On Investor Behavior

Objective Define and discuss the concept of rational behavior

Outline Definition On utility functions The axioms of utility Implications

Investment behavior The “rules” that govern our approach to making investment choices Risk: Probability of loss known Probability distribution known Uncertainty: Probability of loss anywhere between 0 and 100% Probability distribution unknown

Investment behavior: Why is it important? Theories in finance Design of financial institutions Design of investment strategies Performance evaluation

Investment 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 & risk Rational or irrational?

Rational behavior Determined 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 uncertainty Greed (nonsatiation) Decreasing marginal utility Comparability Consistency Measurability

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: Greed Individuals prefer more over less.

Observed behavior: Comparability & measurability Individuals can compare various choices Individuals can measure the performance of each choice

Observed behavior: Decreasing 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 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. are you willing to you pay How much are 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: 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 behavior Under uncertainty and risk, individuals do not simply maximize expected return. What then?

More on observed behavior Do individuals maximize expected utility? EU(x) = (1/2)U($1) + (1/4)U($2) + (1/8)U($4) + …+ (1/2 n )U($2 n-1 ) +… = ?? If U(x) = square root(x) EU(x) = (1/2)($1) + (1/4)($2) 1/2 + (1/8)($4) 1/2 + …+ (1/2 n )($2 n-1 ) 1/2 +… EU(x) = $2.914

More on observed behavior: Decreasing marginal utility Individuals maximize expected utility in a way that appears consistent with concave utility functions.

More 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?

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 return as possible with as little risk as possible

Implication 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

Summary 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