Investment Performance Evaluation

1
Investment Performance Evaluation

• Chapter 16

2
Introduction

• Chapter focuses on security selection decisions
  made by professional money managers, or
  institutional investors, such as
• Bank trust departments
• Mutual funds
• Investment advisory services
• Insurance companies investment management
  departments
• Money management firms

3
Sources of Funds

• Institutional money managers receive funds from
  various sources, including
• Pensions
• Corporate
• Government
• Individual workers
• Wealthy individuals
• Endowments
• Foundations

4
Selection of Money Manager

• These institutions/individuals must select a
  money manager
• This chapter presents tools for measuring and
  ranking money managers performances
• Aids in the selection process
• Money managers also use these tools to appraise
  and improve their skills

5
Information Needed for Evaluation

• To evaluate an investment manager
• Need rates of return
• Many money manager services do not provide
  adequate data
• Investment Company Act of 1940 requires every
  mutual fund in U.S. to disclose investment
  details
• Enables investors to effectively evaluate fund

6
Investments Company Data

• Mutual fund investor redeem shares at the current
  Net Asset Value Per Share (NAVPS)
• One-period rate of return for mutual fund

7
Mutual Funds

• Investment goals
• Open-end investment companies must state the
  portfolios investment objective
• ? 33 categories of objectives
• Closed-end funds
• Differ from open-end funds in that
• Cannot sell shares after initial offering
• Can borrow money, trade options and pursue
  different investment objectives
• Most shares are not redeemable at NAVPS
• Trade on stock exchangescan trade at a premium
  or discount (more common) relative to NAVPS

8
Are Mutual Funds Markowitz Efficient Investments?

• The mutual funds are all inefficient investments
• Funds tend to group into clusters corresponding
  to their investment goals
• Mutual funds are required to publish written goal
  statements
• In a few cases funds stated objective and
  performance differed

This income and growth fund performed in the same
league as the growth funds.
9
Scrutinizing Mutual Funds Goal Statements
Risk Class Range of Betas of funds Average Beta Average Variance Average Rate of Return
Low 0.5 to 0.7 28 0.619 0.000877 9.1
Medium 0.7 to 0.9 53 0.786 0.001543 10.6
High 0.9 to 1.1 22 0.992 0.002304 13.5
of funds claiming each goal of funds claiming each goal of funds claiming each goal of funds claiming each goal Categorys average rate of return Categorys average rate of return Categorys average rate of return Categorys average rate of return
Beta Growth Growth income Income Growth Income, Growth Stability Growth Growth income Income Growth Income, Growth Stability
0.5 to 0.7 3 5 4 16 6.9 10.1 9.7 9.1
0.7 to 0.9 15 24 7 7 11.2 10.0 10.0 12.2
0.9 to 1.1 20 1 None 1 13.8 9.5 None 13.5
Portfolios SDs and Betas were better indicators
of portfolios actual performance than their goal
statements.
10
Analyzing a Portfolio Managers Style

• In 1992 Sharpe introduced model to analyze a
  portfolio managers style (i.e., growth vs value
  investing, etc.)
• Uses modest amount of public information about
  funds
• Uses price indexes for 12 asset classes as
  explanatory variables for a mutual funds return
• Sample explanatory factors
• Soloman Brothers 90-day Treasury bill index
• Lehman Brothers Intermediate-Term Government Bond
  Index
• FTA Japan Index
• Sharpe/BARRA Value Stock Index

11
Analyzing a Portfolio Managers Style

• Uses factor analysis
• The factor loadings are estimates of the weights
  that a fund invests in the twelve asset
  categories
• R2 of 0.70 are common
• Sharpe also suggests that same type of analysis
  could be done using a rolling regression
• Repeating regression when new data is
  releaseddropping oldest data and adding newest
  data

12
Rolling Style Analysis

• Ibbotson Associates uses a rolling regression
  period of 60 months
• Deleting oldest month and adding new month as
  data becomes available

13
Benefits From Using Quantitative Management
Style Analysis

• Quantitative style analysis important due to
• Investment holdings are usually not reported
  publicly until months after they are madetoo
  late for investors to react in a timely manner
• Mutual funds can report misleading investment
  goals
• Can also provide better forecasts of mutual
  funds risk/return than subjective comments in
  newspapers, etc.

14
Sharpes Portfolio Performance Measure

• May wish to rank portfolios performances
• Need a measure that includes both risk and return
• Sharpe devised the reward to variability index

15
SHARPE Example

• The Avon Fund earned an average return of 8
  annually with a standard deviation of 16.6,
  while the Blair Fund earned 13.00 annually with
  a standard deviation of 22.4. During the same
  time period the average risk-free rate was 4.
• Which fund was the better performer?

Since SHARPEBlair gt SHARPEAvon, Blair was the
better performer on a risk-adjusted basis.
16
SHARPE Example
17
Treynors Performance Measure

• Treynor devised measure to evaluate performance
  that uses systematic risk (beta) rather than
  total risk (standard deviation)

Calculated by estimating the funds
characteristic line via regression.
18
TREYNOR Example

• The Avon Fund earned an average return of 8
  annually (Characteristic LineAVON Alpha
  -0.00125 Beta 0.8125), while the Blair Fund
  earned 13.00 annually (Characteristic LineBLAIR
  Alpha 0.014 Beta 1.156). During the same
  time period the average risk-free rate was 4.
• Which fund was the better performer?

Since TREYNORBlair gt TREYNORAvon, Blair was the
better performer on a risk-adjusted basis.
19
TREYNOR Example

• TREYNOR measures the desirability of fund in a
  SML context

20
An Investments Alpha

• Jensen modified the characteristic line equation
• Rather than using periodic rates of return, he
  uses periodic risk-premiums

• With expected values of

21
Explanation of an Investments Alpha

• Jensens alpha represents excess returns from
  asset
• Can be , 0 or
• If asset is correctly priced, Jensens alpha 0
• If alpha gt 0, asset has earned return greater
  than appropriate for its level of undiversifiable
  risk (beta)
• Asset is underpriced
• If alpha lt 0, assets returns are lower than
  appropriate for its level of risk
• Asset is overpriced

22
Jensens Alpha Example

• Using data (risk premiums, not returns) from
  Table 16-7 for the Avon and Blair Funds

• Characteristic LineAvon
• Jensens alpha -0.00875
• Beta 0.8125

• Characteristic LineBlair
• Jensens alpha 0.02062
• Beta 1.1562

Blair earned positive excess returns.
23
Caveats About Alphas

• Jensens alpha cannot be used to rank performance
  of different assets unless its adjusted for the
  assets risks
• The appraisal ratio divides Jensens alpha by the
  standard error of the estimate (SE(u)) which then
  allows for rankings

• The alpha calculated from the original
  characteristic line (Chapter 7) is not the same
  as Jensens alpha and should not be used for
  investment performance evaluation

24
Analyzing Performance Statistics

• Mutual funds with the highest average rate of
  return might not have the highest rank because
• A highly aggressive fund may earn higher returns
  than a less aggressive fund but the higher
  returns may not be sufficient to compensate for
  the extra risk taken

25
Analyzing Performance Statistics
Possible Investments Expected Return Standard Deviation
Yak Fund 30 20
Zebra Fund 15 5
RFR 4 0

• While the Yak Fund earned twice as much as the
  Zebra Fund it is four times as risky.

26
Analyzing Performance Statistics

• By multiplying Zebras low SD by 4, we could
  create a new portfolio on Zebras Asset
  Allocation Line with the same high SD as Yak Fund
• By borrowing 4 times as much as the initial
  equity, one could achieve the following E(rZebra)

27
Analyzing Performance Statistics
The leveraged Zebra portfolio dominates the Yak
Fund thus Zebra is a better fund even though Yak
has a higher average return.
28
General Discussion of Performance Measurement
Tools

• When investors analyze merits of alternative
  investments, usually concerned with
• Asset selection
• Portfolio managers ability to select good
  investments and to not select poor investments
• Sharpe, Treynor Jensens Alpha are good tools
  to evaluate this issue
• Market timing
• Portfolio managers ability to buy low/sell high
  and managers ability to react to changes in
  markets direction
• Sharpe, Treynor Jensens Alpha are not good
  tools for evaluating market timing unless
  theoretical framework is extended

29
Evaluating Timing Decisions

• Treynor Mazuy included a second-order term in
  the characteristic line to evaluate market-timing

30
Evaluating Timing Decisions

• A successful market timer will
• Shift into high beta securities when bull market
  begins
• Shift into low beta securities when bear market
  begins
• If portfolio manager does this, beta2,investment
  gt 0
• If portfolio manager cannot outguess market
  turns, beta2,investment 0 (statistically)
• If portfolio manager incorrectly predicts market
  turns, beta2,investment lt 0

31
Do Winners Repeat?

• Are the best portfolio managers able to repeat
  their high performance?
• If security markets are perfectly efficient,
  there should be no consistency in high
  performance
• When evaluating whether winners repeat, must be
  careful to not flaw study in terms of
  survivorship bias
• Market indexes only contain securities that have
  survivednot experienced bankruptcy, merger,
  etc.
• Goetzmann Ibbotson studied mutual funds
• Mitigated survivorship bias by comparing funds
  within-sample performances through time

32
Goetzmann Ibbotson Study

• Database
• Monthly total returns of several hundred mutual
  funds over a 13-year period
• Management fees deducted, but load, exit fees and
  taxes were not considered
• All cash flows reinvested monthly
• Returns measured over 2-year within-sample
  period, beginning in 1976 to predict
  out-of-sample performance for subsequent 2-year
  period
• Only funds in existence for entire 2-year
  interval included
• Every mutual fund categorized as winner or
  loser based on whether it ranked above or below
  that 2-year samples median return

33
Goetzmann Ibbotson Study
1978-1979 Winners 1978-1979 Losers 1980-1981 Winners 1980-1981 Losers
1976-1977 Winners 84 54 1978-1979 Winners 110 41
1976-1977 Losers 50 88 1978-1979 Losers 38 113
1982-1983 Winners 1982-1983 Losers 1984-1985 Winners 1984-1985 Losers
1980-1981 Winners 63 96 1982-1983 Winners 104 62
1980-1981 Losers 96 63 1982-1983 Losers 71 95
Combined Results Successive Period Combined Results Successive Period
1986-1987 Winners 1986-1987 Losers Winners Losers
1984-1985 Winners 125 72 Initial Winners 486 59.9 325 40.1
1984-1985 Losers 72 125 Initial Losers 327 40.3 484 59.7
The combined results show that there is about a
60 chance a winner will be a winner the
following period.
But, the repeat-winners pattern didnt persist
during this subsample.
34
Goetzmann Ibbotson Study

• However, these high-return mutual funds could
  continue to have high-ranking returns due to high
  risk, not because they were winners
• GI replicate study using risk-adjusted returns
• Computed Jensens Alpha for each fund
• Classified fund as a winner or loser if funds
  alpha gt or lt periods median alpha
• Results show that winners tend to repeat in all 5
  subsamples
• Also, divided sample into growth funds and found
  similar results
• Also, used 1-year subsamples rather than 2-year
• Similar, but weaker, support for the repeat
  winners hypothesis

35
Other Studies

• Malkiel argues that while repeat winners
  phenomenon existed in 1970s, it was not present
  during 1980s
• Carhart finds that winning funds tend to have a
  winning performance the following year, but not
  afterwards
• Losers have a strong tendency to persist with the
  worst performers persisting for years

36
The Bottom Line

• About mutual fund investments
• Average American buying round lots can afford
  only about 7 different stocks
• Not enough to minimize diversifiable risk
• Mutual funds are usually able to reduce their
  diversifiable risk
• Investors can maintain their desired risk-class
  by mutual fund investing
• Most investors should focus on a mutual funds
  fees and favor funds charging smallest fees

37
The Bottom Line

• About Portfolio Performance Measures
• To adequately evaluate a portfolio, must analyze
  both risk and return
• SHARPE measures risk-premium per unit of total
  risk
• TREYNOR measures risk-premium per unit of
  systematic risk
• Jensens alpha measures risk-adjusted returns for
  both portfolios and individual assets
• All three measures tend to rank mutual funds
  similarly
• Additional tools are available for measuring a
  managers market timing skills