EC3333 Notes01 - Lecture 1 Risk Aversion and Capital...

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Lecture 1 Risk Aversion and Capital Allocation to Risky Assets
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Return and Risk P D P P HPR 0 1 0 1 + = HPR = Holding Period Return P 0 = Beginning price P 1 = Ending price D 1 = Dividend during period one Rates of Return: Single Period
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Ending Price = 48 Beginning Price = 40 Dividend = 2 HPR = (48 - 40 + 2 )/ (40) = 25% Rates of Return: Single Period Example
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Expected returns p ( s ) = probability of a state r ( s ) = return if a state occurs s = state Expected Return and Standard Deviation () ()() s Er psrs =
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State Prob. of State r in State 1 .1 -.05 2 .2 .05 3 .4 .15 4 .2 .25 5 .1 .35 E ( r ) = (.1)(-.05) + (.2)(.05)… + (.1)(.35) E ( r ) = .15 Scenario Returns: Example
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Standard deviation = [variance] 1/2 Variance: Variance or Dispersion of Returns Var =[(.1)(-.05-.15) 2 +(.2)(.05- .15) 2 …+ .1(.35-.15) 2 ] Var= .01199 S.D.= [ .01199] 1/2 = .1095 Using Our Example : [ ] 2 2 () () () s p sr s E r σ =−
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Risk Premium of a risky investment is the difference between the expected return and the return of risk-free investment Risk Premium f p r r E R = ) (
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Time Series Analysis of Past Rates of Return = = = = n s n s s r n s r s p r E 1 1 ) ( 1 ) ( ) ( ) ( Expected Returns and the Arithmetic Average
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Geometric Average Return 1 / 1 = n TV g n TV = Terminal Value of the Investment g= geometric average rate of return ) 1 )...( 1 )( 1 ( 2 1 n n r r r TV + + + =
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Standard Deviation Formula y Variance = expected value of squared deviations y When eliminating the bias, Variance and Standard Deviation become: 2 2 1 1 () n s rs r n σ = =− = = n s r s r n 1 2 ] ) ( [ 1 1
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The Reward-to-Volatility (Sharpe) Ratio Sharpe Ratio for Portfolios = Risk Premium SD of Excess Return
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Risk and Risk Aversion y Speculation Considerable risk x Sufficient to affect the decision Commensurate gain y Gamble Bet or wager on an uncertain outcome
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EC3333 Notes01 - Lecture 1 Risk Aversion and Capital...

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