3. Prospects Theory
Economists assume each individual has a function that maps from every
possible relevant level of wealth to a number that represents his or her
happiness,
and that under uncertainty each individual acts to maximize the expected level
of happiness.
(Exception - One objection to expected utility is known as the Allais Paradox.)
A second problem with expected utility maximization lies in the assumption
that individuals make decisions under uncertainty based solely on the eventual
levels of his or her wealth.
4. The Reference Point
According to Kahneman
In addition to what you already own, you receive $1,000 for sure and either:
Another $500 for sure, or
A 50 percent chance of nothing and a 50 percent chance of $1,000.
Second, consider this alternative set of choices.
In addition to what you already own, you receive $2,000 for sure and either:
Lose $500 for sure, or
Face a 50 percent chance of losing nothing and a 50 percent chance of losing
$1,000.
A large majority of respondents picked the first option in the first choice set and
the second option in the second choice set.
5. The Reference Point
What is different in the two examples is the reference point.
In the first example, individuals use an initial wealth of $1,000 as their
beginning reference point.
When considering their choices, they exhibit risk aversion, preferring the
certain gain of $500 over a risky choice with an identical expected value.
In the second choice set, individuals consider $2,000 as their reference point
and see a decision between a certain loss or a risky alternative with the
identical expected value.
In this case, the majority of individuals choose the latter option—the risky
one—even though there is no risk premium to compensate them for the
expected risk.
In this second choice situation, individuals tend to be risk seekers, not risk
averters, as in the first choice.
6. The S-Curve
Consider another choice between two lotteries:
- Get $900 for sure, or
- Have a 90 percent chance of getting $1,000.
Now consider this alternative set of choices:
- Lose $900 for sure, or
- Have a 90 percent chance of losing $1,000.
7. The S-Curve
In the first choice set, the expected value of each option is $900. Since
the latter option carries more risk,
- a risk-averse individual would choose the first option,
- a risk-loving individual would choose the second.
In the latter choice set, both options have an expected value of —$900
(i.e., losing $900).
- The second option would be chosen only by a risk-loving person,
- A risk-averse individual would choose the first option.
8. The S-Curve
In practice,
- most individuals choose the first option in the first choice set as
expected.
- most choose the second option in the second choice set.
In other words, when facing potential losses, individuals become risk
loving rather than risk averse.
This occurrence is irrespective of their initial levels of wealth
all that matters is that they take their current levels of wealth as their
reference points and face losses from there.
9. The S-Curve
- Typical of the way people make choices
when facing potential losses, which is
fundamentally different than the way
people make choices when facing potential
gains
- For gains, an individual's utility function is
concave, representing his or her risk
aversion.
- Conversely, for losses, the utility function is
convex, representing risk-loving behavior.
10. Loss Aversion
- The segment of the curve representing losses is steeper than that representing gains.
- This reflects the fact that for the representative individual, losses hurt much more
than commensurate gains help.
- As an example, consider choosing whether to take a gamble in which you have
- a 50 percent chance of getting $150 .
- a 50 percent chance of losing $100.
Despite the positive expected value, most people find this lottery unappealing because
the psychological cost of losing $100 is greater than the psychological gain of earning
$150.
- This phenomenon is called loss aversion.
- In the previous example, some may need a potential gain of $200 or so, or about
twice as high as the loss, to accept the gamble.
- This loss aversion ratio has been estimated at between 1.5 and 2.5 in practice.
11. Loss Aversion (Matthew Rabin)
- Rabin shows that any individual with a concave utility function in
wealth that rejects the gamble
- “50 percent chance of losing $100 and 50 percent chance of gaining
$200” also rejects the gamble
- “50 percent chance of losing $200 and 50 percent chance of winning
$20,000.”
In practice, many people might reject the former gamble, whereas very
few would reject the latter.
12. Loss Aversion (Matthew Rabin)
- Rabin showed that under traditional decision theory,
- an individual with initial wealth of $290,000 who would reject a 50/50 gamble of
losing $100 or gaining $110 for any initial level of wealth under $300,000 must also
reject a 50/50 gamble of losing $1,000 or gaining $718,190.
- Finally, one who would reject a 50/50 gamble of losing $100 or gaining $125 for any
initial level of wealth must also reject a 50/50 gamble of losing $600 or gaining any
positive amount of money, regardless of how large the potential gain .
It is not likely that these implications would hold up in practice.
- One could envision an individual rejecting a 50/50 gamble of winning $100 or losing
$110,
- but it is hard to envision someone rejecting a 50/50 gamble of losing $600 or winning
$10 million.
13. Loss Aversion (Matthew Rabin)
- When looking at the decisions an individual makes over time,
- traditional wealth-based utility theory looks at the net change in
wealth over the course of all decisions to assess the overall impact on
utility.
- Under prospect theory, one must look at each of the movements in
wealth in turn because the path one takes to get from initial wealth
to ending wealth impacts the overall change in happiness.
14. Prospect Theory in Practice
- Prospect theory has been tested in a variety of experimental
settings, even in contexts outside of finance
- behavior of individuals in a well-functioning marketplace and found
that newcomers to the marketplace behaved in better accordance
with prospect theory than with traditional utility models.
- Bleichrodt and colleagues examine the behavior of individuals
when the payoffs are in states of health rather than in monetary
amounts and also finds that prospect theory explained the agents'
behavior better than traditional expected utility theory
15. Prospect Theory in Practice
- If investors consider paper gains and losses each time they check
their portfolios, then not only will loss aversion tend to drive their
choices, but the frequency with which they check their portfolios will
greatly affect the decisions they make as well
- How frequently one checks one's portfolio will lead to different levels
of utility and to different investment decisions. Such behavior could
account for a significant premium in markets with more active
investors despite any risk factors for which such a premium should be
rewarded
16. Drawback of Prospect Theory
- Despite the benefits of prospect theory in modeling how humans
make decisions, the theory is not complete.
- There are many aspects of human behavior that are inconsistent with
the implications of prospect theory
- A one in a thousand chance to win $1 million.
- A 90 percent chance to win $10 and a 10 percent chance to win
nothing.
- A 90 percent chance to win $1 million and a 10 percent chance to win
nothing.
17. Drawback of Prospect Theory
Second drawback of prospect theory, consider the following gamble
choice:
- A 90 percent chance to win $1 million and a 10 percent chance to win
nothing, or
- Receiving $10 with certainty
- versus this one:
- A 90 percent chance to win $1 million and a 10 percent chance to win
nothing, or Receiving $100,000 with certainty, and consider how one
would feel after choosing the gamble and receiving nothing in each
case.