Utility Theory Investors maximize Expected Utility U = f(W) U(W) W Risk Averse Investor.
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Transcript of Utility Theory Investors maximize Expected Utility U = f(W) U(W) W Risk Averse Investor.
![Page 1: Utility Theory Investors maximize Expected Utility U = f(W) U(W) W Risk Averse Investor.](https://reader036.fdocuments.in/reader036/viewer/2022082506/5697c01f1a28abf838cd18c2/html5/thumbnails/1.jpg)
Utility Theory
Investors maximize Expected UtilityU = f(W)
U(W)
W
Risk Averse Investor
![Page 2: Utility Theory Investors maximize Expected Utility U = f(W) U(W) W Risk Averse Investor.](https://reader036.fdocuments.in/reader036/viewer/2022082506/5697c01f1a28abf838cd18c2/html5/thumbnails/2.jpg)
Utility Theory (Cont’d)U(W)
W
U(W)
W
Risk Taker
Risk Neutral
![Page 3: Utility Theory Investors maximize Expected Utility U = f(W) U(W) W Risk Averse Investor.](https://reader036.fdocuments.in/reader036/viewer/2022082506/5697c01f1a28abf838cd18c2/html5/thumbnails/3.jpg)
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
![Page 4: Utility Theory Investors maximize Expected Utility U = f(W) U(W) W Risk Averse Investor.](https://reader036.fdocuments.in/reader036/viewer/2022082506/5697c01f1a28abf838cd18c2/html5/thumbnails/4.jpg)
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
![Page 5: Utility Theory Investors maximize Expected Utility U = f(W) U(W) W Risk Averse Investor.](https://reader036.fdocuments.in/reader036/viewer/2022082506/5697c01f1a28abf838cd18c2/html5/thumbnails/5.jpg)
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