Investment Style of Portfolio Management: Excel Applications

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Investment Style of Portfolio Management Excel
Applications

• Journal of Applied Finance, 2001
• Stan Atkinson and Yoon Choi

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(No Transcript)
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Introduction

• to investigate Sharpe's (1988, 1992) investment
  style model of managed portfolios in terms of
  asset allocation (style), using the Solver
  function.
• Style analysis (or asset allocation) models are a
  valuable tool for investors, plan sponsors, and
  consultants.
• 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.

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Sharpes Style Model

• Sharpe introduces an objective style
• model based on asset classes (or factors).
• He assumes that a mutual funds 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.

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Empirical Supports

• Trzcinka (1995) defends Sharpes style model,
• Easy to implement and very objective.
• The assumptions and data are clear to the
  analyst, so the results can be replicated.
• In spite of some debates about its merits, the
  Sharpe style analysis has been popular and
  applied to actual portfolios.

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Style Analysis

• 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.
• Consider the following equation
• Ri bi1F1 bi2F2 . binFn ei, (1)
• where Ri is the mutual fund return, Fn is the
  value of the nth factor, bin is the factor
  sensitivities, and ei is the unsystematic
  residual.

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• 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.
• Mathematically, It is the one for which the
  variance of ei in Equation (1) is the least.
  Thus, we rearrange Equation (1) as follows
• ei Ri bi1F1 bi2F2 . binFn (2)

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Interpretation

• 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).
• 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).

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Guidelines in choosing the asset class factors

• such asset classes should be mutually exclusive
  and exhaustive.
• 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.

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Sharpes 12 asset classes

• Treasury bills,
• Intermediate government bonds,
• long-term government bonds,
• corporate bonds,
• mortgage-related securities,
• large-cap value (growth) stocks
• Medium (small) -cap stocks,
• non-U.S. bonds,
• European stocks, and
• Japanese stocks.

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I
In Excel Solver

• 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).

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I
Excel Solver

• MIN Var (ei)
• Changing Cell exposure coefficients
  Or bi
• Constraints
• bi gt 0,
• bi lt 1,
• bi1 bi2 . bin 1.

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DATA

• We obtain the asset classes from various sources,
  including BARRA investment data (available
  through the Internet, www.barra.com).
• We concentrate on the domestic asset world
• SP 500/Barra Growth (Value) Index,
• SP MidCap 400/Barra Growth (Value) Index
• SP SmallCap 600/Barra Growth (Value) Index
  IBBS Corporate Bond Index,
• IBBS Government Bond Index, and
• IBBS Treasury Bill Index.

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Style Drift

• 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.
• 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.
• Since he uses the past returns in this procedure,
  the Sharpe model only detect style drift with a
  lag.

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Style Drift

• Israelsen (1999) finds that style drift happens
  to quite a number of funds.
• He also finds that funds with the greatest style
  drift have managers
• with less tenure, more fluctuations in annual
  returns, lower tax efficiency, higher expense
  ratios, higher turnover ratios, and fewer assets.

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Style Drift

• Tergesen (1999) finds that,
• 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.