Utility Theory

1
Utility Theory
Investors maximize Expected Utility U f(W)
U(W)
W
Risk Averse Investor
2
Utility Theory (Contd)
U(W)
Risk Taker
W
U(W)
Risk Neutral
W
3
Utility Theory (Contd)
Assume the following Utility function U(w)
2w - 0.01w2 where w represents change in
Wealth. Prob Stock A Stock B 0.30
19 64 0.40 64 51 0.30 91 36 E(UA)
19x0.30 64x0.40 91x0.30
58.60 E(UB) 64x0.30 51x0.40 36x0.30
50.40 Choose A
4
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 if E(RA) gt E(RB) and ?A ? ?B or E(RA)
? E(RB) and ?A lt ?B
5
Return and Risk of a Portfolio
Expected return of a portfolio
Variance of a portfolio