Ch14 Decision-Making Under Uncertainty
14.1 Assessing Risk
To measure risk we must know:
1. All of the possible outcomes.
2. The probability that each outcome will occur.

Two measures to help describe and compare risky choices are:
1. Expected value (The weighted average of the values resulting from all possible outcomes.)
2. Variability (Variability comes from deviations in actual payoffs relative to the expected payoff.)
3. Standard Deviation (Standard Deviation is the square root of Variance.)

Probability distribution
Mutually exclusive – only one of these outcomes can occur in a given period.
Exhaustive – no other outcomes are possible

14.2 Attitude Towards Risk

Which one will you choose depends on your attitude towards risk as reflected in your utility function.

Fair bet – a wager with an expected value of zero
Risk Averse - someone who is unwilling to make a fair bet. They will choose a bundle with higher risk only if its expected value is substantially higher than that of a less-risky bundle.
Risk Neutral – a person who is indifferent about making a fair bet
Risk preferring – a person who will make a fair bet

Expected Utility
- E(U) is probability weighted average of Utility.
- E(U)= P1 U(X1) + P2 U(X2).
- Fair bet= E(x)=0
Risk Aversion
A risk averse person picks the less risky choice if both choices have the same E(X). (her utility from certain wealth is greater than her expected wealth from the risky activity)
The person has a diminishing marginal utility of income and the utility function is concave.
Variability in potential payoffs increases the risk premium. The greater the variability, the more the person would be willing to pay to avoid the risk and the larger the risk premium. (positive risk premium)
E U(E(X)) from a risky option < U(X) from a certain option, where E(X) = X.

Risk premium – the amount that a risk-averse person would pay to avoid taking a risk. (the different between different wealth under same utility)

Risk Neutrality - A person is risk neutral if she shows no preference between a certain income, and an uncertain income with the same E(X).
A risk neutral person has a constant marginal utility of income. (straight-line utility curve)
A risk neutral person chooses the option with the highest expected value, because maximizing expected value maximizes utility.
Risk premium is 0 for risk neutral person cuz they choose the risker option if it has a slightly higher E(x)
E U(E(X)) = U(X)

Risk Preference
A person is risk loving if she shows a preference toward an uncertain income over a certain income with the same expected value, E(X).
A person with an increasing marginal utility of wealth. The utility curve is convex to the horizontal axis.
Negative risk premium
EU(E(X))> U(X)

Risk Attitude of Managers
Managers may be either risk averse or risk preferring even if shareholders prefer risk neutral decisions.
Risk averse: worried about being fired or losses => avoid extreme risks => pay risk premium
Risk Loving: can walk away from bad outcomes => take risk => high compensation from short-run profit

If bankruptcy => avoid bad outcomes even at the expense of reduced expected profit.

14.3 Reducing Risk
Abstain from optional activities
Obtain accurate information => increase E(x) and EU(E(x))
Diversification => making many risky investments instead of only one
1. If two investments are independent they are uncorrelated.
2. Diversification can eliminate risk if two investments are perfectly negatively correlated.
3. Diversification reduces risk even if the two investments are uncorrelated or imperfectly positively correlated.
4. Diversification does not reduce risk if two investments have a perfect positive correlation.

Mutual funds – issued by a company that buys stocks in many other companies. => reduce risk associated with uncorrelated price movements across stocks. However, a systematic risk (price of all stocks fall during recession but increase during expansion) cannot be avoided.