Week 2_Risk and Return

Week 2_Risk and Return - Risk and Return Portfolio...

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Risk and Return Portfolio Optimization
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2 Last Time ± Developed ways of measuring ² Risk (variance or standard deviation) ² Return (average return) ² How investments move together (covariance or correlation) ± Now we want to use these estimates to build collections of investments that achieve optimal performance ² Diversified portfolios
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3 Calculating returns ± Discrete period returns (PR) ± Continuously compounded return (CCR) + = + = 0 0 1 1 0 1 1 1 P P D P P D P PR + = 0 1 1 ln P D P CCR
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4 Time weighted averages Arithmetic: Sum of the returns in each period divided by the number of periods Geometric: ± add 1 to each return ± multiply the series ± take the n th root ± subtract 1 = n t t r 1 = r * 1 n () + = n t t r 1 1 n 1 1 = G r
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5 Risk ± Deviations from expectation ² Variance/standard deviation 0 0.05 0.1 0.15 0.2 0 5 10 15 20 Return (%) Probability σ B =4% σ A =2% E(R A ) = E(R B ) = 10%
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6 Portfolio Risk Standard Deviation Number of stocks Systematic (market) risk Non-systematic (firm-specific) risk
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7 Portfolio Risk ± Diversification benefit depends on covariance. ² Smaller correlation leads to greater benefit. ² Benefit exists when Cor(r A ,r B ) < 1. ± Let w i = 1/n, Average σ 2 = ( ∑σ i 2 )/n, and Average Cov = ∑∑ Cov(r i ,r j )/[n(n-1)]. ± Then since σ 2 = Ave σ 2 /n + (n-1)/n AveCov as n →∞ , σ 2 AveCov . == σ= σ + ∑∑ nn 22 2 2 Pi i j i1 i1ji nC o v ( r , r ) n
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8 Text reference ± This week’s lecture: Chapters 6 & 7 ² Tutorial problems due this week: ± Ch3: 4-6,10,12 ± Ch5: 2,4,6-9; CFA: 1-7 ± Ch24: 4 ± Next week’s lecture: Chapter 8 ² Tutorial problems due next week: ± Ch6: 1-19,26-28, CFA: 1-9 ± Ch7: 1-11,13-19, CFA: 4-13
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9 Today ± Utility ± Mean-variance analysis ± Capital allocation between risky and risk-free assets ±
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This note was uploaded on 05/02/2010 for the course ACCT 3756 taught by Professor Leung during the Three '09 term at University of Sydney.

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Week 2_Risk and Return - Risk and Return Portfolio...

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