week 03 Port Opt_6

week 03 Port Opt_6 - Portfolio Return and Risk Risk and...

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Risk and Return Portfolio Optimization & Index Models Key messages Measuring return and risk Measuring risk preference Capital allocation Connection between them Last Lecture Demand for risky assets Underlying assumptions Normality: mean and variance Rationality: risk aversion Others? Basic stats 3/12/2010 2 Modern portfolio theory (Markowitz, 1952, JF) Diversification and risk Minimum variance set and the efficient frontier The separation property Today’s Topics Portfolio optimization in practice Estimation issues Tiered decision process Strategic and tactic asset allocations The single index model Risk decomposition 3/12/2010 3 Portfolio Return and Risk A portfolio of two stocks: r p = w 1 r 1 +w 2 r 2 (When) Is this true? Check out “Portfolio Statistics”. Portfolio expected return: E(r p ) = w 1 E(r 1 )+w 2 E(r 2 ) P tf li i Portfolio variance: Var(r p ) = Var(w 1 r 1 +w 2 r 2 ) What if you have three stocks, or M>3 stocks? Check out “Portfolio Statistics”. 3/12/2010 FINS5513 4 2 1 12 2 2 2 2 2 1 2 1 2 1 2 2 2 2 2 1 2 1 2 w w ) r , r ( Cov 2 w w σ σ ρ + σ + σ = + σ + σ = Benefit of Diversification Two stocks A & B: E(r A ) = 20%, σ A = 0.4, E(r B ) = 10%, σ B = 0.25. Portfolio weights: w A =w B E(r P ) = ? Week 2 FINS5513 5 If ρ AB = -0.6, Cov(r A ,r B ) = ? Var(r P ) = ? If ρ AB = 0.6, Cov(r A ,r B ) = ? Var(r P ) = ? Portfolio Risk Stock A A+A Week 2 FINS5513 6 Stock B A+B

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Portfolio Risk Standard Deviation Non-systematic (firm-specific) risk Week 2 FINS5513 7 Number of stocks Systematic (market) risk International Diversification Standard Deviation Sample period: 1961-1975 Is the benefit of global diversification still as large in recent years? Week 2 FINS5513 8 Number of stocks U.S. stocks Global stocks 27% 11.7% * Chapter 25 Cor(US stocks, Non-US stocks) Rolling 3-Year Correlations U.S. and Non-U.S. Stocks 1971-2001 0.8 0.9 1.0 3/12/2010 9 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 1974 1975 1977 1978 1979 1980 1982 1983 1984 1985 1987 1988 1989 1990 1992 1993 1994 1995 1997 1998 1999 2000 2002 One share in each stock? One dollar in each stock? The (global) market portfolio? Is there a better way to diversify? How to Diversify? Achieve higher return with the same risk? Achieve the same return with lower risk? Start with two risky assets: stocks and bonds E(r Stock )=11.8%, σ Stock =16%; E(r Bond )=8.5%, σ Bond =9.2%; Corr(Stock, Bond) = 0.23 3/12/2010 10 The Combination Line 11.0 11.5 12.0 12.5 80% Stocks/20% Bonds 60% Stocks/40% Bonds 100% Stocks 3/12/2010 11 7.5 8.0 8.5 9.0 9.5 10.0 10.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 Standard Deviation 40% Stocks/60% Bonds 20%Stocks/80%Bonds Gross Return (%) 100% Bonds
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