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Lecture10

# Lecture10 - Lecture 10 Risk aversion risk diversification...

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Lecture 10 Risk aversion, risk diversification, portfolio choices

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Diversifying risk with independent risks Suppose the company sells policies to Jones and Smith, who live on opposite sides of the country: their flood risk is identical but independent. Each house is worth \$4M. Independent probabilities: p(X and Y)= p(X)p(Y) p(Jones floods) = p(J) = p(Smith floods) = .25 Mean damages = .0625*8+.1875*4+.1875*4+.5625*0 = 2 Variance = .0625*(8-2) 2 +.1875*(4-2) 2 +.1875*(4-2) 2 +.5625*0-2) 2 = 5.34375 Jones’ house floods; p(J) = .25 Jones house doesn’t flood; 1- p(J) = .75 Smith’s house floods, p(S) = .25 p(S)p(J) = .0625; pay out \$8M p(S)(1-p(J))=.1875; pay out \$4M Smith’s house doesn’t flood; 1- p(S) = .75 (1-p(S))p(J) = .1875 Pay out \$4M (1-p(S))(1- p(J))=.5625; pay out nothing
No diversification with perfectly correlated risks Suppose the company sells policies to Jones and Smith, who live next door to each other: their flood risk is identical and perfectly correlated. Perfectly correlated probabilities: p(X and Y)= p(X) = p(Y); p(X and not Y)=0 Expected value = .25*8M + .75*0 = \$2M (previous slide: 2) Variance = .25(8-2)

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Lecture10 - Lecture 10 Risk aversion risk diversification...

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