Navellier Applied Research

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Navellier Applied Research
Exploring Aspects of Investment Statistics

• Navellier Applied Research
• Timothy A. Hope
• Applied Research Analyst
• 775-785-9416

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This formula for standard deviation
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Will NOT be seen for the remainder of this
presentation
Rest easy..lets discuss some ideas!
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Statistics Appearance and Reality

• While statistics can be useful in making
  investment decisions, it is important to
  recognize that they also carry some limitations.
• Remember the old computer adage Garbage
  In/Garbage Out.

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Problem with single computation statistics

• What is the speed of this space shuttle?

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Problem with single computation statistics -
continued

• Answer
• We cant tell. We dont have enough
  information.
• The same problem arises when using a single
  point computation of investment statistics,

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Single Point Computation Example
Risk (standard deviation) seems pretty close.
But is it?
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Is there a story to be told? How can we find out?

• Answer
• Roll the time periods. Then we can see trends
  in the data.

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Concept behind rolling time periods
Window of time otherwise known as window size
Calculate single point of data plot it
Advance Window
Calculate and plot
Advance Window
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This single point
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..turns into this when rolled.
Is there a story here? Is something consistently
more volatile?
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What happens when rolling periods are
changed?36 quarter window advanced annually
Trend still distinct
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16 quarter rolling window, advanced quarterly
Trend less distinct
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Eight quarter window, advanced quarterly
Going
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Six month window advanced quarterly
Going
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Six month window advanced monthly
Gone!
Is this too sensitive of a time period? Can you
draw any conclusions?
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So what?
What if you are being told that all three
investment alternative have about the same level
of risk? Is it true?
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So what about risk?

• Recall that standard deviation is a common
  measure of risk
• Low Good?
• High Bad?
• Really?

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Remember what standard deviation is measuring!
Degree of movement from the average
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Trampoline Thought Experiment

• Consider the case of two trampolines.
• Trampoline 1 Soft and yielding.
• Trampoline 2 Firm and resilient.
• How can they help to illustrate standard
  deviation?

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Trampoline Example
Of the two, wouldnt this be the preferred
investment manager?
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Semi standard deviation or downside risk
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Here is the Trampoline Math
Standard Deviation
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Assume equal standard deviation. Which investment
is getting riskier? Less risky?
Manager A Risk is Rising
Risk
Manager B Risk is Falling
Time
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Standard deviation and the current credit crisis
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Is this the root of the problem?
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Everything hides in the assumptions!
A physicist, a chemist and an economist are
stranded on an island, with nothing to eat. A can
of soup washes ashore. The physicist says, "Lets
smash the can open with a rock." The chemist
says, "Lets build a fire and heat the can first."
The economist says
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Lets assume we have a can opener!
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Are possible small model errors compounding to
result is major disruptions?
Are academic practitioners building financial
models that assume normal distributions?
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Reality vs. models
The standard statistical approach to risk
management is based on a bell curve or normal
distribution, in which most results are in the
middle and extremes are rare. It is the bell
curve to which investors are referring when they
talk about a nine standard deviation event.
But financial history is littered with bubbles
and crashes, demonstrating that extreme events or
so-called fat tails occur far more often than
the bell curve predicts.
Spooking investors Oct 25th 2007From The
Economist print edition
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Nine standard deviations? Really?

• Lets look at a curve that can be considered
  accepted as normal human height
• Nine deviations from assumed average
• 1 in 8,900,000,000,000,000,000

Source Nassim Taleb, The Black Swan, pg 231
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Deal or No Deal? Normal or Not Normal?
?
?
Twenty Year Histogram of Monthly Index Returns
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If it doesnt fit, you must acquit. - Johnnie
Cochran
The Fatter the distribution tails, the less
reliable the statistics!

• If the population of price changes is strictly
  normal, on average for any stock..an
  observation more than five standard deviations
  from the mean should be observed about once every
  7,000 years. In fact such observations seem to
  occur about once every three or four years
  Eugene Fama, Journal of Business, January 1965
• Under the assumption of normal return
  distributions, the probability of the October
  1987 crash was so remote that according to
  efficient market theory it would have been
  virtually impossible Jackwerth and Rubinstein,
  Journal of Finance, Vol 51 1996
• The problem for traders is that it is much more
  complicated to create models for a world of fat
  tails than for a world of bell curves. As a
  result, traders repeatedly get caught out by
  unprecedented market movements. The collapse of
  two hedge funds, Long-Term Capital Management in
  1998 and Amaranth Advisors in 2006, were cases in
  point The Economist, October 18th 2007.

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So what?

• When attempting to evaluate risk, it is
  important to understand that back tested results
  or new products with short performance histories
  may have risks that may be real (and potentially
  significant) but have yet to be experienced.

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Lets go back to talking about other risk measures

• Which contains more information?
• Single point vs. rolling computations
• Photograph vs. a movie

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Remember, dont be fooled by single point
computations!
Single point
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Adjusting Returns for Risk

• Common Standard
• Sharpe Ratio

Average Return Risk Free Rate
Standard Deviation of Manager Returns
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Other Risk Adjusted Return Measures

• Treynor Ratio
• Treynor Ratio

Average Return Risk Free Rate
Beta of Manager to Market
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Other Risk Adjusted Return Measures - continued

• Sortino Ratio
• Sortino Ratio

Average Return Risk Free Rate
Downside Deviation
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Other Risk Adjusted Return Measures - continued

• Alpha
• Alpha Difference between actual returns and
  expected returns given a certain level of risk.
  The higher the better.
• Assumptions include
• a market risk, as measured by beta is the only
  risk measure needed
• b R-squared is valid

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R What?

• R-Squared
• Allows a means to measure if you are using an
  appropriate benchmark when evaluating a manager
  or fund. If so, MPT statistics are valid.

To

Not

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R What? R-Squared Example

Large Growth Benchmark
Large Growth Manager
Russell 1000 Growth Index
Not

Small Value Benchmark
Large Growth Manager
Russell 2000 Value Index
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R-Squared Where is the validity zone?
70 -75
Below 70
75 - 100


Statistics Unreliable. Tip off is that
statistical results appear strange.
Statistics Valid.
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Other statistics can be brought together to help
solve the puzzle of investment selection.
Beta
Correlation
Style Drift
Significance Level
Information ratio
Percentile Rank
Up/Down Capture
Volatility of Rank
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In Summary

• Many single computation point statistics can be
  misleading as trends are not represented.
• Using rolling periods can help to identify trends
  in statistics.
• Data can change significantly depending on the
  time periods used .
• There are plenty of statistical tools available
  to help in the selection of an investment manager
  or fund.

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Disclosures

• Notes
• 1. Navellier Associates, Inc. is an independent
  investment management firm established in 1987.
  Navellier Associates, Inc. manages a variety of
  equity for primarily U.S. and Canadian
  institutional and retail clients.
• Data is subject to change over time.
• Data has been obtained from sources believed to
  be reliable but there is no guarantee of
  completeness or accuracy.
• None of the information presented herein
  constitutes a recommendation by Navellier or a
  solicitation of any offer to buy or sell any
  securities. INFORMATION PRESENTED IS GENERAL
  INFORMATION THAT DOES NOT TAKE INTO ACCOUNT YOUR
  INDIVIDUAL CIRCUMSTANCES, FINANCIAL SITUATION OR
  NEEDS, NOR DOES IT PRESENT A PERSONALIZED
  RECOMMENDATION TO YOU. Although information has
  been obtained from and is based upon sources
  Navellier believes to be reliable, we do not
  guarantee its accuracy and the information may be
  incomplete or condensed.