1. Utility Theory Investors maximize Expected Utility U = f(W) U(W) W Risk Averse Investor

2. Utility Theory (Cont’d) U(W) W W Risk Taker Risk Neutral

3. Utility Theory (Cont’d) Assume the following Utility function: U(w) = 2w - 0.01w 2 where w represents change in Wealth. ProbStock A Stock B 0.30 1964 0.40 6451 0.30 9136 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(R A ) > E(R B ) and  A   B or E(R A )  E(R B ) and  A <  B

5. Return and Risk of a Portfolio Expected return of a portfolio: Variance of a portfolio: