Active portfolio management @ bec dom s

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Active portfolio management @ bec dom s

  1. 1. Active Portfolio Management <ul><li>Theory of Active Portfolio Management </li></ul><ul><li>Market timing </li></ul><ul><li>portfolio construction </li></ul><ul><li>Portfolio Evaluation </li></ul><ul><li>Conventional Theory of evaluation </li></ul><ul><li>Performance measurement with changing return characteristics </li></ul>
  2. 2. Theory of Portfolio Management- Market Timing <ul><li>Most managers will not beat the passive strategy (which means investing the market index) but exceptional (bright) managers can beat the average forecasts of the market </li></ul><ul><li>Some portfolio managers have produced abnornal returns that are beyond luck </li></ul><ul><li>Some statistically insignificant return (such 50 basis point) may be economically significant </li></ul>
  3. 3. <ul><li>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)) </li></ul><ul><li>buy and hold ? </li></ul>CAL Return SD
  4. 4. Market Timing v.s Buy and Hold <ul><li>Assume an investor puts $1,000 in a 30-day CP ( riskless instrument ) on Jan 1, 1927 and rolls it over and holds it until Dec 31, 1978 for 52 years, the ending value is $3,600 </li></ul>$1,000 $3,600 52 yrs
  5. 5. <ul><li>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 </li></ul><ul><li>Suppose the investor has perfect market timing in every month by investing either in CP or stocks , whichever yields the highest return, the ending value after 52 years is $5.36 billion ! </li></ul>$1,000 $67,500 1/1 1978 Dec 31, 1978
  6. 6. Treynor-Black Model <ul><li>The Treynor-Black model assumes that the security markets are almost efficient </li></ul><ul><li>Active portfolio management is to select the mispriced securities which are then added to the passive market portfolio whose means and variances are estimated by the investment management firm unit </li></ul><ul><li>Only a subset of securities are analyzed in the active portfolio </li></ul>
  7. 7. Steps of Active Portfolio Management <ul><li>Estimate the alpha, beta and residual risk of each analyzed security. (This can be done via the regression analysis.) </li></ul><ul><li>Determine the expected return and abnormal return (i.e., alpha) </li></ul><ul><li>Determine the optimal weights of the active portfolio according to the estimated alpha, beta and residual risk of each security </li></ul><ul><li>Determine the optimal weights of the the entire risky portfolio (active portfolio + passive market portfolio) </li></ul>
  8. 8. Advantages of TB model <ul><li>TB analysis can add value to portfolio management by selecting the mispriced assets </li></ul><ul><li>TB model is easy to implement </li></ul><ul><li>TB model is useful in decentralized organizations </li></ul>
  9. 9. TB Portfolio Selection <ul><li>For each analyzed security, k, its rate of return can be written as: r k -r f = a k + b k (r m -r f ) + e k a k = extra expected return (abnormal return) b k = beta e k = residual risk and its variance can be estimated as s 2 (e k ) </li></ul><ul><li>Group all securities with nonzero alpha into a portfolio called active portfolio. In this portfolio, a A , b A and s 2 (e A ) are to be estimated. </li></ul>
  10. 10. Combining Active Portfolio with Market Portfolio ( passive portfolio) A . M p CML New CAL Return Risk r A =a A + r f +b A (r m -r f )
  11. 11. Given: r p = wr A + (1-w)r m The optimal weight in the active portfolio is: w = w 0 /[1+(1-b A )w 0 ] 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: [(r m -r f )/s m ] 2 + [a A /s 2 (e A )] 2 a A /s 2 (e A ) (r m -r f )/s 2 m where w 0 =
  12. 12. The optimal weights in the active portfolio for each individual security will be: a k /s 2 (e k ) a 1 /s 2 (e 1 )+...+a n /s 2 (e n ) w k =
  13. 13. Illustration of TB Model <ul><li>Stock a b s(e) 1 7% 1.6 45% 2 -5 1.0 32 3 3 0.5 26 </li></ul><ul><li>r m -r f =0.08; s m =0.2 </li></ul><ul><li>Let us construct the optimal active portfolio implied by the TB model as: Stock a/s 2 (e) Weight (w k ) 1 0.07/0.45 2 = 0.3457 (1)/T = 1.1417 2 -0.05/0.32 2 = -0.4883 (2)/T = -1.6212 3 0.03/0.26 2 = 0.4438 (3)/T = 1.4735 Total (T) 0.3012 </li></ul>
  14. 14. Composition of active portfolio: a A = w 1 a 1 +w 2 a 2 +w 3 a 3 =1.1477(7%)-1.6212(5%)+1.4735(3%) =20.56% b A = w 1 b 1 +w 2 b 2 +w 3 b 3 = 1.1477(1.6)-1.6212(1)+1.4735(0.5) = 0.9519 s(e A ) = [w 2 1 s 2 1 +w 2 2 s 2 2 +w 2 3 s 2 3 ] 0.5 = [1.1477 2 (0.45 2 )+1.6212 2 (0.32 2 ) +1.4735 2 (0.26 2 )] 0.5 = 0.8262 Composition of the optimal portfolio : w 0 = (0.2056/0.8262 2 ) / (0.08/0.2 2) = 0.1506 w = w 0 /[1+(1-b A ) w 0 ] = 0.1495
  15. 15. Composition of the optimal portfolio: Stock Final Position w (w k ) 1 0.1495(1.1477)=0.1716 2 0.1495(-1.6212)=-0.2424 3 0.1495(1.1435)=0.2202 Active portfolio 0.1495 Passive portfolio 0.8505 1.0

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