People don’t like to lose things or money. Earlier this year I
wrote a post called “It’s hard to say good bye” which described applied loss aversion. In this post I’ll focus more on the
theoretical part of loss aversion.
Loss aversion is the trait that
people don’t like losses. Not only we
don’t like to lose, we actually hate losing. In order to better understand
let’s go in the world of decision making research and focus on a couple of
gambles.
In the first gamble is 50% chance of gaining 100 Euros and a 50%
chance of losing 100 Euros.
What is your attitude about this
gamble? Would you be willing to take it?
It’s a 50-50 chance of either winning or losing 100 Euros. Will you take it?
Most likely your answer is a definite “NO” and most people in the
world would be giving the same answer.
From a strictly rational (normative economics) perspective, this answer is at
least weird. The reason is that the objective value of this gamble is 100*0.5
+ (-100)*0.5=0. If the objective expected value is zero, then you should be
indifferent to the gamble and take it (or at least more people would take it).
But you and most (normal) people in the world would not even consider taking
this gamble.
The idea of being indifferent to
a gamble basically means that you are equally inclined to take and to not
taking it.
The second gamble is 50% chance of gaining 110 Euros and a 50%
chance of losing 100 Euros.
What is your attitude about this
gamble? Would you be willing to take it?
It’s a 50-50 chance of either winning 110 Euros or losing 100 Euros. Will
you take it?
Most likely your answer is still “No”. At the same time you have already
learned how to compute the objective value of the gamble and by applying the
very simple formula of 110*0.5 + (-100)*0.5=5. As you can see this gamble has a
positive objective expected value. From
a normative economics (rational) perspective everyone should be willing to take
this gamble, but again most people are not willing to take it.
The third gamble I am proposing is 50% chance of gaining 150 Euros
and a 50% chance of losing 100 Euros.
What is your attitude about this
gamble? Would you be willing to take it?
It’s a 50-50 chance of either winning 150 Euros or losing 100 Euros. Will you
take it?
To be honest I don’t know your
answer here, but I would guess it is more
likely “No” than it is “Yes”. Again you can compute the objective expected
value of the gamble by applying the very simple formula of 150*0.5 +
(-100)*0.5=25. From a rational
perspective everyone should be willing to take this gamble… after all its
objective expected value is 25 Euros which is not exactly spare change.
Compared with the second gamble,
in the third one I believe that more people would be willing to take the
gamble. At the same time, there would still be people who would refuse to take
this gamble, although it has an objective value that is positive and
significant.
The fourth gamble I am proposing is 50% chance of gaining 200 Euros
and a 50% chance of losing 100 Euros.
What is your attitude about this
gamble? Would you be willing to take it?
It’s a 50-50 chance of either winning 200 Euros or losing 100 Euros. Will you
take it?
Again I’m not sure that your
answer is “Yes”, but I would assume it to
be most likely “yes”. The objective expected value of this gamble is 50
Euros and I guess most people would take the risk of losing 100 Euros for the
equal opportunity to gain 200 Euros.
A skeptic would say that in order for people to accept a gamble they
need a consistent expected value outcome such as 50 Euros. But let me address
this objection through the following (fourth)
gamble:
50% chance of gaining 10 Euros and a 50%
chance of gaining nothing.
Would you take this gamble? The answer is most likely “Yes”. At the same time you were not willing to
take gamble number two (50% chance of gaining 110 Euros and a 50% chance of
losing 100 Euros) which has the exact same expected value of 5 Euros.
This (apparent) paradox can be
explained by looking at the differences between gamble number two and four.
Although they have the same objective expected value (5 Euros) they are very
different in the sense that gamble number two involves the possibility of a
loss, while gamble number four has no potential loss. In the worst case
scenario in gamble number four you will not win anything. In the worst case scenario
in gamble number two you would lose 100 euros.
This is an illustration of loss
aversion. In other words losses hurt more than winnings bring pleasure. To
better understand this, imagine that there is a unit of measure for pleasure and pain called “hedon” (from
hedonic). A gain of 100 Euros gives a
pleasure of X “hedons”. At the same time, a loss of 100 Euros gives a pain
(negative pleasure) of –A*X “hedons”. Here “A” is the loss aversion
coefficient.
Going back a bit to the first
three gambles, we see that the main differences among them consist of the ratio
between the amount of gain and amount of loss. In the first gamble the ratio is
1, in other words the amounts of gain and loss are equal (100 Euros). In the
second and third gambles this ratio is not 1, namely the amount of gain is
bigger than the amount of loss. Still (most) people would not be willing to
take these gambles.
Only in the fourth gamble where
the ratio is 2, the amount of gain is double that of loss (200 vs. 100 Euros)
most people would be willing to take the gamble. This is an illustration of the
existence of the “Loss aversion
coefficient” called “A” in the previous paragraph. A series of studies have
shown that this coefficient is roughly “2”
in the sense that a loss looms twice as
large as an equal gain.
I have to make a note here. The
loss aversion coefficient is ROUGHLY 2, namely this is an average. For some
people it is smaller, for others larger. In some situations it is smaller in
other situations it is larger. At the same time, there is little variation, so
saying that the loss aversion coefficient is “2” is overall a safe estimation.
Loss aversion has two major implications. First, people would put in
more effort to avoid a loss than they would in order to obtain an equal gain.
For example people would work twice as hard to avoid losing 10 Euros already paid
and non-refundable than they would work to gain 10 Euros.
The second implication is that when it comes to losses people become
risk seeking.
When it comes to gains people are risk averse. I’ve detailed this
in Certainty and Possibility Effects
To refresh your memory, if you
would have to choose between the
following two options:
Option A: 100 Euros For sure
Option B: 50% chance of winning
220 Euros and 50% chance of winning nothing.
Most likely your choice is option A. The same goes for most people.
At the same time if we look at the second option and compute the objective
expected value, it is 110 Euros. In essence you (and most people) prefer a smaller objective expected value for
sure than a higher objective expected value with risk involved. This is called “Risk
Aversion”.
When it comes to losses, however, things are quite different.
Again, you have to make a choice between
two options:
Option C: losing 100 Euros for sure
Option D: 50% chance of losing 220 Euros and 50% chance
of losing nothing.
Most likely your choice is option D. The same goes for most people.
If we look at the objective values of the two options we see that option D has
a higher negative expected value (-110 Euros).
If we look at options A&B and
C&D, we see that they are very similar. The only difference is that options
A&B are gains while options C&D are loses. This (small) difference is
the cause of the big differences in preferences about risk. This is the second implication
of loss aversion, that it makes people more willing to take risks.
Up to this point I have presented
loss aversion and now it is time to acknowledge that there are some limitations
to it. I believe that loss aversion (really) exists and it plays a huge role in
human life. At the same time, loss
aversion is not always present. For example there are studies which have
shown that asking people to “Think like a trader” lead to the loss aversion to
decline or even disappear.
Another limitation of loss aversion is in the area of costs. For example a
shop keeper will not feel a loss when selling one of the products in the shop.
After all that is why he has a shop. Similarly the client will not feel the
money spent on the product (paid price) as a loss. The key idea is that costs
are not losses.
There is one note to be made
here. Costs are not losses as long as
people expect them. Remember that prospect theory states that any outcome
is perceived as a loss or a gain in relation with a reference point. For
example if you go to a restaurant for dinner, you expect to pay for the food,
for the drinks and to leave a tip (pay for service). None of these costs are
perceived as losses since you expect to pay them. But if you see on your bill
that the restaurant charged you for using their cutlery and for siting on a
chair then you will feel those costs as losses because they are unexpected.
To sum up, loses are perceived twice as larger than equal amount of
gains. People work harder to avoid losses and when it comes to loosing people
are more inclined to take risks of a higher loss in order to avoid a sure
smaller loss. Loss aversion is not always present; thinking like a trader makes
loss aversion smaller. Expected costs are not perceived as loses, but
unexpected ones are.
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