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Unformatted text preview: FINM2401 Financial Management Portfolio Analysis 1 Lecture 7 2 Concept of Risk and Return Risk is the probability of making substantially m o r e or l e s s than your expected return (a.k.a. variability of returns) For increased risk, we normally require higher returns (known as riskreturn tradeoff) 3 Risk Attitudes or Preferences Riskindifferent (neutral) investor: One who does not require increased expected returns for a rise in risk Riskseeking investor: One who is willing to accept lower expected returns even when risk rises Riskaverse 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 5 10 15 20 25 30 50 100 150 200 Wealth (000s) U t i l i t y ()  = 1 1 W U W 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? () = Assume = 0.5, so U 2 W W 6 Using Utility Functions 5 10 15 20 25 30 50 100 150 200 Wealth (000s) U t i l i t y 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 = 19.84U(98.41) = 1.59 This is the most you wo 10098.41 uld pay () = U 2 W W 7 Try it out p If you were more risk averse would you pay more for insurance? p Assume =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 p If your wealth is $100k, what would you pay to avoid a 50/50 chance of winning or losing $25k? 8 Solution p If you lose $25k, your utility will be: () ( ) = = 0.4 2.510025 U W 14.0593 p If you win $25k, your utility will be: () ( ) = + = 0.4 2.510025 U W 17.2466 p So, your expected utility without insurance is: () ( )( ) = + = 14.059350% 17.246650% 15.65295 E U W 9 Solution p Your expected utility with insurance will be: () ( ) = = 0.4 2.5100 cost ? U W p 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 2.5100 maxcost 15.65295 U W 10 Solution p Define x=100maxcost: p Therefore, you will be willing to pay up to 100x=$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 p If your initial wealth is greater, will you be willing to pay more for insurance? p Rework the problem on slide 7 assuming you have an initial wealth of $500k instead of $100k 12 Utility Theory Each individual has different preferences and, therefore, a different utility function...
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This note was uploaded on 03/13/2010 for the course ECON econ1010 taught by Professor Margretfinch during the Three '08 term at Griffith.
 Three '08
 margretfinch

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