CHAPTER TWENTY-FOUR

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CHAPTER TWENTY-FOUR

• PORTFOLIO PERFORMANCE EVALUATION

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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 Dollar-Weighted
  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
• SP500
• 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
  assets long-run performance

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RISK-ADJUSTED MEASURES OF PERFORMANCE

• THE REWARD TO VOLATILITLY 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
• where 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

SML
arp
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 portfolios beta
• the higher the slope, the more sensitive is the
  portfolio to the market

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TREYNOR MEASURE

• THE CHARACTERISTIC LINE

SML
arp
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 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
CML
arp
sp
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THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE

• BASED ON THE CAPM EQUATION
• measures the average return on the portfolio over
  and above that predicted by the CAPM
• given the portfolios beta and the average market
  return

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THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE

• THE JENSEN MEASURE
• known as the portfolios 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
• subtracting RFR from both sides

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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 RISK-ADJUSTED PERFORMANCE MEASURES

• Use of a market surrogate
• Roll criticized any measure that attempted to
  model the market portfolio with a surrogate such
  as the SP500
• 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 RISK-ADJUSTED 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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• END OF CHAPTER 24