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Behavioural Finance

Prospect Theory and Loss AversionSession 3:Read Shefrin and Statman, 1984

Kahneman and Tversky, 1979

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Overview

Prospect theory as an alternative to utility theory attitudes towards risk might be different

under different circumstancesLoss aversion in financial behaviour

riding losers for too long selling stocks with gains

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What would you do?

A real estate investment example: Bill and his wife are in their early thirties and just

had their first child. A good friend James is an expert in real estate. James can find underdeveloped property that looks like mess but has great potential. After purchasing James cleans it up, divides into parcels and resells at substantial profit. During the past three years he sold most of his properties to one to two times what he has paid for them.Since he makes the purchases with borrowed funds, James has been earning a very high rate of return!

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What would you do?A real estate example (cont’d)

Some years ago James has gone through some personal problems and Bill was very helpful and supportive during those times. James wants to repay Bill for his kindness. So last year James recommended Bill join him by investing in a small rural tract and Bill did. This year James sold the tract for a 75% profit. Bill and wife are very happy! They bumped into James one evening and James is very enthusiastic about another deal. Bill and his wife want to set aside money for their baby doughter’s future, particularly her university education

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What would you do?

A real estate example (Cont’d) James tells them the details: Clear Lake is

worth $205,000. James will invest $102,500 and will be equal partners will Bill and his wife and follow the usual formula. Within a year he will sell all the lots for $459,000. Bill and his wife have $17,500 in savings and James assures them they can borrow the remaining $85,000 at an attractive interest rate. James is a great believer in leverage as it can offset inflation and taxes.

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What would you do?

On a scale of 1 to 10, how would you rank Clear Lake as an investment whose purpose is to fund university education in 15 years?

10.…9….8.…7.…6.…5.…4.…3.…2.…1 10 extremely suitable ,1 entirely

unsuitable

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What would you do?

A real estate example (Cont’d)Bill is making the payments on the $85,000 loan and not

earning anything on the $17,000 savings. Three months later Bill sees James and asks him how Clear Lake is doing. James says there is a small problem. Apparently the property has not been surveyed properly and lots can not be sold until the survey is complete and the survey is taking more time than anticipated. Moreover the original loan $85,000 has come due. Renewal is no problem but the bank renews only $75,000. Bill has to come up with the additional $10,000 himself. James is embarrassed but remains upbeat about the success of the project. Bill and his wife have saved exactly $10,000 in recent months.

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What would you do?

If you were in Bill’s or his wife’s position, how would you react emotionally?

Worried or anxious?Patient and believing?

If you were in Bills’ or his wife’s position

would you begin feeling regret?Would you feel anyone should be blamed?

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What would you do?

If you answered yes Who would you blame most?

James? Yourself? The situation?

How obvious does it seem to you that it would have gone that way?

Answer on a scale of 1 to 10

1….2….3…..4….5….6….7….8….9….101 very obvious, 10 impossible to predict

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What would you do?

A real estate example (Cont’d) Time passes…A year later James apologizes that it has taken

so long to get things moving. James says he will work things out so that Bill and his wife will not have to make any more payments on the loan. James will handle the financial details. To move up sales he will put up a model home on one of the lots.

Next time Bill sees James there is good news and there is bad news. Good news is the model home has been built and sold, the bad news is this has not stimulated additional demand. James says he feels terrible and proposes Bill to take over his interest in Clear Lake. Bill thinks OK, if I accept the offer I will avoid extra losses but if investment turns profitable I lose the chance to lower my loss and make a positive return.

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What would you do?

Put yourself in Bill’s shoes. If you sign over your interest to him you will have to

come to terms with your $27,500 loss. If you keep your interest you risk losing more money, but you might also recover your investment!

Would you tell James you understand that he is trying to help and come to terms with your loss and sign your interest over to him?

Would you remind James that he said this would pay for your child’s university education and you still expect to do that (keep your interest)?

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What would you do?

Six years have passed.James proposes that you sign your interest to him. James also tells you that one of the estate agents offers $35,000 for the unsold lots and together with the sale of the lot with model home ($8,900) total amount received would be $43,900. James says he has decided to accept the estate agent’s offer.

Would you tell James you understand that he is trying to help and come to terms with your loss and sign your interest over to him?

Would you remind James that he said this would pay for your child’s university education and you still expect to do that (keep your interest)?

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Prospect theoryKahneman and Tversky,1979

Utility theory is a normative model of choice under uncertaintysystematic violations of axioms

Prospect theory as a descriptive model of decision under uncertaintyrisk aversion in gainsrisk seeking in lossesinconsistent preferences when the same choice is

presented in different formsover-weighting of low probabilities

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What would you do?

You toss a coin. If you lose you lose £100 What is the minimal gain that would

make this gamble acceptable?

What sure gain is as attractive as 50% chance to gain £1,000 50% chance to gain nothing

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Value FunctionValue

Losses Gains

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What would you do?

You are facing the chance to win £20,000 Consider the following.

Are the differences significant to you? Can you order them by their impact on your

preferences?A. The probability is either 0 or 1?B. The probability is either 41% or 42%c. The probability is either 99% or 100%

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Non linear weighing of probabilities

Rational choice multiply utility by probability! Probabilities have equal weighting!

People deviate overweight low probabilities underweight high probabilities

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Who is more upset?

Andy owns stocks he bought for £100. The value of the stock was £160 yesterday and today it dropped to £150.

Becky owns stocks she bought for £200. The value of the stock was £160 yesterday and today it dropped to £150.

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Purchase price as a reference point

Disposition effect reluctance to realize losses!

A will perceive as a reduction in gainB will perceive as increased loss!

Odean, 1998 Investors are more likely to sell when

price increases

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What would you do?

Chose betweenA sure gain of £2400 25% chance to win 10,000

75% chance to gain nothing

Chose betweenA sure loss of £2400 75% chance to lose 10,000

75% chance to lose nothing

Chose between25% chance to win 2,400 25% chance to win 2,000 75% chance to lose 7,600 75% chance to lose 7,500

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Narrow framing

Investors consider decision problems one at a time do not adopt a broader frame

Narrow framing is mainly due to multiple mental

accounts (details next week!)

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Prospect theory

Accounts for observed attitudes towards risk risk aversion in gains risk seeking in

losses Over-weighting of small probabilities

lottery tickets, insurance policies

Gains and losses defined with a reference pointFraming (details next week!)

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Riding losers too long

Shefrin and Statman, 1985 Aversion to loss realization in financial

marketstax considerations can not explain patterns

in loss and gain realizationa wider theoretical framework

• mental accounting• regret aversion• self control

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Riding losers too longResearch Design

Question: Do investors time the realization of their losses differently from the realization of their gains?

Data:Individual Investors

• roundtrip duration of trades• 1964-1970

Mutual Funds• purchases and redemption of mutual fund shares• 1961-1973

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Riding losers too long

Analysis For all values of roundtrip duration (1

month to 12 months) 40% of trades realize losses!

The ratio of redemptions to purchases in gains is higher than that in losses!

Conclusion Investors ride losers for too long! Why?

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Summary

Prospect theory Risk aversion in gains risk seeking in

losses Over-weighting small probabilities narrow framing loss aversion-reference points

Riding losers for too long