Portfolio Performance Analysis continued'''

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Portfolio Performance Analysis continued...

• Business 4179

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Measurement of Performance

• In the other slide set we looked at some other
  approaches used to measure single portfolio
  performance (equity based portfolios)Sharpe,
  Treynor and Jensen measures.
• These are all risk-adjusted measures.
• Famas measures help us to decompose realized
  returns to ascertain the source of the returns
  and by implication, begin the process of
  determining the effectiveness of the manager.

3
Famas Measures
4
Components of Investment Performance

• Following the work of Treynor, Sharpe, and
  Jensen, Eugene Fama suggested a somewhat finer
  breakdown of performance.
• The basic premise for Famas technique is that
  overall performance of a portfolio, which is its
  excess return in excess of the risk-free rate,
  can be decomposed into measures of risk-taking
  and security selection skill
• Overall Performance Excess Return
• Excess Return Portfolio Risk Selectivity

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Selectivity

• The selectivity component represents the portion
  of the portfolios actual return beyond that
  available to an unmanaged portfolio with
  identical systematic risk.
• This selectivity measure is used to assess the
  managers investment prowess.
• Famas evaluation model asumes that returns to
  managed portfolios can be compared to those of
  naively selected portfolios with similar risk
  levels.
• The technique is based on the ex ante market line
  summarizing the equilibrium relationship between
  expected return and risk for portfolio j

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Selectivity ...

• This equation indicates that the expected return
  on portfolio j is the riskless rate of interest
  (RF), plus a risk premium that is E(Rm -
  RF/s(RM), called the market price per unit of
  risk, times the risk of asset j, which is
  Cov(Rj.RM)/s(RM).
• If a portfolio manager believes that the market
  is not completely efficient and that she can make
  better judgments than the market, then an ex post
  version of this market line can provide a
  benchmark for the managers performance.

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Selectivity ...

• Given that the risk variable, Cov(Rj.RM)/s(RM)
  bx, the ex post market line is as follows
• This ex post market line provides the benchmark
  used to evaluate managed portfolios in a sequence
  of more complex measures.

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Components of Investment Performance (Eugene
Fama, 1972)
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Components of Investment Performance (Eugene
Fama, 1972)

• Formally, you can measure the return due to
  selectivity as follows
• Where Ra actual return on the portfolio being
  evaluated
• Rx(Ba) the return on the combination of the
  riskless asset and the market portfolio m that
  has risk Bx, the risk of the portfolio being
  evaluated.
• As shown in the previous slide, selectivity
  measures the vertical distance between the actual
  return and the ex post market line and is quite
  similar to the Treynor measure.

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Components of Investment Performance (Eugene
Fama, 1972)

• Hence you can examine overall performance in
  terms of selectivity and the returns assuming
  risk as follows
• Overall performance is the total return above the
  risk-free return and includes the return that
  should have been received for accepting the
  portfolio risk (ba).
• This expected return for accepting risk (ba) is
  equal to Rx (ba) RF
• Any excess return over this expected return is
  due to selectivity.

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Performance Attribution Analysis
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Performance Attribution

• The previously mentioned risk-adjusted measures
  of performance concentrate on the question of HOW
  a portfolio did relative to both a benchmark and
  a set of other portfolios.
• The use of quadratic variable regression is an
  attempt to evaluate separately the managers
  ability at selectivity and timing.
• However, a client might want to know more about
  WHY the portfolio had a certain return over a
  particular time period. Performance ATTRIBUTION
  using a factor model is one method that has been
  used to try to make such a determination.

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Performance Attribution Analysis

• Attempts to distinguish which factors are the
  sources of the portfolios overall performance
  (after the fact).
• Was it because the manager was superior at
  selecting securities, or did they demonstrate
  superior market timing skills by allocating funds
  to different asset classes or market segments?
• This method compares the total return of the
  managers actual investment holdings to the
  return for a predetermined benchmark portfolio
  and decomposes the difference into allocation
  effect and a selection effect.
• The most straightforward way to measure these two
  effects is as follows

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Performance Attribution Analysis

• The most straightforward way to measure these two
  effects is as follows
• Where
• wai, wpi the investment proportions given to
  the ith market segment (eg. Asset class, industry
  group) in the managers actual portfolio and the
  benchmark portfolio, respectively.
• Rai, Rpi the investment return to the ith
  market segment in the managers actual portfolio
  and the benchmark portfolio , respectively
• Rp the total return to the benchmark portfolio

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Performance Attribution Analysis

• Computed in this manner, the allocation effect
  measures the managers decision to over- or
  underweight a particular market segment (ie. wai
  wpi) in terms of that segments return
  performance relative to the overall return to the
  benchmark (ie. Rpi Rp).
• The selection effect measures the managers
  ability to form specific market segment
  portfolios that generate superior returns
  relative to the way in which the comparable
  market segment is defined in the benchmark
  portfolio (ie. Rai Rpi) weighted by the
  managers actual market segment investment
  proportions.
• When constructed in this way, the managers total
  value-added performance is the sum of the
  allocation and selection effects.

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Performance Attribution Analysis (An Example)

• Investment Weights Returns
• Asset Class Actual Benchmark Excess Actual Benc
  hmark Excess
• Stock 0.50 0.60 -0.10 9.7 8.6 1.10
• Bonds 0.38 0.30 0.08 9.10 9.2 -0.10
• Cash 0.12 0.10 0.02 5.6 5.4 0.20
• Thus the manager beat the benchmark by 52 basis
  points ( 0.0898 0.0846) over this particular
  time horizon.

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Performance Attribution Analysis (An Example)

• Investment Weights Returns
• Asset Class Actual Benchmark Excess Actual Benc
  hmark Excess
• Stock 0.50 0.60 -0.10 9.7 8.6 1.10
• Bonds 0.38 0.30 0.08 9.10 9.2 -0.10
• Cash 0.12 0.10 0.02 5.6 5.4 0.20
• The goal of attribution analysis is to isolate
  the reason for this value-added performance. The
  managers allocation effect can be computed by
  multiplying the excess asset class weight by that
  classs relative investment performance.
• This shows that if the investor had made just his
  market timing decisions and not picked different
  securities than those represented in the
  benchmark, his performance would have lagged the
  target return by two basis points.

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Performance Attribution Analysis (An Example)

• This total allocation effect can be broken down
  further into an equity allocation return of 2
  basis points (-0.10)(0.086 0.0846)
• a bond allocation return of 6 basis points
• (0.08)(0.092 0.0846)
• and a cash allocation return of 6 basis
  points
• (0.02)(0.054 0.08460
• Therefore, the decision to underweight stock and
  overweight cash ( asset classes that generated
  returns above and below the benchmark,
  respectively) resulted in diminished performance
  that was more than enough to offset the benefit
  of emphasizing bonds.
• Since the investor knows that he outperformed the
  benchmark overall, a negative allocation effect
  necessarily implies that he exhibited positive
  security selection skills.

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Performance Attribution Analysis (An Example)

• Since the investor knows that he outperformed the
  benchmark overall, a negative allocation effect
  necessarily implies that he exhibited positive
  security selection skills.
• His selection effect can be computed as
• In this example, the investor formed superior
  stock and cash portfolios, although his bond
  selections did not perform quite as well as the
  Lehman Long Bond index.
• One IMPORTANT caveatbecause the returns are not
  risk-adjusted, it is possible that the asset
  class portfolios formed by the investor are
  riskier than their benchmark counterparts.

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Performance Attribution Analysis (An Example)

• TOTAL VALUE ADDED ALLOCATION EFFECT SELECTION
  EFFECT
• 0.52 (-0.02) (0.54)
• USING A PROCEDURE SIMILAR TO THE ONE JUST
  DESCRIBED, BRINSON, HOOD, AND BEEBOWER EXAMINED
  THE RETURN PERFORMANCE OF A GROUP OF 91 U.S.
  PENSION PLANS OVER THE DECADE FROM 1974 TO 1983.
  THEY ESTABLISHED THAT THE MEAN ANNUAL RETURN FOR
  THIS SAMPLE WAS 9.01 PERCENT COMPARED TO 10.11
  FOR THEIR BENCHMARK. THUS, THEY DOCUMENTED THAT
  ACTIVE MANAGEMENT COST THE AVERAGE PLAN 110 BASIS
  POINTS OF RETURN PER YEAR.
• THIS VALUE SUBTRACTED RETURN INCREMENT
  CONSISTED OF A 77 BASIS POINT ALLOCATION EFFECT
  AND A 33 BASIS POINT SELECTION EFFECT.
• FURTHER, THEY CONCLUDED A PLANS INITIAL
  STRATEGIC ASSET ALLOCATION CHOICE, RATHER THAN
  ANY OF ITS ACTIVE MANAGEMENT DECISIONS, WAS THE
  PRIMARY DETERMINANT OF PORTFOLIO PERFORMANCE.