve for their gratification.”

Karl Marx , Wage

Labour and Capital, chapter 6The Most Prominent Economists Can Be Read as Relative Utility Proponents

Hard Wired For Envy

Relative Status makes more evolutionary sense than absolute wealth as a utility functionEvidence for this instinct

87Slide88

Evolutionary Biology

genetic success is always relative, why spite works

88Slide89

Evolutionarily Robust

Special Utility needed for interest rate to be stable over generations But then, refinement really has to varyEye cones and colorRayo

and Becker (2007)

89Slide90

Reverse Dominance Hierarchies

Chris Boehmprimates usually have dominant malesWith tools, easy to kill dominant males, so hierarchies are not ‘natural’ for humans

90Slide91

Imitating Others Dominant Strategy

We copy all the time: parents, then peers, then anyone doing wellMark Pagel: zero, soap, the wheel, language,

iPads.Division of labor, accumulation of science, implies innovating only after a lot of copying, and generally relying on others

91Slide92

Social Context Hard Wired

Specialized neural mechanisms process social information, empathyCan’t ‘not see’ contextMirror neurons tie others to us

92Slide93

Relative Utility Matters more than Absolute

EconometricsfMRIPsychologistsrank in one’s peer group is more important than the level of income

93Slide94

Endocrinology of Envy

Robert Sapolsky found baboon status related to glucocorticoid levels Whitehall Studies found correlation between British civil servant grade level and mortality.

94Slide95

Moderation in All Things

Greek proverbtoo much, too little, both bad:Vitamin A

RadiationOxygenPolitenessLoyalty

Honesty

Exposure



-

Risk

Relative

Standard

95Slide96

Courage Premium

Aristocracy asserted their privileged position came from battlefield courageThe upper classes truly were courageous in battle, as WW1

showed, but no one will pay for that, and taxes on the rich went up

96Slide97

Why Take Uncompensated Risk?

Necessary, not sufficient condition for successEvery irrevocable act entails some kind of riskWe all take risks (marriage, jobs)Taking the right risks, at the right time, given our particular strengths, is good

97Slide98

Why a Negative Premium?

With relative risk, an abnormal demand for highly volatile assets is not totally countered in equilibrium, leaving a price impactHigher demand, higher price, lower future return

98Slide99

High Vol Demand: Winner’s Curse

no short selling….assets with higher valuation uncertainty will have higher prices, lower returns

99Slide100

High Vol Demand: Overconfidence

People are generally overconfident about their relative competency on socially desirable trates

Overconfidence makes one happier, lowers mortality

100Slide101

High Vol Demand: Risk-Loving

Preference for positive skewConsistent with global risk aversion only if skew risk premium <15% of standard risk premium

Risk loving looks like overconfidence

101Slide102

High Vol Demand: Gambling Preferences

Robert Sapolsky and dopamine generation based on rewards:

Higher for probabilistic payoffs

102Slide103

High Vol Demand: Information Costs

High volatility stocks generate more newsEasier to form opinion

Easier to sell a storyFalkenstein (1996) looked at mutual fund ownership and news stories, stock age

103Slide104

High Vol Demand: Representativeness Bias

Great stocks of past had great risk….“To get rich, you have to take risk

.”Prob( higher return|higher

risk)=

Prob

(big

return|big risk ) >0So risk is correlated with higher returns (?)

104Slide105

High Vol Demand: Alpha Discovery

Many people jump in and want to know if they have ‘it’Trade bio-techs, not utilities

105Slide106

High Vol Demand: Convex Payoffs to Stock Pickers

Top stock analysts often have 100% winnersMutual fund inflows highly convex

Greater value to greater volatility via call option

106Slide107

High Vol Demand: Asset Buyers Bullish

Most equity buyers tend to think the market is going to rise more than the ‘equity risk premium’

107Slide108

Academic Confabulations

108Slide109

‘

it would be irresponsible to assume that [the CAPM] is not true’

William Sharpe

‘theoretical

tour de force

’ though ‘empirically vacuous’

Eugene Fama‘stochastic discount factor(s) … so general, they place almost no restrictions on financial data’

John CampbellFinance is “the only part of economics that works” Andy Lo

Praise for a Vacuous Theory

109

Oil pricesConsumption growthPer-capita labor income

Consumption/wealth ratioStatistical (latent) Factors

Etc.Snipe hunt for factor that works

110

Implications

111Slide112

Find weights with added constraintsNo shortsCap on weight of 2% for S&P500, 4% for other indices

Stocks found generally at max limit for longsRedo each 6 months based on daily data from prior year

MVP Construction

112Slide113

FTSE

FTSE-

MVP

MSCI-

Eur

MSCI-

MVP

Nikkei

Nikkei-

MVP

S&P500

S&P500-

MVP

AnnRet

2.7%

7.4%

-0.6%

2.6%

-1.6%

0.0%

4.2%

9.2%

AnnStdev

15.0%

12.0%

19.5%

13.1%

19.8%

13.5%

16.5%

12.3%

Beta

0.65

0.59

0.50

0.47

Indexes are not near 'Efficient'

113Slide114

Beta Strategies

Data from Jul-1962 to Jun-2012 monthly returns, annualized used top 80% of NYSE market cap (about 1500 stocks today)

Portfolios with 100 stocks

Beta-Low

Beta-05

Beta-10

Beta-15

Beta-High

S&P500

GeoMean

11.3%

11.9%

12.2%

9.6%

6.4%

10.1%

AnnStDev

13.0%

11.6%

17.4%

26.2%

34.4%

15.1%

Sharpe

0.45

0.56

0.39

0.16

0.03

0.31

Inf. Ratio

0.10

0.22

0.21

0.15

-0.02

SMB Beta

0.53

0.34

0.69

1.45

1.78

0.26

HML

Beta

-0.06

0.10

-0.29

-0.96

-1.35

-0.39

Mkt

eta

0.60

0.57

1.04

1.44

1.82

114Slide115

Total Vol vs. Beta vs. IdioVol

Volatility

Beta

Idio

low

high

low

high

low

high

Arith

10.3%

7.9%

12.1%

11.1%

10.5%

9.0%

Geo

10.2%

2.2%

12.0%

5.3%

10.5%

3.7%

Stdev

10.2%

33.5%

11.9%

34.1%

10.2%

32.5%

Sharpe*

1.00

0.07

1.01

0.16

1.03

0.11

Top 2000 stocks, extrapolated backward, 1952-2008, Sorted differently

115Slide116

Assume people want to do what everyone else is doingAppealing asset allocation based on consensus, not volatilitySell idea of trading envy for greed

MVPsBeta ArbitrageWill deviate from the benchmark

Investment Advisor

116Slide117

Focus on payoffs and probabilitiesnot expected returnsNot discount rates

Don’t derive an expected return from a covariance or factor loading

Implication

117

Implications

Don’t expect to be rewarded for risk taking per seAccept some envy; moderation in all thingsPeople like being appreciated: it shows they are relatively competent, a status maximizing metric

118

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