Chapter6 - EFFICIENT DIVERSIFICATION Chapter 6 1...

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Chapter 6 EFFICIENT DIVERSIFICATION 1
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Diversification: Roulette Wheel Fair roulette wheel 40 slots, 20 black, 20 red (no house slots) probability of red = 50% Bet $10,000 on red, one spin. Is it risky? 50% prob of 100% loss Bet $1 per spin on 10,000 spins: as risky? Why is it less risky? Law of Large Numbers: the idea that as the number of independent trials of a random process increases, the percentage difference between the expected and actual values goes to zero. Independence is the key: what if you made thousands of tiny bets on the same spin?
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Diversification and Portfolio Risk Systematic risk (market risk) : Risk factors common to the whole economy (e.g. business cycle, inflation rate, interest rate, exchange rate) Nonsystematic risk (unique risk, firm-specific risk, idiosyncratic risk) : Risk that can be eliminated through diversification 3 σ n Nonsystematic risk Systematic risk
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Diversification and Portfolio risk Portfolio risk decreases as diversification increases. 4 Most of the diversifiable risk is eliminated at 25 or so stocks Investment Management
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Covariance and Correlation (I) 5 State p Stock Bond Depression 0.05 -37% -9% Mild recession 0.25 -11% 15% Normal growth 0.40 14% 8% Boom 0.30 30% -5% Expected return 10.00% 5.00% Standard deviation 18.63% 8.27% Consider the returns of a stock fund and a bond fund in different states of the economy: Portfolio (40% S & 60% B) -20.2% 4.6% 10.4% 9% 7.00% 6.65%
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Covariance and Correlation (II) Portfolio risk is reduced most when returns of the two assets most reliably offset each other. But, how can we measure the tendency of the returns on two assets to vary either in tandem or in opposition to each other? Covariance! 6 j i ij ij j i j js S s i is s ij j i R R Corr R E R R E R p R R Cov , , 1
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Covariance and Correlation (III) Covariance is a measure of the average tendency of asset returns to vary together. Correlation is a standardized measure of covariance between –1 and +1. 8 00748 . 0 05 . 0 05 . 0 10 . 0 30 . 0 3 . 0 05 . 0 08 . 0 10 . 0 14 . 0 4 . 0 05 . 0 15 . 0 10 . 0 11 . 0 25 . 0 05 . 0 09 . 0 10 . 0 37 . 0 05 . 0 SB 4855 . 0 0827 . 0 1863 . 0 00748 . 0 SB
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Portfolio Basics Suppose you combine 2 stocks: A and B into a portfolio. A portfolio is a set of value weights (proportions) that add up to 1.
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