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Chapter 19 Performance Evaluation

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Fund A has $40 million in investments and earned 12% last period ... Approximates the internal rate of return for the investment over the period in question ... – PowerPoint PPT presentation

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Title: Chapter 19 Performance Evaluation


1
Chapter 19Performance Evaluation
2
  • And with that they clapped him into irons and
    hauled him off to the barracks. There he was
    taught right turn, left turn, and quick
    march, slope arms, and order arms, how to
    aim and how to fire, and was given thirty strokes
    of the cat. Next day his performance on parade
    was a little better, and he was given only twenty
    strokes. The following day he received a mere ten
    and was thought a prodigy by his comrades.
  • - From Candide by Voltaire

3
Outline
  • Introduction
  • Importance of measuring portfolio risk
  • Traditional performance measures
  • Performance evaluation with cash deposits and
    withdrawals
  • Performance evaluation when options are used

4
Introduction
  • Performance evaluation is a critical aspect of
    portfolio management
  • Proper performance evaluation should involve a
    recognition of both the return and the riskiness
    of the investment

5
Importance of Measuring Portfolio Risk
  • Introduction
  • A lesson from history the 1968 Bank
    Administration Institute report
  • A lesson from a few mutual funds
  • Why the arithmetic mean is often misleading a
    review
  • Why dollars are more important than percentages

6
Introduction
  • When two investments returns are compared, their
    relative risk must also be considered
  • People maximize expected utility
  • A positive function of expected return
  • A negative function of the return variance

7
A Lesson from History
  • The 1968 Bank Administration Institutes
    Measuring the Investment Performance of Pension
    Funds concluded
  • Performance of a fund should be measured by
    computing the actual rates of return on a funds
    assets
  • These rates of return should be based on the
    market value of the funds assets

8
A Lesson from History (contd)
  • Complete evaluation of the managers performance
    must include examining a measure of the degree of
    risk taken in the fund
  • Circumstances under which fund managers must
    operate vary so great that indiscriminate
    comparisons among funds might reflect differences
    in these circumstances rather than in the ability
    of managers

9
A Lesson from A Few Mutual Funds
  • The two key points with performance evaluation
  • The arithmetic mean is not a useful statistic in
    evaluating growth
  • Dollars are more important than percentages
  • Consider the historical returns of two mutual
    funds on the following slide

10
A Lesson from A Few Mutual Funds (contd)
11
A Lesson from A Few Mutual Funds (contd)
12
A Lesson from A Few Mutual Funds (contd)
  • 44 Wall Street and Mutual Shares both had good
    returns over the 1975 to 1988 period
  • Mutual Shares clearly outperforms 44 Wall Street
    in terms of dollar returns at the end of 1988

13
Why the Arithmetic Mean Is Often Misleading
  • The arithmetic mean may give misleading
    information
  • E.g., a 50 decline in one period followed by a
    50 increase in the next period does not return
    0, on average

14
Why the Arithmetic Mean Is Often Misleading
(contd)
  • The proper measure of average investment return
    over time is the geometric mean

15
Why the Arithmetic Mean Is Often Misleading
(contd)
  • The geometric means in the preceding example are
  • 44 Wall Street 7.9
  • Mutual Shares 22.7
  • The geometric mean correctly identifies Mutual
    Shares as the better investment over the 1975 to
    1988 period

16
Why the Arithmetic Mean Is Often Misleading
(contd)
  • Example
  • A stock returns 40 in the first period, 50 in
    the second period, and 0 in the third period.
  • What is the geometric mean over the three
    periods?

17
Why the Arithmetic Mean Is Often Misleading
(contd)
  • Example
  • Solution The geometric mean is computed as
    follows

18
Why Dollars Are More Important than Percentages
  • Assume two funds
  • Fund A has 40 million in investments and earned
    12 last period
  • Fund B has 250,000 in investments and earned 44
    last period

19
Why Dollars Are More Important than Percentages
  • The correct way to determine the return of both
    funds combined is to weigh the funds returns by
    the dollar amounts

20
Traditional Performance Measures
  • Sharpe and Treynor measures
  • Jensen measure
  • Performance measurement in practice

21
Sharpe and Treynor Measures
  • The Sharpe and Treynor measures

22
Sharpe and Treynor Measures (contd)
  • The Treynor measure evaluates the return relative
    to beta, a measure of systematic risk
  • It ignores any unsystematic risk
  • The Sharpe measure evaluates return relative to
    total risk
  • Appropriate for a well-diversified portfolio, but
    not for individual securities

23
Sharpe and Treynor Measures (contd)
  • Example
  • Over the last four months, XYZ Stock had excess
    returns of 1.86, -5.09, -1.99, and 1.72. The
    standard deviation of XYZ stock returns is 3.07.
    XYZ Stock has a beta of 1.20.
  • What are the Sharpe and Treynor measures for XYZ
    Stock?

24
Sharpe and Treynor Measures (contd)
  • Example (contd)
  • Solution First compute the average excess return
    for Stock XYZ

25
Sharpe and Treynor Measures (contd)
  • Example (contd)
  • Solution (contd) Next, compute the Sharpe and
    Treynor measures

26
Jensen Measure
  • The Jensen measure stems directly from the CAPM

27
Jensen Measure (contd)
  • The constant term should be zero
  • Securities with a beta of zero should have an
    excess return of zero according to finance theory
  • According to the Jensen measure, if a portfolio
    manager is better-than-average, the alpha of the
    portfolio will be positive

28
Jensen Measure (contd)
  • The Jensen measure is generally out of favor
    because of statistical and theoretical problems

29
Performance Measurement in Practice
  • Academic issues
  • Industry issues

30
Academic Issues
  • The use of traditional performance measures
    relies on the CAPM
  • Evidence continues to accumulate that may
    ultimately displace the CAPM
  • APT, multi-factor CAPMs, inflation-adjusted CAPM

31
Industry Issues
  • Portfolio managers are hired and fired largely
    on the basis of realized investment returns with
    little regard to risk taken in achieving the
    returns
  • Practical performance measures typically involve
    a comparison of the funds performance with that
    of a benchmark

32
Industry Issues (contd)
  • Famas decomposition can be used to assess why an
    investment performed better or worse than
    expected
  • The return the investor chose to take
  • The added return the manager chose to seek
  • The return from the managers good selection of
    securities

33
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34
Performance Evaluation With Cash Deposits
Withdrawals
  • Introduction
  • Daily valuation method
  • Modified Bank Administration Institute (BAI)
    Method
  • An example
  • An approximate method

35
Introduction
  • The owner of a fund often taken periodic
    distributions from the portfolio and may
    occasionally add to it
  • The established way to calculate portfolio
    performance in this situation is via a
    time-weighted rate of return
  • Daily valuation method
  • Modified BAI method

36
Daily Valuation Method
  • The daily valuation method
  • Calculates the exact time-weighted rate of return
  • Is cumbersome because it requires determining a
    value for the portfolio each time any cash flow
    occurs
  • Might be interest, dividends, or additions and
    withdrawals

37
Daily Valuation Method (contd)
  • The daily valuation method solves for R

38
Daily Valuation Method (contd)
  • MVEi market value of the portfolio at the end
    of period i before any cash flows in period i but
    including accrued income for the period
  • MVBi market value of the portfolio at the
    beginning of period i including any cash flows at
    the end of the previous subperiod and including
    accrued income

39
Modified BAI Method
  • The modified BAI method
  • Approximates the internal rate of return for the
    investment over the period in question
  • Can be complicated with a large portfolio that
    might conceivably have a cash flow every day

40
Modified BAI Method (contd)
  • It solves for R

41
An Example
  • An investor has an account with a mutual fund and
    dollar cost averages by putting 100 per month
    into the fund
  • The following slide shows the activity and
    results over a seven-month period

42
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43
An Example (contd)
  • The daily valuation method returns a
    time-weighted return of 40.6 over the
    seven-months period
  • See next slide

44
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45
An Example (contd)
  • The BAI method requires use of a computer
  • The BAI method returns a time-weighted return of
    42.1 over the seven-months period (see next
    slide)

46
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47
An Approximate Method
  • Proposed by the American Association of
    Individual Investors

48
An Approximate Method (contd)
  • Using the approximate method in Table 19-6

49
Performance Evaluation When Options Are Used
  • Introduction
  • Incremental risk-adjusted return from options
  • Residual option spread
  • Final comments on performance evaluation with
    options

50
Introduction
  • Inclusion of options in a portfolio usually
    results in a non-normal return distribution
  • Beta and standard deviation lose their
    theoretical value of the return distribution is
    nonsymmetrical

51
Introduction (contd)
  • Consider two alternative methods when options are
    included in a portfolio
  • Incremental risk-adjusted return (IRAR)
  • Residual option spread (ROS)

52
Incremental Risk-Adjusted Return from Options
  • Definition
  • An IRAR example
  • IRAR caveats

53
Definition
  • The incremental risk-adjusted return (IRAR) is a
    single performance measure indicating the
    contribution of an options program to overall
    portfolio performance
  • A positive IRAR indicates above-average
    performance
  • A negative IRAR indicates the portfolio would
    have performed better without options

54
Definition (contd)
  • Use the unoptioned portfolio as a benchmark
  • Draw a line from the risk-free rate to its
    realized risk/return combination
  • Points above this benchmark line result from
    superior performance
  • The higher than expected return is the IRAR

55
Definition (contd)
56
Definition (contd)
  • The IRAR calculation

57
An IRAR Example
  • A portfolio manager routinely writes index call
    options to take advantage of anticipated market
    movements
  • Assume
  • The portfolio has an initial value of 200,000
  • The stock portfolio has a beta of 1.0
  • The premiums received from option writing are
    invested into more shares of stock

58
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59
An IRAR Example (contd)
  • The IRAR calculation (next slide) shows that
  • The optioned portfolio appreciated more than the
    unoptioned portfolio
  • The options program was successful at adding
    about 12 per year to the overall performance of
    the fund

60
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61
IRAR Caveats
  • IRAR can be used inappropriately if there is a
    floor on the return of the optioned portfolio
  • E.g., a portfolio manager might use puts to
    protect against a large fall in stock price
  • The standard deviation of the optioned portfolio
    is probably a poor measure of risk in these cases

62
Residual Option Spread
  • The residual option spread (ROS) is an
    alternative performance measure for portfolios
    containing options
  • A positive ROS indicates the use of options
    resulted in more terminal wealth than only
    holding stock
  • A positive ROS does not necessarily mean that the
    incremental return is appropriate given the risk

63
Residual Option Spread (contd)
  • The residual option spread (ROS) calculation

64
Residual Option Spread (contd)
  • The worksheet to calculate the ROS for the
    previous example is shown on the next slide
  • The ROS translates into a dollar differential of
    1,452

65
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66
The M2 Performance Measure
  • Developed by Franco and Leah Modigliani in 1997
  • Seeks to express relative performance in
    risk-adjusted basis points
  • Ensures that the portfolio being evaluated and
    the benchmark have the same standard deviation

67
The M2 Performance Measure
(contd)
  • Calculate the risk-adjusted portfolio return as
    follows

68
Final Comments
  • IRAR and ROS both focus on whether an optioned
    portfolio outperforms an unoptioned portfolio
  • Can overlook subjective considerations such as
    portfolio insurance
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