The Missing Risk Premium:
Why Low Volatility Investing Works
Eric Falkenstein
2013
Copyright 2013 Eric G Falkenstein
1
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
Copyright 2013 Eric G Falkenstein
2
My Interest
• 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 wellknown 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
Copyright 2013 Eric G Falkenstein
3
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
4
“most returns and price variation
come from variation in risk premia”
John Campbell
E  FutValue 
Price 
1 r  g
Risk free
rate
Copyright 2013 Eric G Falkenstein
Risk premium
5
Big Idea: this is the Risk-Return Tradeoff
Copyright 2013 Eric G Falkenstein
6
Risk and Return
• In general, in practice:
risk is not positively related to return
Copyright 2013 Eric G Falkenstein
7
Standard Theory is Intuitive
• 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
Copyright 2013 Eric G Falkenstein
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…And Wrong
 Leveraged Firms
 B vs. BBB rated Bonds
 Out-of-the-money options vs. at-the-money options
 S and C corps vs. equity indexes
 Highest volatility vs. modest vol stocks
 R rated movies vs. G rated movies
 Lotto vs. ‘quick pick’ lotteries
 50-1 horses vs. 3-1 horses
 Mutual funds, currencies, futures, countries, yield curve
Copyright 2013 Eric G Falkenstein
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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
10
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
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Standard Theory
Copyright 2013 Eric G Falkenstein
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Marginal Utility
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
1
1
1
1
E  1   2   4   8  ...
2
4
4
16
1 1 1 1
E      ...
2 2 2 2
 1
E   j 1  
2
Why not? Diminishing marginal returns
Copyright 2013 Eric G Falkenstein
13
Basic Idea of Utility
• 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
Copyright 2013 Eric G Falkenstein
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Where does Risk Premium Come
From?
• Global concavity of utility is the necessary and
sufficient condition for the existence of a risk
premium
Copyright 2013 Eric G Falkenstein
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Utility Theory and Risk Aversion
• Utility not applied between goods, but to
everything
• Von-Neumann-Morgenstern (1944)
Copyright 2013 Eric G Falkenstein
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U  E  r   a 2
Copyright 2013 Eric G Falkenstein
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Why we like efficient portfolios
No points plot above
the red line
Expected Return
All portfolios
on the red line
are efficient
100% investment in security
with highest E(R)
100% investment in minimum
variance portfolio
Standard Deviation
Copyright 2013 Eric G Falkenstein
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Exp
Return
Port-1
U1
U2
Port-2
U3
U4
Volatility
Copyright 2013 Eric G Falkenstein
Port-3

19
Expected Return
C
B
Rf
Rz  1  z  rf  zrB
 z  z B
A
Standard Deviation
Copyright 2013 Eric G Falkenstein
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Copyright 2013 Eric G Falkenstein
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How to Derive The Capital Asset
Pricing Model
1. E  ri   a im  k every asset has same marg. value
2. E  rf   a fm  k  rf  k ,risk free rate is k
3. E  rm   a  k  a 
2
m
4. E  ri  
E  rm   rf

5. E  ri   rf 
2
m
E  rm   rf
 m2
 im  rf
 im
E  rm   rf 
2 
m
6. E  ri   rf  i  E  rm   rf
 aka the CAPM the SML
Copyright 2013 Eric G Falkenstein
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Market Portfolio
E ( Ri )  R f  i  E ( Rm )  R f 
Expected Return
where E ( Ri )  expected return on security i
E(R)
R f  risk-free rate of interest
i  beta of Security i
E ( Rm )  expected return on the market
Rf
1.0
Beta
Copyright 2013 Eric G Falkenstein
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General Equilibrium aka Stochastic
Discount Factor  CAPM
1. U  EU  1  r 
'
0
'
1
U1'
 1  E ' 1  r 
U0
U1'
2. 1  E  MR given M= '
U0
8. E[ R]  R f 
3. E[MR]  E[M ]E[ R]  cov( M , R)  1
4. E[ R] 
 U 0'    cov( Ri , Rm ) 
7. E[ R]  R f   '  

U 0'
 U1 

1
cov( M , R)

E[ M ]
E[ M ]
9. letting R i =R m U1' 
10. E[ R]  R f 
1
5. E[ R f ]  R f 
E[ M ]
U1' - Rm
6. M  '  '
U0
U0
U ' 1
Rm
cov( M , R)  
 cov( Ri , Rm )
U1'
 var( Rm )
E[ Rm  R f ]
 cov( Ri , Rm )
  var( Rm ) 


 E[ Rm  R f ] 
11. E[ Ri ]  R f  E[ Rm  R f ]
 cov( Ri , Rm )
U
'
0
cov( Ri , Rm )
var( Rm )
12. E[ Ri ]  Rf   E[ Rm  Rf ]
Copyright 2013 Eric G Falkenstein
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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)
Copyright 2013 Eric G Falkenstein
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Hope for Final Theory
• linear in risk factors, covariances with
something
• include something very like the stock market
as one of the prominent factors
Copyright 2013 Eric G Falkenstein
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Empirical Evidence
Copyright 2013 Eric G Falkenstein
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Volatility Often Used as a Risk
Shorthand
Brealey and Myers Investments Book
Return
17.30%
13%
6.0%
5.70%
3.90%
Small Stocks
Stocks
Corporate Bonds
Government Bonds
T-bills
Volatility
33.4%
20.2%
8.7%
9.4%
3.2%
From Cam Harvey (editor
of Journal of Finance)
website
Copyright 2013 Eric G Falkenstein
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If only this worked in more places…
Copyright 2013 Eric G Falkenstein
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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
Copyright 2013 Eric G Falkenstein
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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
Copyright 2013 Eric G Falkenstein
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Example of how small firm effect showed up in
beta tests
Theory:
Longer hair people
are short
Omitted variable:
gender
Theory:
high beta firms have
high returns
Omitted variable: size
Copyright 2013 Eric G Falkenstein
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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
Copyright 2013 Eric G Falkenstein
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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 nonfalsifiable
• However, it’s hard to conceive of one not
correlated with total volatility
Copyright 2013 Eric G Falkenstein
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Total Volatility and Returns
• My Dissertation (1994) page 53
Copyright 2013 Eric G Falkenstein
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Cross-Sectional Annual Returns Sorted
by Idiosyncratic and Total Volatility
Ang,, Hodrick, Xing and Zhang (JoF 2006)
Copyright 2013 Eric G Falkenstein
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Beta and Returns: 1962-2011
Beta-Low
Beta0.5
Beta1.0
AnnRet
10.8%
11.4%
11.4%
8.2%
4.5%
AnnStdev
13.1%
11.6%
17.4%
26.2%
33.9%
0.57
0.57
1.04
1.44
1.78
Beta
Copyright 2013 Eric G Falkenstein
Beta1.5 Beta-High
37
Equities and bond ratings (Distress)
• Low Rated Equities also have lower returns
StockReturns
AAA
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
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Leverage and Equity Returns
Penman, Richardson, and Tuna. 2007
Equity Returns Practice
Theory
Copyright 2013 Eric G Falkenstein
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Penny Stocks: Eraker and Ready (2009)
Volume($)
>
Price>
2,000
0.01
50,000
500,000
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%
Copyright 2013 Eric G Falkenstein
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Call Options
Sophie Ni (2007)
Should amplify the equity risk premium the greater the out-of-the-money
Copyright 2013 Eric G Falkenstein
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Initial Public Offerings (IPOs)
• IPO has a lot of Uncertainty
• Jay Ritter (see his website). 1970-2011.
• 8k observations
Copyright 2013 Eric G Falkenstein
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Analyst Disagreement
• Deither, Malloy, and Scherbina (2002). Table
2. Data from 1983-2000.
Copyright 2013 Eric G Falkenstein
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Total Volatility over Time
• Steve Sharpe and Gene Amromin (2005).
People have higher expected returns when
they have lower expected volatilities


E rm  rf  a m2  b mf
a, b  0
Copyright 2013 Eric G Falkenstein
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Total Volatility over Time
• Contemporaneous Correlation Clearly
Negative


E rm  rf  a m2  b mf
a, b  0
Copyright 2013 Eric G Falkenstein
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SPY Total Return to Overnight vs. Daily
Return Periods
Copyright 2013 Eric G Falkenstein
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Small Business Returns
• Moskowitz, and Vissing-Jorgensen (2002)
Copyright 2013 Eric G Falkenstein
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Currencies: Uncovered Interest Rate
Parity
rAUD  ryen  % change in yen+riskprem?
Sharpe 0.99 from 1976-2008 in Burnside et
al (2009)
Here’s Long AUD, Short JPY
Copyright 2013 Eric G Falkenstein
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Corporate Bonds
• Merrill High Yield Master II (HOAO) Merrill
BBB-AA Index (COCO)
• Indices here overstate realized returns
Copyright 2013 Eric G Falkenstein
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World Country Returns
• Dimson, Marsh, Staunton (2005)
• 17 Countries, 1900-2005, Annual Data
Copyright 2013 Eric G Falkenstein
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Emerging market Returns
Copyright 2013 Eric G Falkenstein
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Treasury Yield Curve
• 1% premium from 0.25 to 3 years
• No premium from 5 to 30 years
• Volatility, Covariance, increasing linearly
Copyright 2013 Eric G Falkenstein
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Treasury Yield Curve
• 1% premium from 0.25 to 3 years
• No premium from 5 to 30 years
• Volatility, Covariance, increasing linearly
Copyright 2013 Eric G Falkenstein
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Futures
• 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
Copyright 2013 Eric G Falkenstein
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Movie Returns by Rating
• Devany and Walls (1999), 2015 movies from
1984-96
Copyright 2013 Eric G Falkenstein
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Sports Books: Longshot Bias
• Snowberg and Wolfers (2009)
Copyright 2013 Eric G Falkenstein
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Initial Public Offerings (IPOs)
• IPO has a lot of Uncertainty
• Jay Ritter (see his website). 1980-2008.
• IPO Returns -3.7% annually below sizematched firms for first 5 years
Copyright 2013 Eric G Falkenstein
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Trading Volume
• Turnover of stock a proxy for disagreement
• Highly correlated with beta
Copyright 2013 Eric G Falkenstein
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Equity Risk Premium
• Top line return is not the same as average or
marginal return
Copyright 2013 Eric G Falkenstein
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What is the Equity Risk Premium?
Eri  rf  E  i  rm  rf
E  rm  rf


The most important constant in finance
Copyright 2013 Eric G Falkenstein
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Equity Premium Evolution
• 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%
Copyright 2013 Eric G Falkenstein
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Geometric vs. Arithmetic Averages
• 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
rG  rA 
2
2
Copyright 2013 Eric G Falkenstein
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Bad Market Timing
• 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
Copyright 2013 Eric G Falkenstein
63
Transaction Costs
• 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%)
Copyright 2013 Eric G Falkenstein
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Survivorship Bias
• 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
Copyright 2013 Eric G Falkenstein
65
Peso Problem
•
•
•
•
•
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
Copyright 2013 Eric G Falkenstein
66
Taxes
• 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%
Copyright 2013 Eric G Falkenstein
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People ignore costs all the time
•
•
•
•
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
Copyright 2013 Eric G Falkenstein
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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
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Returns not Like in Representative
Agent Model
Equity Return Uncorrelated with GDP growth over
a Century
Copyright 2013 Eric G Falkenstein
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Hedge Fund Money Goes to Insiders
• From Simon Lack
Copyright 2013 Eric G Falkenstein
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Equity Premium Subtractions
•
•
•
•
•
•
•
Geometric vs. Arithmetic Averaging
Survivorship Bias
Peso Problems
Taxes
Adverse Market Timing
Transaction Costs
Sum
1.0%
1.0%
1.0%
1.0%
1.0%
1.0%
6.0%
• Most estimates around 3.5% for equity premium.
With these additions, the Marginal Investor
clearly could be seeing a 0% equity premium.
Copyright 2013 Eric G Falkenstein
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Scope of the Risk Premium Failure
Positive Risk Premium (3)
1.
2.
3.
Short End of Yield Curve
BBB-AAA Corporate
Spread
Efficient Equity Investor
Zero Risk Premium (14)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
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
Negative Risk Premium (12)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Average Equity Investor
Betas
Volatility
Financial Distress
Trading Volume
Analyst Disagreement
Equity Options
Lotteries
Sports Betting
Currencies
IPO equity Returns
MVPs
Copyright 2013 Eric G Falkenstein
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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
74
Basic Idea of Relative Risk and no
Premium
Total Return
Avg.
X
Y
State 1
0
-10
State 2
20
30
Relative Return
X
Y
–5
5
–5
25
–5
5
Copyright 2013 Eric G Falkenstein
75
Utility Proof
• Taking the first order condition, we have
m = R f + a s 2 (a Ei - a E- i )
a Ei = a E- i
• Since each agent is identical, in equilibrium
each agent holds the same amount
m = Rf
• So
• Which means, the expected return on risky
assets is te risk free rate
Copyright 2013 Eric G Falkenstein
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Utility Proof Benchmark
• Taking the first order condition in the standard
model we have
m = R f + as 2a Ei
• 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
Copyright 2013 Eric G Falkenstein
77
Relative Utility and Different Beliefs
• 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
m = R f + a s 2 (a Ei - a E- i )
m = R f + as 2a Ei
Copyright 2013 Eric G Falkenstein
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Relative Risk in academia
1
• Abel (1990): U  ct , Ct 1   1     ct C 
t 1 

1
• Gali (1995): U  c, C   1  a 1 c1aC  a
• DeMarzo,, Kandiel, Kremer (2003):
U  cg , cs   1  a 
• Roussanov (2010):
1
c
1 a
g
1 a
s
c

i


W
C 1 a
1 a
s
 Ws 

1 a
 Ws 
Copyright 2013 Eric G Falkenstein
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Outside the Box Evidence
• Like any truth, it has lots of footprints
Copyright 2013 Eric G Falkenstein
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Easterlin’s Paradox (1974)
•
•
•
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.
Copyright 2013 Eric G Falkenstein
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Easterlin’s Paradox
• 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
Copyright 2013 Eric G Falkenstein
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Buy Recommendations exclude low
risk firms
• Half of all stocks have expected returns below the market
• Zero recommendations for firms with expected returns below
the market return
Buy!
Expected Return
Who
cares?
Risk
Copyright 2013 Eric G Falkenstein
83
Home Bias
• 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
Copyright 2013 Eric G Falkenstein
84
Everyone Benchmarks
• “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
Copyright 2013 Eric G Falkenstein
85
The Most Prominent Economists Can
Be Read as Relative Utility Proponents
• “…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
Copyright 2013 Eric G Falkenstein
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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
87
Evolutionary Biology
• genetic success is always relative, why spite
works
Copyright 2013 Eric G Falkenstein
88
Evolutionarily Robust
• Special Utility needed for interest rate to be
1 a
C
stable over generations U  C  
1 a
• But then, refinement really has to vary
• Eye cones and color
• Rayo and Becker (2007)
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Reverse Dominance Hierarchies
• Chris Boehm
• primates usually have dominant males
• With tools, easy to kill dominant males, so
hierarchies are not ‘natural’ for humans
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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
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Social Context Hard Wired
• Specialized neural mechanisms process social
information, empathy
• Can’t ‘not see’ context
• Mirror neurons tie others to us
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Relative Utility Matters more than
Absolute
•
•
•
•
Econometrics
fMRI
Psychologists
rank in one’s peer group is more important
than the level of income
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Endocrinology of Envy
• Robert Sapolsky found baboon status related
to glucocorticoid levels
• Whitehall Studies found correlation between
British civil servant grade level and mortality.
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Moderation in All Things
–
–
–
–
–
–
Vitamin A
Radiation
Oxygen
Politeness
Loyalty
Honesty
Risk
• Greek proverb
• too much, too little, both bad:
-
Relative
0
Exposure
Copyright 2013 Eric G Falkenstein

95
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
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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
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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
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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
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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
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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
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High Vol Demand: Gambling
Preferences
• Robert Sapolsky and dopamine generation
based on rewards:
– Higher for probabilistic payoffs
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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
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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 (?)
P  A  prob risky
P  B   prob high return
P  A | B P  B
P  B | A 
P  A
Copyright 2013 Eric G Falkenstein
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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
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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
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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
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Academic Confabulations
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Praise for a Vacuous Theory
‘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 Campbell
Finance is “the only part of economics that works”
Andy Lo
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Snipe hunt for factor that works
•
•
•
•
•
Oil prices
Consumption growth
Per-capita labor income
Consumption/wealth ratio
Statistical (latent) Factors
• Etc.
Copyright 2013 Eric G Falkenstein
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Implications
Copyright 2013 Eric G Falkenstein
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MVP Construction
• 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
Min w HFA w
s.t. w '  1
0  wi  0.02  i
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Indexes are not near 'Efficient'
AnnRet
FTSE
FTSEMVP
MSCIEur
MSCIMVP
NikkeiS&P500Nikkei
MVP S&P500
MVP
2.7%
7.4%
-0.6%
2.6%
-1.6%
AnnStdev 15.0%
Beta
0.0%
4.2%
9.2%
12.0% 19.5% 13.1% 19.8% 13.5% 16.5% 12.3%
0.65
0.59
Copyright 2013 Eric G Falkenstein
0.50
0.47
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Beta Strategies
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
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
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Total Vol vs. Beta vs. IdioVol
• Top 2000 stocks, extrapolated backward,
1952-2008, Sorted differently
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
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Investment Advisor
• 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
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Implication
• Focus on payoffs and probabilities
– not expected returns
– Not discount rates
• Don’t derive an expected return from a covariance or factor
loading
E  ret   a
2
E  ret   a pi
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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
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