On Investor BehaviorOn Investor Behavior

ObjectiveObjective

Define and discuss the concept of rational behaviorDefine and discuss the concept of rational behavior

OutlineOutline

• Definition

• On utility functions

• The axioms of utility

• Implications

Investment behaviorInvestment behavior

The “rules” that govern our approach to making investment choices

Risk:

Probability of loss

Probability distribution known

Uncertainty:

Probability of loss anywhere between 0 and 100%

Probability distribution unknown

Investment behavior: Why is it important?Investment behavior: Why is it important?

• Theories in finance

• Design of financial institutions

• Design of investment strategies

• Performance evaluation

Investment choice under certaintyInvestment choice under certainty

Choice A: 10% return with a probability of 100%

Choice B: 16% return with a probability of 100%

Decision rule: Maximum return

Investor behavior under uncertainty & riskInvestor behavior under uncertainty & risk

Rational or irrational?

Rational behaviorRational behavior

Determined by the utility functionDetermined by the utility function

Utility function:

A theoretical construction describing how individuals relate wealth (money) and personal satisfaction (utility)

Utility functions axioms that describe investor behavior under Utility functions axioms that describe investor behavior under uncertaintyuncertainty

• Greed (nonsatiation)

• Decreasing marginal utility

• Comparability

• Consistency

• Measurability

Do individuals are aware of their utility functions?Do individuals are aware of their utility functions?

That’s beside the point

What matters:

If behavior can be described by a utility function

Observed behavior: Observed behavior: GreedGreed

Individuals prefer more over less.

Observed behavior: Observed behavior: Comparability & measurabilityComparability & measurability

Individuals can compare various choices

Individuals can measure the performance of each choice

Observed behavior: Observed behavior: Decreasing marginal utilityDecreasing marginal utility

Choose between options A and B:• A: do nothing• B: toss a coin; gain $5,000 if heads, lose $5,000 if tails

Your choice is consistent with a concave utility function

More on observed behaviorMore on observed behavior

Toss a coin. You receive:

• $1 if heads appears on the first throw

• $2 if heads first appears on the second throw

• $4 if heads first appears on the third throw

• $8 if heads first appears on the fourth throw

• etc.

How much are you willing to you payare you willing to you pay to be allowed to play this game?

Should the admission ticket reflect the expected payoff of the game?

More on observed behavior:More on observed behavior:

Expected game payoff: E(x)

E(x) = (1/2)($1) + (1/4)($2) + (1/8)($4) + …+ (1/2n)($2n-1) +...

E(x) = 1/2 + 1/2 + 1/2 +….+ =……infinity

In theory, one should be willing to pay an infinite amount to be allowed to play this game!

More on observed behaviorMore on observed behavior

Under uncertainty and risk, individuals do not simply maximize expected return.

What then?

More on observed behaviorMore on observed behavior

Do individuals maximize expected utility?

EU(x) = (1/2)U($1) + (1/4)U($2) + (1/8)U($4) + …+ (1/2n)U($2n-1) +… = ??

If U(x) = square root(x)

EU(x) = (1/2)($1) + (1/4)($2)1/2 + (1/8)($4)1/2 + …+ (1/2n)($2n-1)1/2 +…

EU(x) = $2.914

More on observed behavior: More on observed behavior: Decreasing marginal utilityDecreasing marginal utility

Individuals maximize expected utility in a way that appears consistent with concave utility functions.

More on investment choice under risk and uncertaintyMore on investment choice under risk and uncertainty

How do individuals choose among A, B, and C?

Why do individuals buy insurance?

Why do individuals gamble?

A B CReturn Probability Return Probability Return Probability

-8% 0.25 -4% 0.25 -20% 0.116% 0.5 8% 0.5 0 0.624% 0.25 12% 0.25 50% 0.3

How do individuals choose among A, B, and C?How do individuals choose among A, B, and C?

If utility functions are concave (rational behavior):

maximizing expected utility =

maximizing expected return while minimizing risk

Individuals want as much Individuals want as much return return as possible with as little risk as possibleas possible with as little risk as possible

Implication of rational behaviorImplication of rational behavior

Individuals:

• produce the best estimates of future cash flows and risk, given the available information

• optimize their portfolios

• accommodate their risk preferences by choosing an optimum mix of cash and risky securities

…always

SummarySummary

Rational behavior is describing how we make investment decisions.

Rational behavior is a a view that has shaped our financial markets and institutions

Rational behavior is a belief widely held by many financial professionals and regulators