Chapter 19 Performance Evaluation

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Chapter 19Performance Evaluation

• Business 4179

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Key Issues

• Any measurement of performance should somehow tie
  together the return of the investment and the
  riskiness of that return.
• Sharpe and Treynor performance measures are
  classic elements of performance evaluation and
  are useful.
• They become less useful when there are additions
  to or withdrawals from the portfolio. In such a
  case the internal rate of return becomes the
  appropriate measure of return.
• The presence of options in a portfolio
  complicates the performance evaluation process.
  Two methods for comparing an optioned portfolio
  with an unoptioned counterpart are the Residual
  Option Spread and the Incremental Rate of Return
  from Options.

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Question 19 - 1

• Risk, by definition, the chance of loss. A risky
  situation involves an uncertain outcome, and some
  possible outcomes are adverse. Repeated draws
  from the probability distribution will
  periodically result in the selection of an
  adverse outcome. It is important to know
  something about the distribution before choosing
  to draw one. Because you were lucky once does
  not mean you will be again.

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Question 19 - 2

• Investors like return and dislike risk.
• Utility comes from getting more return and
  reducing risk. Securities are priced to provide
  a level of return consistent with their perceived
  level of risk. Over the long term, a portfolio
  of risky securities should earn a higher return
  than a safer portfolio.
• Some portfolio components, however, probably will
  be losers. Risk-adjusted performance measurement
  seeks to associate a measure of the likelihood of
  loss with the return statistic.

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Question 19 - 3

• Investors do not like risk.
• Everything else being equal, they prefer the
  least risky alternative.

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Question 19 - 4

• You would want to know how long it took to
  double, and what its interim price behaviour
  looked like. It also would be useful to compare
  the security to the return and risk of a market
  index over the same period.

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Question 19 - 5

• Examples include legal lists of eligible
  investments, regulatory constraints, special tax
  incentives/disincentives, and statutory
  restrictions.

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Question 19 - 6

• It makes no difference. The geometric mean
  return is invariant to the order of the returns.

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Question 19 - 7

• A. Arithmetic
• B. Geometric
• C. Geometric or arithmetic, depending on what you
  were going to do with the information.

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Question 19 - 8

• Returns can be negative.
• You cannot take an even root of a negative
  number, and if you have an odd number of negative
  returns the geometric mean will be an imaginary
  number.
• Return relatives are only positive.

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Question 19 - 9

• When looking at a single security, it is best to
  use the Treynor measure, as the market only
  rewards you for bearing systematic risk. The
  Treynor measure is based on beta, which measures
  systematic risk.

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Question 19 - 10

• Writing covered calls partially offsets changes
  in the value of the portfolio either up or down.
  This attenuates the volatility of the portfolio.

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Problem 19 - 1
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Problem 19 - 2

• The annual returns of the equally weighted
  portfolio are 5, 0, -6.33, 12 and 5.67.
  Their mean is 3.27 with a standard deviation of
  .0613. The Sharpe measure is then
• SHp .0327 - .03 / .0613 .0440

Portfolio
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Problem 19 - 3

• A (1.05)(1.0)(.95)(1.08)(1.05)2 - 1 .0250
• B (1.04)(1.01)(.96)(1.10)(1.05)2 - 1 .0310
• C (1.06)(.99)(.90)(1.18)(1.07)2 - 1 .0358
• Portfolio (1.05)(1.0)(.9367)(1.12)(1.0567)2 -
  1 .0308
• Ranking by geometric mean
• C (best)
• B
• Portfolio
• A (worst)

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Problem 19 - 4

• The monthly IRR is 0.0026, for an annual rate of
  3.12

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Problem 19 - 4

• IRAR (SH0 - SHU)s0 (.0433)-(-0.087)(.0462)
  0.0060

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Problem 19 - 6

• IRAR (SH0 - SHU)s0
• (.0433)-(-0.087)(.0462) 0.0060

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Problem 19 - 7
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Problem 19 - 9
Using the data in Table 19 - 6 we are redoing the
calculations assuming the investor deposited
300. (I have done this Excelso just
double-click the table to see the underlying
formulae.)
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Problem 19 - 9 ...
Product of MVE/MVB values 1.406 V 40.6
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Problem 19 - 9 ...

• The daily valuation worksheet with 300/month
  gives precisely the same answer as with the
  100/month investment, while the approximate
  method produces an answer considerably different.
  This illustrates that while the time-weight rate
  of return is invariant to the size of the
  periodic investments (and is therefore more
  accurate), the approximate method is sensitive to
  them.