risk aversion

Question 1

what does it mean to be risk-adverse?

Answer 1

basic definition: where the expected utility of two bets are the same, with initial wealth of Y1

A: Y1, no bets made
B: Y1, 1/2 probability will earn +H, 1/2 prob. -H

an agent will prefer A

mathematically: U’‘(Y)<0
necessary and sufficient condition

interpretation: the benefit from an additional dollar is not sufficient to make up for the pain of losing the previous

graphically: it’s the decreasing gradient of U’(Y)

Question 2

What is the absolute risk aversion?

Answer 2

it is a way of measuring the magnitude of risk-aversion; U’(Y) is just to preserve the integrity of the value

mathematically: -U’‘(Y)/U’(Y)
U’(Y) has no economic significance; j mathematical, to ensure results are not affected by changes to the function

intuitively: as Ra (sign for abs risk aversion) decreases, an agent gets less risk averse

Question 3

what is the relationship between certainty equivalence (CE) and risk premium (RP) ?

Answer 3

if I make an investment with uncertain payoffs, given that I am risk-adverse, I would prefer to not take the bet (utility is wealth + knowledge of the bet) versus taking the bet (uncertain - expected utility of initial wealth + investment w risky payoffs)

CE is the way to measure my level of risk-aversion, RP is the way to value safety (two sides of a coin)

The lower the CE, the more risk-adverse. The higher your RP, the more you value safety, the more you will pay to not risk making a bet.

CE = E(X) - RP
RP = E(X) - CE