Eric Falkenstein

There are a few areas where we see a risk premiumInsurance against accidentsShort end of the yield curve

On average, no risk premiumNegative risk premium to high riskPeople seem to be gambling, not investing, in

practice, with the same expected return to gambling

Say utility is relative

Y riskier than X in standard approachY and X same risk in relative senseRisk is unnecessary: choose ½(X+Y)Like idiosyncratic risk, unnecessary risk

unpriced

U x U x x

X Y avg X-avg Y-avg

State 1 0 -10 -5 5 -5

State 2 20 30 25 -5 5

Avg 10 10 10 0 0

Easterlin ParadoxBenchmarking, tracking error as riskNot a new idea

Adam Smith, Karl Marx, Thorsten Veblen, Max Weber, all focused on status (didn’t formalize)

Pesendorfer (1995) and Rayo and Becker (2006) modeled status orientation formally

Two assets, a risky security and a risk-free security, with returns RE and Rf

Where (risk free return is certain)There are two identical agents, i and –i, who

have wealth in period 0 of k, and spends money, , on the two assets

No consumption. In the next period, agent i’s wealth is thus

i iE fk a a³ +

( ) ( )2~ , , ~ ,0E ffR N R N Rms

1 i ii E f E Ew k R R

Utility is relativeMax utility subject to budget constraint

Substituting for , because the budget constraint holds with equality.

( ) ( )1 1 1 1

, E

2

. .

i iE f

i iE f

i i i i

k

aw w Var w w

st

Maxa a

a a

- -

³ +

- - -

( ) ( ) ( )2 2

+ 2ff

iE

i i i i i iE E E E E Ek R k R

aMaxa

m ms

a a a a a a- - -- -- - - -

( ) { }1 1 1 1expi i i i iU w w a w wæ ö÷ç ÷ç ÷ç- -è ø- = - - -

i if Eka a= -

Taking the first order condition, we have

Since each agent is identical, in equilibrium each agent holds the same amount

SoOr Which means, the expected return on risky

assets is te risk free rate

( )2 i if E ER am s a a-= + -

i iE Ea a-=

fRm=( )2~ ,fER N R s

Utility is absoluteMax utility subject to budget constraint

Substituting for , because the budget constraint holds with equality.

( ) ( )1 1

,

. . . .

E2

i iE f

i iE f

k

i i

st st

aw Var wMaxa a

a a³ +

-

( ) ( )2 2

+ 2rf

iE

i i iE E Ek R

aMaxa

ms

a a a- -

( ) ( )1 1expi i iU w aw=- -

i if Eka a= -

Taking the first order condition, we have

This is the standard result

2 iEfR a am s= +

Basically, if people are benchmarking against the market, =1 has no risk

Then, Through arbitrage

Which means, trivially, that all assets have the same return

22 21 mi i

1 1i iRisk Risk

Return 1 Return 1i i

Search for alpha like ‘Optimal stopping problem’

Sample various ‘investments’ xj where xj~N(,2 )

Each investment costs c>0You get T draws (eg, 100)At any stage n, can stop and receive xn in

until TOptimal to sample until xn>k(c,n, 2 ,T),

where k is the criterion for stopping

As the cost of sampling goes up, propensity to stop searching increases

As the variance of the sampling information increases, the propensity to stop searching decreases

As the time left in the draw goes down, the propensity to stop increases

0kc

20k

0kj

You are willing to pay to take risk because you get value from the extra sampling in many cases (c>0)

Sampling more than once, for most parameters, will be the optimal solution for most situations

As time goes on, the ability to take such risk decreases because the benefits are not as great

High variance increases value for searchForms our intuition

Trying something to see if you have alphaTrying out for footballWriting poetryAppearing on American Idol

Most fail, miserably. Why it hurts to fail, it reflects on you.

Finding your best fit has big payoffsOutside of organized sampling as in school,

generally people will tell you, you have no chance

“That the automobile has practically reached the limit of its development”

Scientific American 1909 “Heavier-than-air flying machines are impossible”

Lord Kelvin 1895 “There is no reason anyone would want a computer in their

home”

Ken Olson 1977 “We stand on the threshold of rocket mail”

US postmaster general Arthur Summerfield 1959 “Nuclear-powered vacuum cleaners will probably be a reality in

10 years”

Alex Lewyt President of Lewyt Vacuums, 1955

People overconfident when they search for alpha

Good meta-strategy , bad investment strategyLeads to excess demand for super risky

assets

AAA-BBB spread, 3mo to 2 yr T-billsNo alpha searching herePrescience too hard to prove

Everyone needs some amount of safety assets, cash

Cash is a ‘medium of exchange’, a property many investments do not haveRepos (cash) have T-bills, AAA securities as

collateral

Risk

ExpectedReturn

No Alpha Possible, no hope,no benchmarking

Expensive Alpha Searching,Too much hope

Alpha Possible,Benchmarking