Active Management and Performance Measures

1
Active Management and Performance Measures

• Chapter 21
• Introduction
• Performance Evaluation conventional
  risk-adjusted measures
• Market Timing
• Can exclude 21.4, and will only do 21.6 if we
  have time

2
Introduction

• Active vs. passive portfolio management
• Active selection will mean some non-systematic
  risk ? not holding a diversified portfolio
• Measures applied to actively managed portfolios
• Portfolio performance tied to managers
  compensation (directly or indirectly)
• Managers role stock selection and management of
  fund (and for institutional fund managers sales
  as well)

3
Introduction

• For passive/index managers, measure performance
  using tracking error
• Where Rpt is the portfolio return in period t,
  and RBt is the benchmark return in period t
• Tracking error is a standard deviation concept
  it measures deviations from benchmark

4
Introduction (contd)

• Measure of abnormal performance
• What is abnormal?
• Relative to a market index
• e.g., SP 500, EFEA, depending on portfolio
  mandate
• Relative to a benchmark portfolio or sub-index
• SP MidCap 400, EFEA value
• Risk-adjusted measures

5
B. Performance EvaluationRisk-adjusted measures

• Is the return adequate compensation for the risk?
• 1) Sharpe Ratio

6
Risk-adjusted Measures (contd)

• 2) Treynor Measure

7
Risk-adjusted Measures(contd)

• 3) Jensens alpha
• If ?p gt 0, then there is abnormal portfolio
  return, over and above the systematic
  risk-adjusted return (i.e., whats predicted by
  the CAPM)
• Instead of using averages, use regression
  analysis estimate ? and ? together, and
  determine statistical significance

8
Risk-adjusted Measures (Contd)

• Industry version of alpha
• rp rB
• Managers performance is benchmarked
• Also referred to as value added

9
Risk-adjusted Measures(contd)
4) Appraisal/information Ratio ap / sep

• Divides the alpha of the portfolio by the
  measure of nonsystematic risk
• From regression analysis, obtain alpha, beta and
  ep simultaneously
• Then calculate the standard deviation of ep
• Nonsystematic risk could, in theory, be
  eliminated by diversification

10
Risk-adjusted Measures(contd)

• Industry version of the information ratio
• ?p/?(rp rB)
• Numerator industry version of alpha
• Denominator tracking error (deviations from the
  benchmark)

11
M2 Measure

• Developed by Modigliani and Modigliani
• First, create a hypothetical portfolio made up of
  T-bills and the managed portfolio
• This hypothetical portfolio is set up to have the
  same standard deviation as the market
• Compare return to the hypothetical portfolio and
  the market return

12
M2 Measure Numerical Example

• Managed Portfolio return 35 s 42
• Market Portfolio return 28 s 30
• T-bill return 6
• Hypothetical Portfolio
• To have the same s as the market, what must the
  weights be?
• Show that the return on this portfolio is 26.7
• M2 Measure 26.7 28 -1.3
• Since this return is less than the market, the
  managed portfolio underperformed

13
M2 MeasureGraphical Representation
Return
M
M2
P
F
s
42
30
14
Which Measure is Appropriate?

• In general,
• If the portfolio represents the entire investment
  of an individual, use the Sharpe ratio (uses
  total risk). Compare SP with SM
• If many alternative portfolios are to be
  selected, use the Treynor measure, i.e.,
  contribution of risk matters
• If an active portfolio is to be added to an index
  portfolio, use the appraisal ratio (gaining alpha
  at the expense of nonsystematic risk)

15
Issues

• Assumptions underlying measures limit their
  usefulness, e.g., mean-variance
• Short horizon small sample problems
• Many rankings in the media still use raw
  portfolio returns
• Risk-adjusted measures becoming popular
• Hedge funds can manipulate volatility using
  derivatives Sharpe ratio may not be a good
  measure

16
Market Timing

• Adjust the portfolio for movements in the market
• Shift between stocks and money market instruments
  or bonds
• Results higher returns, lower risk (downside is
  eliminated)
• With perfect ability to forecast behaves like an
  option

17
Rate of Return of a Perfect Market Timer
rp
0
18
Returns from 90 - 99
19
With Perfect Forecasting Ability

• Switch to T-Bills in 90 and 94
• Mean 18.94,
• Standard Deviation 12.04
• Invested in large stocks for the entire period
• Mean 17.41
• Standard Deviation 14.11
• Results are clearly sample-period dependent.
  Example period of stock market boom

20
Characteristic Lines (A) No Market Timing (B)
Beta Increases with Return (C) Two Values of Beta
21
With Imperfect Ability to Forecast

• Need longer horizon to judge ability
• Judge proportions of correct calls
• Identifying market timing
• Statistical method regression analysis
• Idea
• Low market return - low portfolio beta
• High market return - high portfolio beta

22
Other specification

• Can use other nonlinear specifications
• For example,
• rp- rf a b(rm rf) c(rm rf)D ep
• where D is a dummy variable
• D 1 when rm rf gt 0, and zero otherwise
• Again, c gt 0 can be used as evidence of
  successful market timing
• When stock market is doing well, want slope (b
  c) to be steeper