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Utility Theory

Utility Theory. Investors maximize Expected Utility U = f(W). U(W). W. Risk Averse Investor. Utility Theory (Cont’d). U(W). Risk Taker. W. U(W). Risk Neutral. W. Utility Theory (Cont’d). Assume the following Utility function: U(w) = 2w - 0.01w 2

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Utility Theory

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

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

  3. Utility Theory (Cont’d) 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) > E(RB) and A  B or E(RA)  E(RB) and A < B

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

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