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Chapter Twenty FourPortfolio Performance EvaluationINVESTMENTS |
BODIE, KANE, MARCUS2014 McGraw-Hill EducationIntroductionIf markets
are efficient, investors must be able to measure asset management
performanceTwo common ways to measure average portfolio
return:Time-weighted returnsDollar-weighted returns
Returns must be adjusted for risk.INVESTMENTS | BODIE, KANE,
MARCUSDollar- and Time-Weighted ReturnsTime-weighted returns
The geometric average is a time-weighted average.Each periods
return has equal weight.
INVESTMENTS | BODIE, KANE, MARCUSDollar- and Time-Weighted
ReturnsDollar-weighted returnsInternal rate of return considering
the cash flow from or to investmentReturns are weighted by the
amount invested in each period:
INVESTMENTS | BODIE, KANE, MARCUSExample of Multiperiod
Returns
INVESTMENTS | BODIE, KANE, MARCUSDollar-Weighted Return
Dollar-weighted Return (IRR):-$50-$53$2$4+$108INVESTMENTS |
BODIE, KANE, MARCUSTime-Weighted Return
The dollar-weighted average is less than the time-weighted
average in this example because more money is invested in year two,
when the return was lower.rG = [ (1.1) (1.0566) ]1/2 1 =
7.81%INVESTMENTS | BODIE, KANE, MARCUSDollar-Weighted
ReturnHouseholds should maintain a spreadsheet of time-dated cash
flows (in and out) to determine the effective rate of return for
any given period.
Examples include:IRA, 401(k), 529
INVESTMENTS | BODIE, KANE, MARCUSAdjusting Returns for RiskThe
simplest and most popular way to adjust returns for risk is to
compare the portfolios return with the returns on a comparison
universe.The comparison universe is a benchmark composed of a group
of funds or portfolios with similar risk characteristics, such as
growth stock funds or high-yield bond funds.
INVESTMENTS | BODIE, KANE, MARCUSFigure 24.1 Universe
Comparison
INVESTMENTS | BODIE, KANE, MARCUSRisk Adjusted Performance:
Sharpe1) Sharpe Indexrp = Average return on the portfolio
rf = Average risk free ratep= Standard deviation of portfolio
return
INVESTMENTS | BODIE, KANE, MARCUSRisk Adjusted Performance:
Treynor2) Treynor Measurerp = Average return on the portfolio rf =
Average risk free rate
p = Weighted average beta for portfolio
INVESTMENTS | BODIE, KANE, MARCUSRisk Adjusted Performance:
Jensen3) Jensens Measurep= Alpha for the portfoliorp = Average
return on the portfolio
p = Weighted average Beta
rf = Average risk free rate
rm = Average return on market index portfolio
INVESTMENTS | BODIE, KANE, MARCUSInformation RatioInformation
Ratio = ap / s(ep)The information ratio divides the alpha of the
portfolio by the nonsystematic risk.Nonsystematic risk could, in
theory, be eliminated by diversification.INVESTMENTS | BODIE, KANE,
MARCUSMorningstar Risk-Adjusted ReturnINVESTMENTS | BODIE, KANE,
MARCUSM2 MeasureDeveloped by Modigliani and ModiglianiCreate an
adjusted portfolio (P*)that has the same standard deviation as the
market index.Because the market index and P* have the same standard
deviation, their returns are comparable:
INVESTMENTS | BODIE, KANE, MARCUSM2 Measure: ExampleManaged
Portfolio: return = 35%standard deviation = 42%Market Portfolio:
return = 28%standard deviation = 30% T-bill return = 6%P*
Portfolio:30/42 = .714 in P and (1-.714) or .286 in T-billsThe
return on P* is (.714) (.35) + (.286) (.06) = 26.7%Since this
return is less than the market, the managed portfolio
underperformed.
INVESTMENTS | BODIE, KANE, MARCUSFigure 24.2 M2 of Portfolio
P
INVESTMENTS | BODIE, KANE, MARCUSWhich Measure is Appropriate?It
depends on investment assumptionsIf P is not diversified, then use
the Sharpe measure as it measures reward to risk.
2) If the P is diversified, non-systematic risk is negligible
and the appropriate metric is Treynors, measuring excess return to
beta.
INVESTMENTS | BODIE, KANE, MARCUSTable 24.1 Portfolio
Performance
Is Q better than P?INVESTMENTS | BODIE, KANE, MARCUSFigure 24.3
Treynors Measure
INVESTMENTS | BODIE, KANE, MARCUSTable 24.3 Performance
Statistics
INVESTMENTS | BODIE, KANE, MARCUSInterpretation of Table 24.3If
P or Q represents the entire investment, Q is better because of its
higher Sharpe measure and better M2.If P and Q are competing for a
role as one of a number of subportfolios, Q also dominates because
its Treynor measure is higher.If we seek an active portfolio to mix
with an index portfolio, P is better due to its higher information
ratio.
INVESTMENTS | BODIE, KANE, MARCUSPerformance Manipulation and
the MRARAssumption: Rates of return are independent and drawn from
same distribution.Managers may employ strategies to improve
performance at the loss of investors.Ingersoll, et al. study leads
to MPPM.Using leverage to increase potential returns.MRAR fulfills
requirements of the MPPMINVESTMENTS | BODIE, KANE, MARCUSFigure
24.4 MRAR scores with and w/o manipulation
INVESTMENTS | BODIE, KANE, MARCUSPerformance Measurement for
Hedge FundsWhen the hedge fund is optimally combined with the
baseline portfolio, the improvement in the Sharpe measure will be
determined by its information ratio:
INVESTMENTS | BODIE, KANE, MARCUSPerformance Measurement with
Changing Portfolio CompositionWe need a very long observation
period to measure performance with any precision, even if the
return distribution is stable with a constant mean and
variance.What if the mean and variance are not constant? We need to
keep track of portfolio changes.
INVESTMENTS | BODIE, KANE, MARCUSFigure 24.5 Portfolio
Returns
INVESTMENTS | BODIE, KANE, MARCUSMarket TimingIn its pure form,
market timing involves shifting funds between a market-index
portfolio and a safe asset.Treynor and Mazuy:
Henriksson and Merton:
INVESTMENTS | BODIE, KANE, MARCUSFigure 24.6 : No Market Timing;
Beta Increases with Expected Market Excess. Return; Market Timing
with Only Two Values of Beta.
INVESTMENTS | BODIE, KANE, MARCUSFigure 24.7 Rate of Return of a
Perfect Market Timer
INVESTMENTS | BODIE, KANE, MARCUSStyle AnalysisIntroduced by
William SharpeRegress fund returns on indexes representing a range
of asset classes.The regression coefficient on each index measures
the funds implicit allocation to that style.R square measures
return variability due to style or asset allocation. The remainder
is due either to security selection or to market timing.
INVESTMENTS | BODIE, KANE, MARCUSTable 24.5 Style Analysis for
Fidelitys Magellan Fund
INVESTMENTS | BODIE, KANE, MARCUSFigure 24.8 Fidelity Magellan
Fund Cumulative Return Difference
INVESTMENTS | BODIE, KANE, MARCUSFigure 24.9 Average Tracking
Error for 636 Mutual Funds, 1985-1989
INVESTMENTS | BODIE, KANE, MARCUSPerformance AttributionA common
attribution system decomposes performance into three
components:
Allocation choices across broad asset classes. Industry or
sector choice within each market. Security choice within each
sector.
INVESTMENTS | BODIE, KANE, MARCUSAttributing Performance to
ComponentsSet up a Benchmark or Bogey portfolio:Select a benchmark
index portfolio for each asset class.Choose weights based on market
expectations.Choose a portfolio of securities within each class by
security analysis.INVESTMENTS | BODIE, KANE, MARCUSAttributing
Performance to ComponentsCalculate the return on the Bogey and on
the managed portfolio.Explain the difference in return based on
component weights or selection.Summarize the performance
differences into appropriate categories.INVESTMENTS | BODIE, KANE,
MARCUSFormulas for Attribution
Where B is the bogey portfolio and p is the managed
portfolioINVESTMENTS | BODIE, KANE, MARCUSFigure 24.10 Performance
Attribution of ith Asset Class
INVESTMENTS | BODIE, KANE, MARCUSPerformance AttributionSuperior
performance is achieved by:overweighting assets in markets that
perform wellunderweighting assets in poorly performing
marketsINVESTMENTS | BODIE, KANE, MARCUSTable 24.7 Performance
Attribution
INVESTMENTS | BODIE, KANE, MARCUSSector and Security
SelectionGood performance (a positive contribution) derives from
overweighting high-performing sectors
Good performance also derives from underweighting poorly
performing sectors.INVESTMENTS | BODIE, KANE, MARCUS
