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ECOS3997 finance

创建日期：2024-06-01 14:56:30

所属分类：经济Economics

标签： ECOS3997

finance

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Prospect Theory in Gambling

ECOS3997
Prospect Theory: Review
Reference Dependence: the value function is defined over gains and losses relative
to some reference point.
Loss Aversion: the value function is steeper over losses than for gains.
Diminishing Sensitivity: the value function is concave over gains, and convex over
losses.
Probability Weighting: people tend to overweight low-probability events, and
underweight high-probability ones.

Gambling and Loss Aversion?
Upon “discovering” prospect theory, gambling researchers recognised that the concept
of loss aversion was of prima facie relevance to them. The trouble is that loss aversion
seemed to have two contradictory implications for gambling ...
It should make gambling less attractive in the first place. On slide 3, a loss averter
whose reference point is at zero would refuse a 50/50 gamble to win or lose $10.
This suggests that gamblers might be less loss averse than non-gamblers.
On the other hand, loss aversion seems pertinent to loss chasing: continuing to
gamble in an effort to recoup past losses. A gambler who already lost $10 would
accept a new 50/50 gamble, because it offers a chance to get back up to zero.
So gamblers who chase losses might be more loss averse than ones who don’t.

Gambling and Loss Aversion?
Given these conflicting hypotheses, it’s unsurprising that no significant difference in loss
aversion was found when comparing problem gamblers (PG) to “healthy controls” (HC).
But for the first hypothesis we should really compare gamblers to non-gamblers,
while for the second we should compare gamblers who do and don’t chase losses.
In light of this, the most interesting finding may be that problem gamblers appear to
have a more bimodal distribution of loss aversion than the controls.

Digression: The Disposition Effect
The preceding discussion is reminiscent of earlier debates over the role of prospect
theory in explaining the disposition effect in finance. This describes the reluctance of
investors to sell off assets that have fallen in value since they were first purchased.
The explanation in terms of prospect theory is that, by continuing to hold a losing
asset, the investor can take a chance that it might bounce back to its original value,
thereby escaping a loss.
It was later pointed out that prospect theory does not provide a complete account:
If investors are loss averse, they would be reluctant to buy assets in the first place!

Loss Chasing, Revisited
It’s worth emphasising that loss chasing is a key feature of at-risk gambling behaviour:
of the DSM criteria for Gambling Disorder, it is the one that is most frequently reported.
Moreover, Kahneman and Tversky (1979) themselves recognised it as an implication of
prospect theory:
a person who has not made peace with his losses is likely to accept gambles that
would be unacceptable to him otherwise.
However, both loss chasing and the disposition effect have less to do with loss aversion
than other features of prospect theory, specifically diminishing sensitivity toward losses.

Loss Chasing, Revisited
Recall that diminishing sensitivity implies risk seeking for losses. This, not loss aversion,
drives both loss chasing (in gambling) and holding on to losers (in investment).
In fairness, the finance literature recognises this; some gambling research may not.
Loss aversion says the value function is less steep for gains than losses. But loss chasing
/ holding takes place entirely on the loss segment of the function!
Loss aversion suggests you would stop chasing / holding when (or if) you manage
to get back to “break even”: after this the incentive to keep going is much reduced.
But this is a relatively minor part of the story (when to stop, not why to chase).

Loss Chasing, Revisited
Finally notice that the diminishing sensitivity story assumes that the reference point
remains fixed at its original position:
The initial position before experiencing any gains or losses from gambling.
For the investor, the original purchase price paid for an asset.
That is, the decision maker does not reset their reference point before moving on to the
next decision (“make peace with their losses”). If they did, they would just stop playing.
Instead they fight to get back to a past position. This suggests a role for two additional
behavioural phenomena: honouring sunk costs, and mental accounting.

Honouring Sunk Costs
We honour sunk costs when we persist in something on account of resources invested
in the past, which can no longer be recovered (“throwing good money after bad”).
Every student of economics and business has learnt that sunk costs shouldn’t influence
choices: rational decision-making only considers avoidable future benefits and costs.
Moreover there are many proverbs that express the same folk wisdom:
Don’t cry over spilt milk.
It’s water under the bridge.
When you’re in a hole, stop digging!
Past gambling (and investment) losses are sunk costs, which should not influence future
behaviour. Loss chasing / disposition honour these sunk costs, and are thus irrational.

Mental Accounting
First developed in a series of articles by Richard Thaler, the idea of mental accounting is
that people compartmentalise money into separate “pots” depending on where it came
from, and what they intend to use it for.
Two established principles of mental accounting are that:
It is painful to close a mental account with a loss.
Money in different accounts may have different rules for how it may be spent.
Mental accounting violates the principle of fungibility of money (every unit of money is
interchangeable with every other), and is thus irrational.

End-of-Day Effect
This is a specific form of loss chasing observed in racetrack betting. It involves choosing
long-shot bets increasingly as the end of the day approaches.
This can be explained by bettors opening a new mental account at the start of each
race day, and closing it at the end. Closing an account with a loss is painful, and the
longshot bet offers a possibility to avoid this.
If the account was left open, it would be just as “effective” to bet on a longshot at the
start of the next day. But this is not what happens.

Realisation Effect
A clever laboratory experiment by Imas (2016) studied the effect of exogenously closing
a mental account, versus leaving it open. Participants made a series of choices over how
much money to bet on a lottery that had a 1-in-6 chance of paying out.
In the “realised” treatment, accumulated gains or (more likely) losses were physical-
ly settled by exchange of cash, immediately before the last round of bets. This was
hypothesised to reset the reference point to zero (like the start of a new race day).
In the “paper” treatment, no gains or losses were paid until the end of the session,
“leaving the account open” at the start of the last round (like last race of the day).
The outcome of interest is whether risk taking increases or decreases in the last round.
What do you think he found?

House Money Effect
Thaler and Johnson (1990) describe another form of mental accounting: people tend to
be more profligate in how they spend windfall gains.
Windfalls might include things like tax refunds, COVID stimulus payments, inheri-
tances, etc., but also wins in gambling and paper profits on investments.
Since money is fungible, we ought to treat windfalls the same as any increase in wealth.
Instead we may put them in a separate “pot”, with different rules for how it can be spent.
Extravagant dinners or holidays instead of paying down debt or saving for the
future, but also riskier gambles and investments using the unexpected winnings.

Loss Chasing vs. House Money
As applied to gambling (and investment), loss chasing and the house money effect
make somewhat conflicting predictions:
Loss chasing implies increased propensity to take risks following a loss.
House money implies increased propensity to take risks following a gain.
The key point is that both behaviours are irrational, and for the exact same reasons:
Money is money (is fungible).
Rational decision-making should only consider avoidable future benefits and costs.
What happened in the past is water under the bridge.ECOS3997 | Dr Stephen L. Cheung
20
Probability Weighting and Gambling
Up to now, short of invoking some unspecified source of consumption utility, we still
lack a good explanation for why people choose to gamble in the first place.
Expected utility requires implausible shapes for the utility function.
In the prospect theory value function, loss aversion serves to deter gambling.
The prospect theory probability weighting function provides a simple explanation:
people tend to overweight low-probability events relative to the objective probability.
Moreover, since overweighting ( ) applies to both the best gains and
worst losses, this also accommodates simultaneous gambling and insurance.

Probability Weighting and Gambling
The only remaining difficulty is to explain gambles over moderate-probability events,
such as betting on red or black in roulette.
In the weighting function on slide 4, a 50/50 event is mildly underweighted:
.
A couple of studies have measured the probability weighting of gamblers. As before for
loss aversion, they focus on comparing problem gamblers to controls.
A first study only considered gains, finding gamblers overweighted more than controls
across the full range of probabilities (for gamblers, ). But this result might
be incomplete if gamblers also treat losses differently to controls.
A second study also considered losses, replicating the result for gains and finding no
difference in probability weighting between groups for losses.

Source: Ligneul et al. (2013). 23
Source: Ring et al. (2018). 24
Source: Ring et al. (2018). 25
Probability Weighting vs. Distorted Beliefs
Remember that probability weighting can occur even when people have correct under-
standing of the true probabilities.
For example, someone might know that a fair dice has 1/6 chance to land on 1, but
still attach a larger than 1/6 weight to that event in their decision making.
In the next topic we’ll examine some reasons why people’s beliefs about the likelihood
of different events may differ from the true probabilities.

Week 5 Tutorial
“Favourite-longshot bias” is the tendency for long-shot bets to be systematically over-
valued given how rarely they win, and favourites undervalued given how often they win.
You will be asked to write about how this bias can be explained, focusing on the pref-
erences and beliefs of bettors, both in standard and behavioural economics models.
Suggested readings:
Thaler and Ziemba (1988), “Parimutuel Betting Markets: Racetracks and Lotteries”,
Journal of Economic Perspectives, 2(2): 161-174 (especially Commentary section).
Snowberg and Wolfers (2008), “Examining Explanations of a Market Anomaly:
Preferences or Perceptions?”, Chapter 7 in Hausch and Ziemba (eds.) Handbook of
Sports and Lottery Markets (Sections 1 to 3 only).

Week 5 Tutorial
Some advice on this assignment:
Not everything in the readings is relevant to the topic at hand. Just skip the rest.
No need to get bogged down in details of racetrack betting, odds arithmetic etc.
You don’t need to worry about any effects driven by the behaviour of bookmakers,
or market-level interactions between different types of bettors.
Some non-academic material on the internet is confused or unclear, because the
writers do not understand the models as well as you do.
In addition to weeks 3 and 4, some concepts from week 2 will also be relevant.
It is better to cover fewer ideas (maybe three major explanations) and show you under-
stand them well, than give a muddled description of overly detailed and complex ideas.

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