Eric Falkenstein
 Assumptions: investor agreement and concave utility
function lead to risk being priced
 Implication: Our marginal utility’s covariance with
returns is priced as risky
 Implication: Something intuitive should be
identifiable as our marginal utility
 As If! Where else does utility, or agreement on
expected returns and volatility, fail?
Securities’ expected
returns
Securities’ standard
deviations
Mean-variance
optimization
Optimal asset
weights
Securities’ correlations
Portfolio choice
3
Select {wi} so as to minimize:
 p2  [w1212  ...  w 2n n2 ] 
[2w1w 21 2 1,2  ...  2w n-1w n n 1 n n 1,n ]
subject to:
(i) E(Rp) > R*
(ii) S wi = 1
Rp
 i wi ri
Expected Return
CAPM, APT, etc. trivial
implication
Single Optimal Risky Portfolio
Rf
Standard Deviation
Finding Alpha
5
 CAPM article originally rejected because the idea that
everyone agreed on returns and covariances absurd.
Editor changed, paper accepted.
 Rubinstein’s aggregation theorem (1974)
 Can model market as an individual if they all agree on
probabilities and covariances
 Can’t model disagreement
 Milgrom-Stokey (1982) no trade theorem
 Trade if have private information—make gross profits
 Grossman-Stiglitz (1980)
 Kyle (1985)
 Fundamental Analysis worthless
 Markets efficient: mutual funds do not outperform
 NYSE turns over 100% per year
 Odean and Barber (2000): People turnover 75% of
stocks in individual accounts. Highest quintile 250%
 Two-fund separation theorem: Investors hold unique
optimal risky portfolio
 Practice: 1000s of mutual funds and ETFs
Less risk
averse
Expected Return
More risk
averse
‘the’ market
everyone holds
Rf
Standard Deviation
 Goetzmann and Kumar (2005): >25% have only 1 stock,
>50% less than 3, 5-10% have more than 10.
 Average portfolio volatility much greater than market
for average investor
Expected Return
Rf
Standard Deviation
 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
 Fundamental to economic reasoning
 Marginal Revolution transformed economics c. 1860s
 Walras, Jevons, Menger
 Pre 1860s ‘classical’ economists: Marx, Smith, Ricardo,
Mill
 Transformed theory of value
X
Slope = Change in Y/Change in X
= MU(Y)/MU(X)
U4
U3
U2
U1
O
X
Y
Income = Px Qx + PyQy
I/Py
Slope = Px/Py
X
O
I/Px
Y
MRS = MUx/MUy= Px/Py
a
b
c
U4
U3
d
U2
e
O
U1
X
Y
a
b
Y1
C’
c
Yo
U5
c”
U4
U3
d
U2
e
U1
O
Xo
X1
X
 Utility not applied between goods, but applied to




everything
Von-Neumann-Morgenstern (1944)
EU(x)=prob(x1 )U(x1)+prob(x2 )U(x2 )
Friedman-Savage (1948)
Risk-averse people prefer less variance
 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
 Rabin (2000)
 Say you reject 50-50 bet to make $11, risking $10
 Then you reject any bet where you lose $100
 Even:
 +$100,000,000,000 if heads
 -$100 if tails
 Comes from global concavity of utility function
 W+11th dollar worth less than 10/11 of W-10th dollar
 W+11th+21th (W+32nd) dollar worth less than 10/11 of W+11
dollar. So W+32nd dollar worth 10/11*10/115/6 dollar
 Etc.
 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.
 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
Libertarians love this:
• with pure greed, individual self-interest
consistent with reciprocal altruism, growth
• With pure envy, not
Torture data to confess
Japan ‘adjustment’
Still not true for USA
 People do not approach the problem of investing as a
mean-variance optimization, or factor risk, problem.
 Invest based on differing beliefs,
 taking lots of idiosyncratic risk when they do,
 reaching for absolute return
 Necessary and Sufficient Condition for Risk Aversion
Wrong
 Absurd extrapolations
 Incorrect implications for happiness
 And, there appear no general priced risk factors