Experimental and Neuro Finance Elena Asparouhova (U Utah) and - - PDF document

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Experimental and Neuro Finance

Elena Asparouhova (U Utah) and Peter Bossaerts (Caltech) Melbourne, July 25, 2012

what we do

• We study financial decision making, all the way from the level of

markets (“asset pricing”) down to the individual (“behavioral finance”).

• We don’t just want to describe (GARCH, Prospect Theory,…);

we want to understand!

• Why do prices move to levels where only systematic risk is priced?
• Why are humans able to track risk – but confused about outliers

(black swans)?

• Our methodology: Experiments
• Observe humans make (financial) decisions and interact in a

controlled setting

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Experiments!?

• We eventually want to understand real-world financial

markets and the creatures that inhabit them (humans).

• Are these markets not “too big” and “too complex” to be

studied in the laboratory?

• Too complex? That is precisely their problem… They cannot be

described in terms of simple equations; so you need control, i.e., laboratory study

• Too big! Sure, but we have to start somewhere. Without

experimentation, we are "likely to go completely astray into imaginary conjecture” [Hannes Alfven, Nobel (Astro)Physics]

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Analogy with astrophysics

The TORPEX at EPFL, a tiny vacuum-like space where physicists generate “plasma” using a microwave “oven” in

• rder to study physical

processes inside stars (that float in a real vacuum). It’s small relative to the real stars, but the only way to be sure that we correctly interpret the “signals” that the stars send to us!

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More about experiments

• Asset pricing theory in particular is not ready for real markets; it

is too stylized, it leaves out too many details (taxes, intermediaries, ambiguity about returns, demographics, politics…)

• Yet it is ready for laboratory experiments (we hope to convince

you of this today): it makes precise predictions about prices and allocations, but still leaves out the details of how to get there

• Experiments lead to a deeper understanding of the theory

(Richard Feynman, Nobel Prize Winner)

• … and to new theory (in our case: about HOW markets

equilibrate)

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Two examples

• The CAPM
• Risk prediction in the human brain

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CAPM

• Theory: In equilibrium, the

expected return on risky securities is solely determined by their covariance with aggregate risk (“beta”)

• Equivalent: the “market

portfolio” will give you maximum expected reward for its risk (risk=return variance),

• r the Sharpe ratio of the market

portfolio is maximal

• Sharpe ratio = Expected return
• n portfolio minus riskfree

rate / return standard deviation

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Lab

• Anywhere from 20 to 30

subjects in the lab (up to 70 if participating from home).

• The participants are given

initial allocations of securities (called, say, A, B and Notes) and cash.

• Initial allocations are risky

and different for different subjects, and they can be improved upon through trading (with other subjects).

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LAB

• Each laboratory session is a repetition of the same situation, and each

repetition is called a period. 6-10 periods in a session.

• Period=Initial endowments, trading, final portfolios, payoff.
• Example:

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• Three markets (one riskfree, shortsales allowed), several pe-

riods.

• Three states; determine liquidation value at end of each pe-

riod; known probabilities. Security State X Y Z A 170 370 150 B 160 190 250 Notes 100 100 100

LAB

• Endowment of risky securities and cash, refreshed every pe-
• riod. E.g., 5 of A, 4 of B, and 400 cash (may vary across

subjects).

• Loan repayment of, say, 1900 at end of period (leverage!).
• Trade through a web-based open book system, Marketscape,

developed at Caltech. Example Of This Experiment: 011126

Draw Subject Signup Endowments Cash Loan Exchange Type Type Reward A B Notes Rate (#) (franc) (franc) (franc) $/franc D 18 125 5 4 400 2200 0.04 18 125 2 8 400 2310 0.04

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Logout Exit Market

Markets -- Actual

Marketplace closes in 01:56:25 Cash on hand: $500.0 A (5) Item: A B (4) Item: B Notes (0) Item: Notes

• Navigation

Order Form Messaging View Transaction Table Marketplace A B Notes

Order Type:

• Market:

A Price: $195.00 Units: 1 Total Value: $195.00

Messaging

Received Messages

mc: Markets will be called in 10 minutes mc: Markets will be called in 9 minutes mc: Markets will be called in 8 minutes mc: Markets will be called in 7 minutes

Message History

Price: 195.00

• CAPM PREDICTIONS
• The expected returns of each of securities A and B are

positively related to the betas of the securities

• The market portfolio is mean-variance efficient.
• The final portfolio of each individual should have risky

securities in the same proportion as in the market portfolio.

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Prices

• Prices of the two

securities are virtually the same.

• Expected payoff of

A is higher, i.e., expected return of A is higher.

• Precisely because

Beta(A)>Beta(B)

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Efficiency of market portfolio

• Compute Sharpe

ratio of market portfolio with each transaction.

• Take the difference

between Sharpe of the market and the highest Sharpe ratio.

• CAPM predicts

this difference should be 0.

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INDIVIDUAL Behavior

• For each of the 8

periods plot each subject’s final holdings of asset A.

• Red dot indicates the

proportion of A in the market portfolio.

• Individuals are all
• ver the place.

Allocations do not improve with time.

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1 2 3 4 5 6 7 8 0.2 0.4 0.6 0.8 1 period proportion

• 2. Risk prediction in

the human brain

• How does the human brain

process risk?

• Specifically, what are the

computational algorithms that the brain uses?

• How general are these

(algorithms)? Any potential flaws (that would explain cognitive biases)?

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On cognitive biases

• The human brain is a remarkably

adapted computational device

• But it does not do everything

right

• Example
• Knowing whether you are level

when flying through clouds

• Pilots need instrument rating to

get permission to fly through clouds)

• Important: there is NO WAY to

teach the brain to do this right! You need instruments

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a simple gamble

• With each card,

update:

• EXPECTED

REWARD

• RISK

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Risk and reward

• Expected reward

increases linearly

• Risk (reward

variance) is quadratic

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Functional magnetic resonance imaging (fMRI)

• Subjects play game

repeatedly while brain is being scanned in fMRI

• Measures brain

activation indirectly (through blood flow)

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Neural activation correlating with risk

• fMRI signal

per level of reward probability; averaged across subjects

• Activation

AFTER seeing first card

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Anterior insula

• Known to “convert” emotions

into “feelings”

• (Ability to sense heartbeat ~

size)

• Related to self-awareness
• Activates especially in reaction

to disgust, pain

• Involved in empathy

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Cool mathematics in a quintessentially emotional part of the human brain!

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Neural activation correlating with risk prediction error

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• Traditional reward prediction

error: reward minus expected reward

• Risk = expectation of size of

reward prediction error

• Risk prediction error

fMRI evidence

Risk prediction error after first and second card. No risk, and hence, no risk prediction error if first card is 1 or 10

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Effectively, brain signals whether there are outliers

• Is size of realized reward

prediction error bigger than expected?

• If so, things may have

changed…

• Regime shifts
• This, however, is not always the

right interpretation! Black swans are not unusual…

• Does the brain distinguish?

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Pupil dilation

• Pupil dilation
• … correlates with risk prediction

error

• There is a link with phasic

changes in norepinephrine levels

• Could study this

pharmacologically (propranolol?)

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Final remarks

• We are bringing finance to the laboratory, in order to distinguish what is

intrinsically wrong from what is wrong because we don’t know the parameters.

• We have seen some fundamentals concepts in asset pricing theory at work, like
• CAPM. What we learned: the system has its own laws, different from the individuals
• We started exploring things where the theory is not quite right
• We have seen excessive volatility, but it does not affect allocations (welfare)!
• We are beginning to understand how markets equilibrate
• We have started to explore the neurobiological foundations of cognitive biases –

the brain uses specific algorithms to track the environment, and these may not always be well adapted to financial markets

• Implementation of the algorithms often engages emotions – emotions are part
• f “reasoned” decision making

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