Transcript Document

CHAPTER
EIGHTEEN
PORTFOLIO PERFORMANCE
EVALUATION
1
MEASURES OF RETURN
• MEASURES OF RETURN
– complicated by addition or withdrawal of
money by the investor
– percentage change is not reliable when the base
amount may be changing
– timing of additions or withdrawals is important
to measurement
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MEASURES OF RETURN
• TWO MEASURES OF RETURN
– Dollar-Weighted Returns
• uses discounted cash flow approach
• weighted because the period with the greater
number of shares has a greater influence on the
overall average
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MEASURES OF RETURN
• TWO MEASURES OF RETURN
– Time-Weighted Returns
• used when cash flows occur between beginning and
ending of investment horizon
• ignores number of shares held in each period
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MEASURES OF RETURN
• TWO MEASURES OF RETURN
– Comparison of Time-Weighted to DollarWeighted Returns
• Time-weighted useful in pension fund management
where manager cannot control the deposits or
withdrawals to the fund
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MAKING RELEVANT
COMPARISONS
• PERFORMANCE
– should be evaluated on the basis of a relative
and not an absolute basis
• this is done by use of a benchmark portfolio
– BENCHMARK PORTFOLIO
• should be relevant and feasible
• reflects objectives of the fund
• reflects return as well as risk
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THE USE OF MARKET
INDICES
• INDICES
– are used to indicate performance but depend
upon
• the securities used to calculate them
• the calculation weighting measures
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THE USE OF MARKET
INDICES
• INDICES
– Three Calculation Weighting Methods:
• price weighting
– sum prices and divided by a constant to determine average
price
– EXAMPLE: THE DOW JONES INDICES
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THE USE OF MARKET
INDICES
• INDICES
– Three Calculation Weighting Methods:
• value weighting (capitalization method)
– price times number of shares outstanding is summed
– divide by beginning value of index
– EXAMPLE:
» S&P500
» WILSHIRE 5000
» RUSSELL 1000
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THE USE OF MARKET
INDICES
• INDICES
– Three Calculation Weighting Methods:
• equal weighting
– multiply the level of the index on the previous day by the
arithmetic mean of the daily price relatives
– EXAMPLE:
» VALUE LINE COMPOSITE
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ARITHMETIC V. GEOMETRIC
AVERAGES
• GEOMETRIC MEAN FRAMEWORK
GM = (P HPR)1/N - 1
where P = the summation of the
product of
HPR= the holding period returns
n= the number of periods
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ARITHMETIC V. GEOMETRIC
AVERAGES
• GEOMETRIC MEAN FRAMEWORK
– measures past performance well
– represents exactly the constant rate of return
needed to earn in each year to match some
historical performance
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ARITHMETIC V. GEOMETRIC
AVERAGES
• ARITHMETIC MEAN FRAMEWORK
– provides a good indication of the expected rate
of return for an investment during a future
individual year
– it is biased upward if you attempt to measure an
asset’s long-run performance
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RISK-ADJUSTED MEASURES OF
PERFORMANCE
• THE REWARD TO VOLATILITY RATIO
(TREYNOR MEASURE)
– There are two components of risk
• risk associated with market fluctuations
• risk associated with the stock
– Characteristic Line (ex post security line)
• defines the relationship between historical portfolio
returns and the market portfolio
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TREYNOR MEASURE
• TREYNOR MEASURE
– Formula
RVOL p 
where
arp  arf
bp
arp = the average portfolio return
arf = the average risk free rate
bp = the slope of the characteristic
line during the time period
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TREYNOR MEASURE
THE CHARACTERISTIC LINE
arp
SML
bp
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TREYNOR MEASURE
• CHARACTERISTIC LINE
– slope of CL
• measures the relative volatility of portfolio returns
in relation to returns for the aggregate market, i.e.
the portfolio’s beta
• the higher the slope, the more sensitive is the
portfolio to the market
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TREYNOR MEASURE
THE CHARACTERISTIC LINE
arp
SML
bp
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THE SHARPE RATIO
• THE REWARD TO VARIABILITY
(SHARPE RATIO)
– measure of risk-adjusted performance that uses
a benchmark based on the ex-post security
market line
– total risk is measured by sp
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THE SHARPE RATIO
• SHARPE RATIO
– formula:
where
SR p 
arp  arf
sp
SR = the Sharpe ratio
sp = the total risk
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THE SHARPE RATIO
• SHARPE RATIO
– indicates the risk premium per unit of total risk
– uses the Capital Market Line in its analysis
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THE SHARPE RATIO
arp
CML
sp
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THE JENSEN MEASURE OF
PORTFOLIO PERFORMANCE
• BASED ON THE CAPM EQUATION
E (ri )  RFR  b [ E (rm )  RFR ]
– measures the average return on the portfolio
over and above that predicted by the CAPM
– given the portfolio’s beta and the average
market return
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THE JENSEN MEASURE OF
PORTFOLIO PERFORMANCE
• THE JENSEN MEASURE
– known as the portfolio’s alpha value
• recall the linear regression equation
y = a + bx + e
• alpha is the intercept
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THE JENSEN MEASURE OF
PORTFOLIO PERFORMANCE
• DERIVATION OF ALPHA
– Let the expectations formula in terms of
realized rates of return be written
R jt  RFRt  b j Rmt  RFRt   u jt
– subtracting RFR from both sides
R jt  RFRt  b j Rmt  RFRt   u jt
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THE JENSEN MEASURE OF
PORTFOLIO PERFORMANCE
• DERIVATION OF ALPHA
– in this form an intercept value for the
regression is not expected if all assets are in
equilibrium
– in words, the risk premium earned on the jth
portfolio is equal to bj times a market risk
premium plus a random error term
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THE JENSEN MEASURE OF
PORTFOLIO PERFORMANCE
• DERIVATION OF ALPHA
– to measure superior portfolio performance, you
must allow for an intercept a
– a superior manager has a significant and
positive alpha because of constant positive
random errors
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COMPARING MEASURES OF
PERFORMANCE
• TREYNOR V. SHARPE
– SR measures uses s as a measure of risk while
Treynor uses b
– SR evaluates the manager on the basis of both
rate of return performance as well as
diversification
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COMPARING MEASURES OF
PERFORMANCE
– for a completely diversified portfolio
• SR and Treynor give identical rankings because total
risk is really systematic variance
• any difference in ranking comes directly from a
difference in diversification
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CRITICISM OF RISKADJUSTED PERFORMANCE
MEASURES
• Use of a market surrogate
• Roll: criticized any measure that attempted to
model the market portfolio with a surrogate such as
the S&P500
– it is almost impossible to form a portfolio whose returns
replicate those over time
– making slight changes in the surrogate may completely
change performance rankings
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CRITICISM OF RISKADJUSTED PERFORMANCE
MEASURES
• measuring the risk free rate
• using T-bills gives too low of a return making it
easier for a portfolio to show superior performance
• borrowing a T-bill rate is unrealistically low and
produces too high a rate of return making it more
difficult to show superior performance
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