week 02 Risk Pref & Cap Allocation_6

week 02 Risk Pref & Cap Allocation_6 - Asset Return...

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Risk and Return Risk Preference, Risk Premium, and Capital Allocation Last Time Course overview Financial assets and markets Cost of trading Margin trading 2/24/2010 FINS5513 2 Short selling Characterizing financial assets: Expected return and risk Others? Characterizing investors: Risk aversion and utility Today Behavioral patterns Capital allocation between risk-free and risky assets 2/24/2010 3 Asset Return Holding period return as a random variable: P E di i $24 + = = t t t 1 t t 1 P D P r HPR P 2/24/2010 4 t = Ending price = $24 P t-1 = Beginning price = $20 D t = Dividend = $1 r t = ( 24 - 20 + 1 )/ ( 20) = 25% Microsoft Price (RHS) & Adjusted Returns (LHS) 0 50 100 150 200 0 10 20 2/24/2010 5 -200 -150 -100 -50 -20 -10 1/1/1988 12/31/1989 1/1/1992 12/31/1993 1/1/1996 1/1/1998 1/1/2000 1/1/2002 1/1/2004 1/1/2006 1/2/2008 1/1/2010 Microsoft Daily Return Distribution 0 25 0.3 0.35 0.4 2/24/2010 6 0 0.05 0.1 0.15 0.2 0.25 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10
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Return as a Random Variable Probability distribution discrete or continuous Describing probability distributions Location: expected value 2/24/2010 7 Dispersion: variance or standard deviation Symmetry: skewness “Tail” properties: kurtosis Expected Value and Variance Expected value =E(r) = Variance = var(r) = Standard deviation = σ m 1 = k k r × ) k Pr( = σ = m 2 2 k k k 1 Pr(k)[r E(r )] 2/24/2010 8 Given a sample r 1 , r 2 , …, r T , the sample mean and the sample variance are = = T t t 1 1 r r T = = T 2 2 t t 1 1 s [r r] T 1 Covariance and Correlation Covariance Cov(r A ,r B )=E[(r A -E(r A ))(r B -E(r B ))] Sample covariance T 1 2/24/2010 9 Correlation coefficient Note that Cov(r A ,r B )= Cov(r B ,r A ) and Cov(r A ,r A )=Var(r A ).
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