Risk, Psychology, and Behavior

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Risk, Psychology, and Behavior

• FIN285a Lecture 5
• Fall 2006
• (no readings)

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Outline

• St. Petersburg paradox
• Mistakes
• Probability mistakes
• Overconfidence
• Gamblers Fallacy
• Behavior
• Uncertainty versus risk
• Envelope problem
• Loss aversion
• Framing
• Regret

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Evaluating a Risky Situation(Try expected value)

• Problems with E(x) or mean
• Dispersion
• Valuation and St. Petersburg

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Dispersion

• Random variable 1
• Values (4 6)
• Probs (1/2, 1/2)
• Random variable 2
• Values (0 10)
• Probs (1/2 1/2)
• Expected Values
• Random variable 1 5
• Random variable 2 5

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Dispersion

• Possible answer
• Variance
• Random variable 1
• Variance (1/2)(4-5)2(1/2)(6-5)2 1
• Random variable 2
• Variance (1/2)(0-5)2(1/2)(10-5)2 25
• Is this going to work?

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Valuation and the St. Petersburg Paradox

• Another problem for expected values

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One more probability reminder

• Compound events
• Events A and B
• Independent of each other (no effect)
• Prob(A and B) Prob(A)Prob(B)

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Example Coin Flipping

• Random variable (H T)
• Probability (1/2 1/2)
• Flip twice
• Probability of flipping (H T) (1/2)(1/2) 1/4
• Flip three times
• Prob of (H H H) (1/2)(1/2)(1/2) (1/8)

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St. Petersburg Paradox

• Game
• Flip coin until heads occurs (n tries)
• Payout (2n) dollars
• Example
• (T T H) pays 23 8 dollars
• Prob (1/2)(1/2)(1/2)
• (T T T T H) pays 25 32 dollars
• Prob (1/2)(1/2)(1/2)(1/2)(1/2)

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What is the expected value of this game?

• Expected value of payout
• Sum Prob(payout)payout

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How much would you accept in exchange for this
game?

• 20
• 100
• 500
• 1000
• 1,000,000
• Answer none

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St. Petersburg Messages

• Must account for risk somehow
• Sensitivity to small probability events

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St. Petersburg Probability Density
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Outline

• St. Petersburg paradox
• Mistakes
• Probability mistakes
• Overconfidence
• Gamblers Fallacy
• Behavior
• Uncertainty versus risk
• Envelope problem
• Loss aversion
• Framing
• Regret

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Probability

• Difficult for humans
• Conditional probabilities harder
• Information -gt Decisions

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Linda is 31 years old, single, outspoken, and
very bright. She majored in environmental
studies. She is an avid hiker, and also
participated in anti-nuclear rallies.
Which is more likely? A.) Linda is a bank
teller. B.) Linda is a bank teller and a member
of Green Peace.
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Probability Mistakes

• Medical tests
• DNA evidence
• Sports
• Game shows (Monty Hall)

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Overconfidence

• Forecasts
• Ask forecasters for 95 confidence bands
• About 60 percent of actual values fall inside
• Trading
• More frequent traders generate inferior
  performance

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Gamblers FallacyLaw of Small Numbers

• Decisions made on short data sets
• Hot Hands
• Mutual funds
• Patterns seen in short data sets
• Technical trading
• Is this really irrational?
• Econometrics and regime changes
• New Economy

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Our proprietary portfolio of New Economy stocks
was up over 80.2 in 1998!
At this rate, 10,000 turns into 3.4 million in
10 years or less!
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Outline

• St. Petersburg paradox
• Mistakes
• Probability mistakes
• Overconfidence
• Gamblers Fallacy
• Behavior
• Uncertainty versus risk
• Envelope problem
• Loss aversion
• Framing
• Regret

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Uncertainty versus Risk(Frank Knight)

• Risk
• Fully quantified (die)
• Know all the odds
• Uncertainty
• Some parameters (probabilities, values) not known
• Risk assessments might be right or wrong

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Ellsberg Paradox

• Important risk/uncertainty distinction

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Ellsberg Paradox

• Urn 1 (100 balls)
• 50 Red balls
• 50 Black balls
• Payout 100 if red
• Urn 2 (100 balls)
• Red black in unknown numbers
• Payout 100 if red
• Most people prefer urn 1

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What are we all doing?

• People chose urn 1 to avoid uncertainty
• Go with the cases where you truly know the
  probabilities (risk)
• Seem to feel
• What you dont know will go against you

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Donald Rumsfeld on Uncertainty
Reports that say that something hasn't happened
are always interesting to me, because as we know,
there are known knowns there are things we know
we know. We also know there are known unknowns
that is to say we know there are some things we
do not know. But there are also unknown unknowns
the ones we don't know we don't know.
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Envelope Problem

• Sealed envelopes (A and B) with money in them
• One has twice the money of the other (random)
• Game
• Randomly hand envelopes to Mary and Jim
• Ask them if they want to trade
• Do they?
• Assume you have x in your envelope
• Expected values x versus (1/2)x or 2x
• (1/2)(1/2)x (1/2)2x (5/4) x
• Switch
• Both want to trade

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Loss Aversion

• Fear of losses
• Reference points
• Worry about changes in wealth, not wealth
• House money
• Where did you buy Yahoo stock?

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Framing

• Context and presentation matters
• People often consider risks in narrow context
  (narrow framing)
• Interesting applications
• Medical diagnoses
• Prob of death versus prob of living
• Portfolio diversification
• One stock at a time

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Implications of Narrow Framing

• Poorly diversified portfolios
• Bad estimates of overall market risk
• Beta (correlation with market)

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Regret

• Negative feelings about past decisions
• Hold losing stocks
• Avoid possible regret if price comes back up
  after you sold
• Hope to regain reference point (price bought at)

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Outline

• St. Petersburg paradox
• Mistakes
• Probability mistakes
• Overconfidence
• Gamblers Fallacy
• Behavior
• Uncertainty versus risk
• Envelope problem
• Loss aversion
• Framing
• Regret

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Where Are we on Risk?

• Need to measure/assess risk
• No definitive measure
• Psychology of risk
• Perceptions of risk
• Probability mistakes
• Well proceed with fairly simple/intuitive
  measures
• Measuring risk
• Presenting risk
• Digesting risk (difficult)