utility theory investors maximize expected utility u = f(w) u(w) w risk averse investor
TRANSCRIPT
Utility Theory
Investors maximize Expected UtilityU = f(W)
U(W)
W
Risk Averse Investor
Utility Theory (Cont’d)U(W)
W
U(W)
W
Risk Taker
Risk Neutral
Utility Theory (Cont’d)
Assume the following Utility function: U(w) = 2w - 0.01w2
where w represents change in Wealth.
Prob Stock A Stock B0.30 19 640.40 64 510.30 91 36
E(UA) = 19x0.30 + 64x0.40 + 91x0.30 = 58.60
E(UB) = 64x0.30 + 51x0.40 + 36x0.30= 50.40
Choose A
Mean-Variance Criterion
(1) Investors are risk averse(2) Returns are distributed normally, or investor Utility functions are quadratic
An investor will prefer A to B ifE(RA) > E(RB) and A B orE(RA) E(RB) and A < B
Return and Risk of a PortfolioExpected return of a portfolio:
N
iiiP REwRE
1
)()(
Variance of a portfolio:
N
iiii
P
N
jijji
N
iP
PRERRER
wwww
ww
1221112
122122
22
21
21
2
11
2
)())(((
Covariance
2
Stocks 2For