2.2 Expected Utility Theory: Risk Aversion

Question 1

Differentiate between risk-averse, risk-neutral and risk-lover.

Answer 1

Risk-averse: strict preference for a certain outcome e to an uncertain outcome with an expected value of e (positive risk premium)

Risk-neutral: indifference between a certain outcome e and an uncertain outcome with an expected value of e (zero risk premium)

Risk-lover: if he strictly prefers an uncertain outcome with an expected value of e to a certain outcome e (negative risk premium)

Question 2

Differentiate between absolute risk and relative risk.
(look at diagram on personal summary notes)

Answer 2

Absolute risk is the absolute difference between e2 and e1. Relative risk is the ratio of e2/e1.

Question 3

To distinguish between CARA, DARA and IARA, we need to look at …

Answer 3

how the absolute income risk is impacted through an increase in wealth.

Absolute income risk: difference between the two.

Question 4

If absolute income risk increases through an increase in wealth, this means that the individual is…

Answer 4

Diminishing Absolute Risk Aversion. DARA.

Question 5

Arrow-Pratt measure of absolute-risk aversion : how to calculate?
What does it mean if the derivative of the Arrow-Pratt measure is 0, <0 or >0?

Answer 5

-u’’(e)/u’(e)

CARA
DARA
IARA

Question 6

Relative risk aversion: What happens with the relative income risk if wealth increases?
(1) if it remains unchanged —>
(2) if it increases —>
(3) If it diminishes —>

Answer 6

constant relative risk aversion CRRA

diminishing relative risk aversion DRRA

increasing relative risk aversion IRRA.

Question 7

Let R(e) = ??? be the Arrow-Pratt measure of relative risk- aversion, then it can be shown:
(1) CRRA —> R’(e) = 0
(2) DRRA —> R’(e)
(3) IRRA —> R’(e)

Answer 7

-eu’’(e)/u’(e)

< 0

> 0