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The Missing Risk Premium:Why Low Volatility Investing Works
Eric Falkenstein2013
Copyright 2013 Eric G Falkenstein
Copyright 2013 Eric G Falkenstein
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
2
Copyright 2013 Eric G Falkenstein
• 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
My Interest
3
Copyright 2013 Eric G Falkenstein 4
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
Copyright 2013 Eric G Falkenstein 5
Price1FutValueEr g
“most returns and price variation come from variation in risk premia” John Campbell
Risk free rate
Risk premium
Copyright 2013 Eric G Falkenstein
Big Idea: this is the Risk-Return Trade-off
6
Copyright 2013 Eric G Falkenstein
• In general, in practice:risk is not positively related to return
Risk and Return
7
Copyright 2013 Eric G Falkenstein
• Risk aversion like aversion to smelliness• The 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
8
Copyright 2013 Eric G Falkenstein
Leveraged FirmsB vs. BBB rated BondsOut-of-the-money options vs. at-the-money optionsS and C corps vs. equity indexesHighest volatility vs. modest vol stocksR 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
9
Copyright 2013 Eric G Falkenstein 10
Finance Misleading
• Most practical finance is about generating expected values
• Finding covariances to generate different discount rates is a massive waste of time, pure rationalization in practice
Copyright 2013 Eric G Falkenstein 11
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
Copyright 2013 Eric G Falkenstein 12
Standard Theory
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 returns13Copyright 2013 Eric G Falkenstein
Marginal Utility
1
1 1 1 11 2 4 8 ...
2 4 4 161 1 1 1
...2 2 2 2
1
2j
E
E
E
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• Fundamental to economic reasoning• Marginal Revolution transformed economics
in 1860s– Walras, Jevons, Menger– Pre 1860s ‘classical’ economists: Marx, Smith,
Ricardo, Mill• Transformed Theory of Value
Basic Idea of Utility
Copyright 2013 Eric G Falkenstein
• Global concavity of utility is the necessary and sufficient condition for the existence of a risk premium
Where does Risk Premium Come From?
15
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• Utility not applied between goods, but to everything
• Von-Neumann-Morgenstern (1944)
Utility Theory and Risk Aversion
Copyright 2013 Eric G Falkenstein 17
2U E r a
Iso-Utility Curves for Return and Volatility
Copyright 2013 Eric G Falkenstein 18
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 portfolios
19Copyright 2013 Eric G Falkenstein
ExpReturn
Volatility
U1
U2
U3
Tobin: Two-Fund Separation Theorem
Port-1
Port-2
Port-3U4
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Always hold some cash: liquidity preference
Standard Deviation
Expected Return
RfA
B
C 1z f B
z B
R z r zr
z
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Regardless of risk preference, everyone uses same risky portfolio
22Copyright 2013 Eric G Falkenstein
How to Derive The Capital Asset Pricing Model
1. every asset has same marg. valuei imaE r k
2. ,risk free rate is kf f fmE a rr k k
22
3. m f
mm mE r a k a
E r r
2
4. i im
fm f
m
E r rrE r
25. im
f m fm
iE r r E r r
6. aka the CAPM the SMLi f m fiE r r E r r
Copyright 2013 Eric G Falkenstein 23
CAPM is the Security Market Line (SML)
Beta
Expected Return
Rf
Market Portfolio
1.0
E(R)
( ) ( )
where ( ) expected return on security
risk-free rate of interest
beta of Security
( ) expected return on the market
i f i m f
i
f
i
m
E R R E R R
E R i
R
i
E R
Copyright 2013 Eric G Falkenstein 24
General Equilibrium aka Stochastic Discount Factor CAPM
'
' ' 10 1 '
0
U1. U U 1 1 1
UE r E r
3. [ ] [ ] [ ] cov( , ) 1E MR E M E R M R
1
[ ]
c4.
ov( , ]
[ ][
)E
M
M
E
R
E MR
15. [ ]
[ ]ff RE RE M
'1' '0 0
'0
-U6.
U U
1 cov( , )
' cov( , )
m
m
i mR
RM
U M RR
UR
'0' '
01
cov( ,7.
)[ ] i m
fEU
RR R
U UR
'1'0
2. 1 givU
Uen M=E MR
'1
cov( , )8. [ ] i m
f
R RE R R
U
cov( , )11. [ ] [ ]
var( )i m
i f m fm
R RE R R E R R
R
12. [ ] [ ]i f m fE R R E R R
'1
var( )9. letting R =R
[ ]m
i mm f
RU
E R R
cov( , )10. [ ]
var( )
[ ]
i mf
m
m f
R RE R R
R
E R R
Copyright 2013 Eric G Falkenstein 25
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 (eg, 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
26Copyright 2013 Eric G Falkenstein
Hope for Final Theory
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Empirical Evidence
Copyright 2013 Eric G Falkenstein
Return VolatilitySmall 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
28
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If only this worked in more places…
Copyright 2013 Eric G Falkenstein
The Risk Premium ProblemAfter 45 years, there are no measure of risk that are generally
positively correlated with returns
Fama and French 1992
30
From Campbell 2000
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Fama-French (1992)
• Show beta is just a size effect• Founding father (Fama) admits CAPM is
‘incomplete’, and beta itself useless
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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
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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
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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 one
• As a ‘framework’, not a theory, it is non-falsifiable
• However, it’s hard to conceive of one not correlated with total volatility
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• My Dissertation (1994) page 53
Total Volatility and Returns
Copyright 2013 Eric G Falkenstein
Cross-Sectional Annual Returns Sorted by Idiosyncratic and Total Volatility
Ang,, Hodrick, Xing and Zhang (JoF 2006)
36
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Beta and Returns: 1962-2011
Beta-Low Beta0.5 Beta1.0 Beta1.5 Beta-High
AnnRet 10.8% 11.4% 11.4% 8.2% 4.5%
AnnStdev 13.1% 11.6% 17.4% 26.2% 33.9%
Beta 0.57 0.57 1.04 1.44 1.78
Copyright 2013 Eric G Falkenstein
• Low Rated Equities also have lower returns
Equities and bond ratings (Distress)
38
StockReturnsAAA 12.4%AA 13.9%A 14.3%BBB 14.2%BB 15.0%B 8.6%C -12.7%
Copyright 2013 Eric G Falkenstein
Leverage and Equity ReturnsPenman, Richardson, and Tuna. 2007
Equity Returns Practice Theory
39
Copyright 2013 Eric G Falkenstein
Volume($)> 2,000 50,000 500,000
Price> 0.01 0.1 0.01 0.1 0.01 0.1Count 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)
40
Copyright 2013 Eric G Falkenstein
Call OptionsSophie Ni (2007)Should amplify the equity risk premium the greater the out-of-the-money
41
Copyright 2013 Eric G Falkenstein
• IPO has a lot of Uncertainty• Jay Ritter (see his website). 1970-2011.• 8k observations
Initial Public Offerings (IPOs)
42
Copyright 2013 Eric G Falkenstein
• Deither, Malloy, and Scherbina (2002). Table 2. Data from 1983-2000.
Analyst Disagreement
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• Steve Sharpe and Gene Amromin (2005). People have higher expected returns when they have lower expected volatilities
Total Volatility over Time
2
, 0
m mf mfE r r a b
a b
44
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• Contemporaneous Correlation Clearly Negative
Total Volatility over Time
2
, 0
m mf mfE r r a b
a b
Copyright 2013 Eric G Falkenstein
SPY Total Return to Overnight vs. Daily Return Periods
46
Copyright 2013 Eric G Falkenstein
• Moskowitz, and Vissing-Jorgensen (2002)
Small Business Returns
47
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Currencies: Uncovered Interest Rate Parity
% change in yen+riskprem?yenAUDr r
Sharpe 0.99 from 1976-2008 in Burnside et al (2009)Here’s Long AUD, Short JPY
Copyright 2013 Eric G Falkenstein
• Merrill High Yield Master II (HOAO) Merrill BBB-AA Index (COCO)
• Indices here overstate realized returns
Corporate Bonds
49
Copyright 2013 Eric G Falkenstein
• Dimson, Marsh, Staunton (2005)• 17 Countries, 1900-2005, Annual Data
World Country Returns
50
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Emerging market Returns
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• 1% premium from 0.25 to 3 years• No premium from 5 to 30 years• Volatility, Covariance, increasing linearly
Treasury Yield Curve
Copyright 2013 Eric G Falkenstein 53
• 1% premium from 0.25 to 3 years• No premium from 5 to 30 years• Volatility, Covariance, increasing linearly
Treasury Yield Curve
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• Futures return from roll• Harvey and Erb (2007) copper, heating oil, and
live cattle were on average in backwardization, • corn, wheat, silver, gold, and coffee were in
contango• It isn’t clear what covariance, volatility has to
do with this
Futures
Copyright 2013 Eric G Falkenstein
• Devany and Walls (1999), 2015 movies from 1984-96
Movie Returns by Rating
55
Copyright 2013 Eric G Falkenstein
• Snowberg and Wolfers (2009)
Sports Books: Longshot Bias
56
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• IPO has a lot of Uncertainty• Jay Ritter (see his website). 1980-2008.• IPO Returns -3.7% annually below size-
matched firms for first 5 years
Initial Public Offerings (IPOs)
Copyright 2013 Eric G Falkenstein 58
Trading Volume
• Turnover of stock a proxy for disagreement• Highly correlated with beta
Copyright 2013 Eric G Falkenstein 59
Equity Risk Premium
• Top line return is not the same as average or marginal return
Copyright 2013 Eric G Falkenstein
What is the Equity Risk Premium?
The most important constant in finance
i f i m fEr r E r r
60
m fE r r
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• 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%• CFO Magazine (2005): 5%• Ivo Welch (2009): 2%-4% at most 1%-8%
Equity Premium Evolution
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• 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
2
2G Ar r
Copyright 2013 Eric G Falkenstein 63
• Dichev (2005)• 1, 2, 1
– return 0% if cf is {-1,0,+1}– return -17.7% if cf is {-1,-1,+1.5}
• Total return different than Internal Rate of Return based on timing of investments
• Distributions Dividends-New Money• Corr(Distributionst,Returnt+1)= +33%
• Corr(Distributionst+1,Returnt)= -27%• bad timing
Bad Market Timing
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• Commissions, – 8.5% load through 1970’s to buy a mutual fund
• bid-ask cross– Stocks quoted at 8 ¾ - 9 in the 1990s– buy 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-ask• Bhardwaj and Brooks (1992): 4.4% total• Currently very low if you are smart (0.2%)
Transaction Costs
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• USA primary data point in World Value Weighted Index• Coincidentally, – 2-0 in World Wars– Never went communist
• Brown, Goetzmann, and Ross (1995)– Czechoslovakia, Hungary, Poland, Russia, and China all
zeroed out• Jorion and Goetzmann (1999)– US real return 350 basis points above median for 39
countries in 20th century
Survivorship Bias
Copyright 2013 Eric G Falkenstein 66
• Peso-Dollar FX rate fixed from 1954-76• Higher interest rate in Peso• Peso ‘floated’ in 1976: lost 45%• Peso devalued by 82% in 1982• Small probability, big loss, explains interest rate
premium• Robert Barro (2006) argues a correct probability of a
significant catastrophe explains much of the equity premium, about 300 basis points– 2% change of a 15% to 45% GDP decline
Peso Problem
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• 10% stock return: 6% post tax with a 40% tax rate• Gannon 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)• Lorie and Fisher (1964) found 2.2% adjustment
• Total after tax equity return 6.72%, vs. 10.62% pre tax• Long Term Municipal Bond Buyer Index return: 6.14%
Taxes
Copyright 2013 Eric G Falkenstein 68
• Beardstown Ladies investment club• 1983-94 return 23.4%• Best selling authors• Audited financials: 9.1%, below 14.9% for
market• Failed to include contributions
People ignore costs all the time
Copyright 2013 Eric G Falkenstein 69
Investors Don’t Match Indices
• Dalbar study from the Investment Company Institute:
• 1990-2010 Annual Returns• S&P500 return: 9.1%• Average equity mutual fund investor: 3.3%
Copyright 2013 Eric G Falkenstein 70
Returns not Like in Representative Agent Model
Equity Return Uncorrelated with GDP growth over a Century
Copyright 2013 Eric G Falkenstein 71
Hedge Fund Money Goes to Insiders
• From Simon Lack
Copyright 2013 Eric G Falkenstein
• 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
72
Copyright 2013 Eric G Falkenstein
Scope of the Risk Premium Failure
73
Positive Risk Premium (3) Zero Risk Premium (14) Negative Risk Premium (12)1. Short End of Yield Curve2. BBB-AAA Corporate
Spread3. Efficient Equity Investor
1. Long-End of Yield Curve2. B to BBB Bond3. Futures4. Private Investments5. Movies6. Mutual Funds7. VIX and Equity8. World Equity9. Emerging Markets10. Hedge Funds11. Real Estate12. CTAs13. Private Equity14. Intraday Stock Return
1. Average Equity Investor2. Betas3. Volatility4. Financial Distress5. Trading Volume6. Analyst Disagreement7. Equity Options8. Lotteries9. Sports Betting10. Currencies11. IPO equity Returns12. MVPs
Copyright 2013 Eric G Falkenstein 74
New Theory
• In general, risk and return are uncorrelated because risk is a deviation from the consensus
• This makes risk symmetric, too much or too little exposure generates similar risk
• Thus, volatile assets don’t need extra return to be held…
Copyright 2013 Eric G Falkenstein
Basic Idea of Relative Risk and no Premium
75
Total Return Avg. Relative Return
X Y X Y
State 1 0 -10 –5 5 –5
State 2 20 30 25 –5 5
Copyright 2013 Eric G Falkenstein 76
• Taking the first order condition, we have
• Since each agent is identical, in equilibrium each agent holds the same amount
• So• Which means, the expected return on risky
assets is te risk free rate
Utility Proof
( )2 i if E ER am s a a-= + -
i iE Ea a-=
fRm=
Copyright 2013 Eric G Falkenstein 77
• 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 aversion
• Because the exponential utility is CARA, not CRRA, higher amount in the risky asset generates a higher risk premium
Utility Proof Benchmark
2 iEfR a am s= +
Copyright 2013 Eric G Falkenstein 78
• See how relative utility model explains– Why when investors take risks, they expect above
average returns– Returns are relative to the risk free rate– Don’t short assets with expected return<Rf
Relative Utility and Different Beliefs
( )2 i if E ER am s a a-= + -
2 iEfR a am s= +
Copyright 2013 Eric G Falkenstein
• Abel (1990):
• Gali (1995):
• DeMarzo,, Kandiel, Kremer (2003):
• Roussanov (2010):
Relative Risk in academia
79
1
1
11
, 1 tt t
t
cU c C C
1 1, 1 a aU c C a c C
1 1 1, 1 a ag s g sU c c a c c
1
1
1
iaa s
ss
WCW
a W
Copyright 2013 Eric G Falkenstein 80
Outside the Box Evidence
• Like any truth, it has lots of footprints
Copyright 2013 Eric G Falkenstein 81
• 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)
Copyright 2013 Eric G Falkenstein 82
• Progress and Happiness a Puzzle– Gregg Easterbrook’s The Progress Paradox, – David Myers’s The American Paradox, and – Barry Schwartz’s The Paradox of Choice
• Japan: 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 – World A: $100,000 a year in perpetuity while others earned $90,000– World B: earn $110,000 while others earned $200,000– Most prefer World A
Easterlin’s Paradox
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• Half of all stocks have expected returns below the market• Zero recommendations for firms with expected returns below
the market return
Buy Recommendations exclude low risk firms
Risk
Expected ReturnBuy!
Who cares?
Copyright 2013 Eric G Falkenstein 84
• Should invest in world portfolio• Chan, Covrig, and Ng (2005): Everyone is
investing mainly in domestic portfolio • Avoiding easy way to diversify risk• Low covariance with risks from home
economy
Home Bias
Copyright 2013 Eric G Falkenstein
• “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’sEugene Fama, Merton Miller
Everyone Benchmarks
85
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• “…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 6
The Most Prominent Economists Can Be Read as Relative Utility Proponents
86
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Hard Wired For Envy
• Relative Status makes more evolutionary sense than absolute wealth as a utility function
• Evidence for this instinct
Copyright 2013 Eric G Falkenstein 88
Evolutionary Biology
• genetic success is always relative, why spite works
Copyright 2013 Eric G Falkenstein 89
Evolutionarily Robust
• Special Utility needed for interest rate to be stable over generations
• But then, refinement really has to vary• Eye cones and color• Rayo and Becker (2007)
1
1
aCU C
a
Copyright 2013 Eric G Falkenstein 90
Reverse Dominance Hierarchies
• Chris Boehm• primates usually have dominant males• With tools, easy to kill dominant males, so
hierarchies are not ‘natural’ for humans
Copyright 2013 Eric G Falkenstein 91
Imitating Others Dominant Strategy
• We copy all the time: parents, then peers, then anyone doing well
• Mark 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
Copyright 2013 Eric G Falkenstein 92
Social Context Hard Wired
• Specialized neural mechanisms process social information, empathy
• Can’t ‘not see’ context• Mirror neurons tie others to us
Copyright 2013 Eric G Falkenstein 93
Relative Utility Matters more than Absolute
• Econometrics• fMRI• Psychologists• rank in one’s peer group is more important
than the level of income
Copyright 2013 Eric G Falkenstein 94
Endocrinology of Envy
• Robert Sapolsky found baboon status related to glucocorticoid levels
• Whitehall Studies found correlation between British civil servant grade level and mortality.
Copyright 2013 Eric G Falkenstein 95
Moderation in All Things
• Greek proverb• too much, too little, both bad:– Vitamin A– Radiation– Oxygen– Politeness– Loyalty– Honesty
Exposure0 -
Risk Relative Standard
Copyright 2013 Eric G Falkenstein 96
Courage Premium
• Aristocracy asserted their privileged position came from battlefield courage
• The upper classes truly were courageous in battle, as WW1 showed, but no one will pay for that, and taxes on the rich went up
Copyright 2013 Eric G Falkenstein 97
Why Take Uncompensated Risk?
• Necessary, not sufficient condition for success• Every irrevocable act entails some kind of risk– We all take risks (marriage, jobs)
• Taking the right risks, at the right time, given our particular strengths, is good
Copyright 2013 Eric G Falkenstein 98
Why a Negative Premium?
• With relative risk, an abnormal demand for highly volatile assets is not totally countered in equilibrium, leaving a price impact
• Higher demand, higher price, lower future return
• Without relative utility, one needs ad hoc constraints
Copyright 2013 Eric G Falkenstein 99
High Vol Demand: Winner’s Curse• If no short selling….assets with higher valuation
uncertainty will have higher prices, lower returns
Copyright 2013 Eric G Falkenstein 100
High Vol Demand: Overconfidence
• People are generally overconfident about their relative competency on socially desirable trates
• Overconfidence makes one happier, lowers mortality
Copyright 2013 Eric G Falkenstein 101
High Vol Demand: Risk-Loving
• Preference for positive skew• Consistent with global risk aversion only if
skew risk premium <15% of standard risk premium
• Risk loving looks like overconfidence
Copyright 2013 Eric G Falkenstein 102
High Vol Demand: Gambling Preferences
• Robert Sapolsky and dopamine generation based on rewards:– Higher for probabilistic payoffs
Copyright 2013 Eric G Falkenstein 103
High Vol Demand: Information Costs
• High volatility stocks generate more news– Easier to form opinion– Easier to sell a story
• Falkenstein (1996) looked at mutual fund ownership and news stories, stock age
Copyright 2013 Eric G Falkenstein 104
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 ) >0– So risk is correlated with higher returns (?)
prob risky
prob high return
|P |
P A
P B
P A B P BB A
P A
Copyright 2013 Eric G Falkenstein 105
High Vol Demand: Alpha Discovery
• Many people jump in and want to know if they have ‘it’
• Trade bio-techs, not utilities
Copyright 2013 Eric G Falkenstein 106
High Vol Demand: Convex Payoffs to Stock Pickers
• Top stock analysts often have 100% winners• Mutual fund inflows highly convex– Greater value to greater volatility via call option
Copyright 2013 Eric G Falkenstein 107
High Vol Demand: Asset Buyers Bullish
• Most equity buyers tend to think the market is going to rise more than the ‘equity risk premium’
• Given those beliefs, it
Copyright 2013 Eric G Falkenstein 108
Academic Confabulations
Copyright 2013 Eric G Falkenstein
‘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
Copyright 2013 Eric G Falkenstein
• Oil prices• Consumption growth• Per-capita labor income• Consumption/wealth ratio• Statistical (latent) Factors
• Etc.
Snipe hunt for factor that works
110
Copyright 2013 Eric G Falkenstein 111
Implications
Copyright 2013 Eric G Falkenstein 112
• Find weights with added constraints– No shorts– Cap on weight of 2% for S&P500, 4% for other
indices– Stocks found generally at max limit for longs– Redo each 6 months based on daily data from
prior year
MVP Construction
. . ' 1
0 0.02
HFA
i
Min w w
s t w
w i
Copyright 2013 Eric G Falkenstein 113
FTSEFTSE-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'
Copyright 2013 Eric G Falkenstein 114
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 Beta 0.60 0.57 1.04 1.44 1.82
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Total Vol vs. Beta vs. IdioVol
Volatility Beta Idiolow 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
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• Assume people want to do what everyone else is doing– Appealing asset allocation based on consensus,
not volatility• Sell idea of trading envy for greed
• MVPs• Beta Arbitrage• Will deviate from the benchmark
Investment Advisor
Copyright 2013 Eric G Falkenstein
• Focus on payoffs and probabilities– not expected returns– Not discount rates
• Don’t derive an expected return from a covariance or factor loading
Implication
117
piE ret a
2E ret a
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Implications
• Don’t expect to be rewarded for risk taking per se
• Accept some envy; moderation in all things• People like being appreciated: it shows they
are relatively competent, a status maximizing metric