Investment Style of Portfolio Management: Excel Applications Journal of Applied Finance, 2001 Stan Atkinson and Yoon Choi
 
Introduction <ul><li>to investigate Sharpe's (1988, 1992) investment style model of managed portfolios in terms of asset a...
Sharpe’s Style Model <ul><li>Sharpe introduces an objective style </li></ul><ul><li>model based on asset classes (or facto...
Empirical Supports <ul><li>Trzcinka (1995) defends Sharpe’s style model,  </li></ul><ul><ul><li>Easy to implement and very...
Style Analysis <ul><li>Sharpe (1992) defines the asset allocation of a mutual fund as the way in which the fund manager al...
<ul><li>Our objective is to find the “best” set of asset class exposures (i.e., bi) that add up to 100% and lie between on...
Interpretation <ul><li>we can interpret the residual (ei) as the difference between the fund return (Ri ) and the return o...
Guidelines in choosing the asset class factors <ul><li>such asset classes should be mutually exclusive and exhaustive. </l...
Sharpe’s 12 asset classes <ul><li>Treasury bills,  </li></ul><ul><li>Intermediate government bonds,  </li></ul><ul><li>lon...
I <ul><li>the investment style problem is to obtain a set of exposure coefficients that minimizes the variance of the resi...
I <ul><li>MIN  Var (ei)  </li></ul><ul><li>Changing Cell:  exposure coefficients  Or  bi </li></ul><ul><li>Constraints:  <...
DATA <ul><li>We obtain the asset classes from various sources, including BARRA investment data (available through the Inte...
Style Drift <ul><li>It could be helpful for investors to know how the style changes over time so that they can rebalance o...
Style Drift  <ul><li>Israelsen (1999) finds that style drift happens to quite a number of funds.  </li></ul><ul><li>He als...
Style Drift <ul><li>Tergesen (1999) finds that,  </li></ul><ul><li>those managers that stick to their styles have higher r...
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Investment Style of Portfolio Management: Excel Applications

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Investment Style of Portfolio Management: Excel Applications

  1. 1. Investment Style of Portfolio Management: Excel Applications Journal of Applied Finance, 2001 Stan Atkinson and Yoon Choi
  2. 3. Introduction <ul><li>to investigate Sharpe's (1988, 1992) investment style model of managed portfolios in terms of asset allocation (style), using the Solver function. </li></ul><ul><li>Style analysis (or asset allocation) models are a valuable tool for investors, plan sponsors, and consultants. </li></ul><ul><li>Investors want to know the investment style so they can create an effective mix of assets that fits their tastes. Plan sponsors and consultants are interested in how well the portfolio manager meets the investment objectives. </li></ul>
  3. 4. Sharpe’s Style Model <ul><li>Sharpe introduces an objective style </li></ul><ul><li>model based on asset classes (or factors). </li></ul><ul><li>He assumes that a mutual fund’s return is assumed to be a function of several factor exposures and firm-specific risks. The factor exposures or sensitivities determine the style or asset allocation of the fund. </li></ul>
  4. 5. Empirical Supports <ul><li>Trzcinka (1995) defends Sharpe’s style model, </li></ul><ul><ul><li>Easy to implement and very objective. </li></ul></ul><ul><ul><li>The assumptions and data are clear to the analyst, so the results can be replicated. </li></ul></ul><ul><ul><li>In spite of some debates about its merits, the Sharpe style analysis has been popular and applied to actual portfolios. </li></ul></ul>
  5. 6. Style Analysis <ul><li>Sharpe (1992) defines the asset allocation of a mutual fund as the way in which the fund manager allocates his assets across a number of major asset classes. </li></ul><ul><li>Consider the following equation: </li></ul><ul><li>Ri = b i1 F1 + b i2 F2 + ….+ b in Fn+ ei, (1) </li></ul><ul><li>where Ri is the mutual fund return, Fn is the value of the nth factor, b in is the factor sensitivities, and ei is the unsystematic residual. </li></ul>
  6. 7. <ul><li>Our objective is to find the “best” set of asset class exposures (i.e., bi) that add up to 100% and lie between one and zero. </li></ul><ul><li>Mathematically, It is the one for which the variance of ei in Equation (1) is the least. Thus, we rearrange Equation (1) as follows: </li></ul><ul><li>ei = Ri – [bi1F1 + bi2F2 + ….+ binFn] (2) </li></ul>
  7. 8. Interpretation <ul><li>we can interpret the residual (ei) as the difference between the fund return (Ri ) and the return of a passive portfolio with the same style (bi1F1 + bi2F2 + ….+ binFn). </li></ul><ul><li>The objective is to choose the style (set of asset class exposures) that minimizes the variance of this difference (or the sum of the residual squared with all constraints). </li></ul>
  8. 9. Guidelines in choosing the asset class factors <ul><li>such asset classes should be mutually exclusive and exhaustive. </li></ul><ul><li>By containing exhaustive classes of assets, the asset class factors (F1 through Fn) as a whole can mirror the market portfolio as closely as possible. </li></ul>
  9. 10. Sharpe’s 12 asset classes <ul><li>Treasury bills, </li></ul><ul><li>Intermediate government bonds, </li></ul><ul><li>long-term government bonds, </li></ul><ul><li>corporate bonds, </li></ul><ul><li>mortgage-related securities, </li></ul><ul><li>large-cap value (growth) stocks </li></ul><ul><li>Medium (small) -cap stocks, </li></ul><ul><li>non-U.S. bonds, </li></ul><ul><li>European stocks, and </li></ul><ul><li>Japanese stocks. </li></ul>
  10. 11. I <ul><li>the investment style problem is to obtain a set of exposure coefficients that minimizes the variance of the residual, var(ei) with the constraints that each of the factor sensitivities (or exposures), bi, lies between zero and one, and that the factor sensitivities should add up to one (e.g., bi1 + bi2 + … .+ bin = 1). </li></ul>In Excel Solver
  11. 12. I <ul><li>MIN Var (ei) </li></ul><ul><li>Changing Cell: exposure coefficients Or bi </li></ul><ul><li>Constraints: </li></ul><ul><li>bi >= 0, </li></ul><ul><li>bi <= 1, </li></ul><ul><li>bi1 + bi2 + … .+ bin = 1. </li></ul>Excel Solver
  12. 13. DATA <ul><li>We obtain the asset classes from various sources, including BARRA investment data (available through the Internet, www.barra.com ). </li></ul><ul><li>We concentrate on the domestic asset world: </li></ul><ul><li>S&P 500/Barra Growth (Value) Index, </li></ul><ul><li>S&P MidCap 400/Barra Growth (Value) Index </li></ul><ul><li>S&P SmallCap 600/Barra Growth (Value) Index IBBS Corporate Bond Index, </li></ul><ul><li>IBBS Government Bond Index, and </li></ul><ul><li>IBBS Treasury Bill Index. </li></ul>
  13. 14. Style Drift <ul><li>It could be helpful for investors to know how the style changes over time so that they can rebalance or reallocate their portfolios of mutual funds. </li></ul><ul><li>Sharpe also shows how to estimate the style drift by performing a series of style analyses, rolling the window used for the analysis over time. </li></ul><ul><li>Since he uses the past returns in this procedure, the Sharpe model only detect style drift with a lag. </li></ul>
  14. 15. Style Drift <ul><li>Israelsen (1999) finds that style drift happens to quite a number of funds. </li></ul><ul><li>He also finds that funds with the greatest style drift have managers </li></ul><ul><ul><li>with less tenure, more fluctuations in annual returns, lower tax efficiency, higher expense ratios, higher turnover ratios, and fewer assets. </li></ul></ul>
  15. 16. Style Drift <ul><li>Tergesen (1999) finds that, </li></ul><ul><li>those managers that stick to their styles have higher risk-adjusted returns than do their more eclectic peers. These results held across all types of funds. </li></ul>

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