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Lecture07c

Lecture07c - FINM2401 Financial Management Concept of Risk...

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FINM2401 Financial Management Portfolio Analysis 1 Lecture 7 2 Concept of Risk and Return Risk is the probability of making substantially more or less than your expected return (a.k.a. variability of returns) For increased risk, we normally require higher returns (known as risk-return trade-off) 3 Risk Attitudes or Preferences Risk-indifferent (neutral) investor: One who does not require increased expected returns for a rise in risk Risk-seeking investor: One who is willing to accept lower expected returns even when risk rises Risk-averse investor: One who requires increasing expected returns for a rise in risk (in finance theory, rational investors are assumed to be risk averse) 4 Utility Functions 0 5 10 15 20 25 30 0 50 100 150 200 Wealth (000s) Utility ( ) γ γ - = - 1 1 W U W

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5 Using Utility Functions Assume your wealth (W) is \$100,000 Suppose you face a 50% chance of either losing or winning \$25,000 What is your expected ending wealth and utility? How much would you pay to avoid this chance? ( ) γ = Assume = 0.5, so U 2 W W 6 Using Utility Functions 0 5 10 15 20 25 30 0 50 100 150 200 Wealth (000s) Utility U(75)=17.32 U(100)=20 U(125)=22.36 = + = ( ) .5(125) .5(75) 100 E W = + = (U( )) .5(22.36) .5(17.32) 19.84 E W = 19.84 U(98.41) - = 1.59 This is the most you wo 100 98.41 uld pay ( ) = U 2 W W 7 Try it out… pentasterisk6 If you were more risk averse would you pay more for insurance? pentasterisk6 Assume γ =0.6 describes your level of risk aversion and your utility function is ( ) = = 0.4 0.4 1 2.5 0.4 measured in thousands U W W W W pentasterisk6 If your wealth is \$100k, what would you pay to avoid a 50/50 chance of winning or losing \$25k? 8 Solution pentasterisk6 If you lose \$25k, your utility will be: ( ) ( ) = - = 0.4 2.5 100 25 U W 14.0593 pentasterisk6 If you win \$25k, your utility will be: ( ) ( ) = + = 0.4 2.5 100 25 U W 17.2466 pentasterisk6 So, your expected utility without insurance is: ( ) ( ) ( ) = × + × = 14.0593 50% 17.2466 50% 15.65295 E U W
9 Solution pentasterisk6 Your expected utility with insurance will be: ( ) ( ) = - = 0.4 2.5 100 cost ? U W pentasterisk6 You will be willing to pay up to whatever amount reduces your expected utility to 15.65295. Thus the most you will pay is: ( ) ( ) = - = 0.4 2.5 100 maxcost 15.65295 U W 10 Solution pentasterisk6 Define x=100-maxcost: pentasterisk6 Therefore, you will be willing to pay up to 100-x=\$1.906k or \$1,906 for the insurance ( ) 0.4 2.5 15.65295 x = ( ) 0.4 15.65295 2.5 x = ( ) ( ) 2.5 2.5 0.4 15.65295 2.5 x = 98.09355 x = 11 For Tutorials pentasterisk6 If your initial wealth is greater, will you be willing to pay more for insurance?

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Lecture07c - FINM2401 Financial Management Concept of Risk...

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