EC4004Lecture 5

Uncertainty

Dr Stephen Kinsella

“I always avoid prophesying beforehand because it is much better to prophesy after the event has taken place.”

--Winston Churchill

Market DemandElasticityDiddy!

UncertaintyInduction

ProbabilityTurkeys!

3 Big Questions...

What is Risk?

What is Uncertainty?

How do we deal with their existence?

Bertrand Russell on Certainty:

“The demand for certainty is one which is natural to man, but is nevertheless an intellectual vice. If you take your children for a picnic on a doubtful day, they will demand a dogmatic answer as to whether it will be fine or wet, and be disappointed when you cannot be sure...”

...but so long as men are not trained to withhold judgement in the absence of evidence, they will be led astray by cocksure prophets...For the learning of every virtue there is an appropriate discipline, and for the learning of suspended judgement the best discipline is philosophy.

“The message is: That there are known knowns, There are things we know that we know, There are known unknowns, That is to say there are things that we now know, we don't know. But there are also unknown unknowns, There are things we do not know we don't know. And each year we discover a few more. Of those unknown unknowns.”

Epistemology

Study of the nature, sources, and limits of

knowledge

There is a turkey in this picture.

Growth of Turkey(Weight (kilos))

DaysXmas

Subprime CrisisIrish Budget DeficitSarah PalinHarry Potter

Induction+Uncertainty=Black Swan

Get it wrong in a Black Swan World:World of Pain

086 399 83 06

Probability of an event happening: is the relative frequency with which an event occurs

Gamblor Likes Probability.

Probability of “heads” coming up on a toss of a fair coin is ½.

That is, when the coin is tossed many times, we can expect “heads” to come up in approximately one-half of tosses.

Expected value of game with a number of uncertain outcomes: is the size of the prize that player will win on average.

On a single toss of a coin, Jones pays Smith €1 (X1 = + €1) if a tail comes up. Smith will pay Jones €1 (X2 = - €1) if a head comes up, the expected value of a game for both players is

If game changes so that, from Smith’s point of view, X1 = €10, and X2 = - €1, the expected value for Smith would be:

Because Smith would stand to win €4.50 on average, she might be willing to pay Jones up to this amount to play.

• Fair games are games that cost precisely their expected value.

When people face risky but fair situations, they will usually choose not to participate.

Risk aversion is tendency for people to refuse to accept fair games.

Mathematica

U

Income(thousandsof euros)

0 35 40 503020

Utility

33

Current €35,000 provides utility of U3.

Utility of €5,000 bet is the average of the utility of €40,000 (if a player wins) and utility of €30,000 (if a player loses).

Average utility is U2< U3.

The utility (U1< U2) of the €5000 bet is the average of the utility of winning (€50,000) and losing (€20,000).

U

U3U2

U1

Income(thousandsof euros)

0 35 40 503020

Utility

33

086 399 83 06

Insurance

U

U1

Income(thousandsof euros)

0 25 3520

Utility

Fair insurance: the premium equals the expected value of the loss.

UU2

U1

Income(thousandsof euros)

0 27.525 3520

Utility

UU2

U1

U0

Income(thousandsof euros)

0 27.52523 3520

Utility

Some risks are so unique or difficult to evaluate that insurers are unable to set premium rates - risks become uninsurable.

If events are so infrequent or totally unpredictable (such as wars, “Acts of God” etc.) then insurers have no basis for establishing premiums.

Diversification: is an economic version of “Don’t put all your eggs in one basket.”

• Diversification spreads risk among several options rather than choosing only one.

Suitably spreading risk may increase utility above that obtain by a single transaction.

Investing in 15,000 shares of company A yields a 50 percent chance of having €50,000 and a 50 percent chance of having €20,000.

Yields a utility level of U1.

If the person invests in 7,500 shares of each company, they face four possible outcomes shown in Table 5-1.

U

U1

Income(thousandsof euros)

0 35 5020

Utility

Each of four outcomes is equally likely; with half of cases, the investor ends up with the original €35,000.

Diversification strategy, while it still has an expected value of €35,000, has less risk.

Figure 5-3, point C represents when B does poorly, and D represents when B does well.

Point E, (the average of C and D) results from diversification, and yields utility U2 > U1.

086 399 83 06

A Utility-Maximizing Model

U1

U2

D

B

A

E

Certainty line

C2E

C2A

C1CE1 CA

1

C2

U1

U2

D

B

A

E

Certainty line

C2E

C2A

C1C1E C1

A

C2

Try: 5.1, 5.3, 5.5

UncertaintyInductionProbabilityTurkeys!

Game Theory

EC4004Lecture 5

Uncertainty

Dr Stephen Kinsella