Active Portfolio Management - University of Missouri ….pptVIP

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Active Portfolio Management - University of Missouri ….ppt

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Active Portfolio Management - University of Missouri ….ppt

Active Portfolio Management;Theory of Portfolio Management- Market Timing; According the mean-variance asset pricing model, the objective of the portfolio is to maximize the excess return over its standard deviation(ie., according to the Capital Allocation Line (CAL)) buy and hold?;Market Timing v.s Buy and Hold; An investor buys $1,000 stocks in in NYSE on Jan 1, 1978 and reinvests all its dividends in that portfolio. The the ending value of the portfolio on Dec 31, 1978 would be: $67,500;Treynor-Black Model;Steps of Active Portfolio Management;Advantages of TB model;TB Portfolio Selection;Combining Active Portfolio with Market Portfolio (passive portfolio);Given: rp = wrA + (1-w)rmThe optimal weight in the active portfolio is: w = w0/[1+(1-bA)w0] The slope of the CAL (called the Sharpe index) for the optimal portfolio (consisting of active and passive portfolio) turns out to include two components, which are: [(rm-rf)/sm]2 + [aA/s2(eA)]2;The optimal weights in the activeportfolio for each individual security will be: ;Illustration of TB Model;Composition of active portfolio: aA = w1a1+w2a2+w3a3 =1.1477(7%)-1.6212(5%)+1.4735(3%) =20.56% bA = w1b1+w2b2+w3b3 = 1.1477(1.6)-1.6212(1)+1.4735(0.5) = 0.9519 s(eA) = [w21s21+w22s22+w23s23]0.5 = [1.14772(0.452)+1.62122(0.322) +1.47352(0.262)]0.5 = 0.8262 Composition of the optimal portfolio: w0 = (0.2056/0.82622) / (0.08/0.22) = 0.1506w = w0 /[1+(1-bA) w0 ] = 0.1495;Composition of the optimal portfolio: Stock Final Position w (wk)1 0.1495(1.1477)=0.17162 0.1495(-1.6212)=-0.24243 0.1495(1.1435)=0.2202Active portfolio 0.1495 Passive portfolio 0.8505 1.0