Surviving Or Thriving 1

Volatility

Surviving or Thriving With New Market Challenges

Navellier Applied Research

22

Volatility Defined

Please see important disclosures at the end of the presentation

Volatility: A measure of risk based on the standard deviation of the asset return.

Source: Prof. Campbell R. Harvey’s Hypertextual Finance Glossary

33

This is the formula for standard deviation, a common measure for

risk.


44

Will NOT be seen for the remainder of this presentation

Rest easy…..let’s discuss some ideas!


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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

Please see important disclosures at the end of the presentation. Graphs for discussion purposes only.

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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 ExampleOf the two, wouldn’t this be the preferred investment manager?

Semi standard deviation or “downside risk”

#1 #2


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Here is the Trampoline Math

5 9

-5 -1

5 9

-5 -1

5 9

-5 -1

5.48 5.48Standard Deviation =


1010

Assume equal standard deviation. Which investment is

getting riskier? Less risky?

Time

Ris

k

Manager “A” Risk is Rising

Manager “B” Risk is Falling


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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


1313

Other Risk Adjusted Return Measures - continued

Sortino Ratio

Sortino Ratio =Average Return – Risk Free Rate

Downside Deviation


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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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“Deal or No Deal?” Normal or Not Normal?

Twenty Year Histogram of Monthly Index Returns

Histogram of Monthly Returns

May 1986 - April 2006

Per

cent

age

of M

onth

s (%

)

0

2

4

6

8

10

12

14

15

Returns Range (%)

< -10 -10 to -9 -9 to -8 -8 to -7 -7 to -6 -6 to -5 -5 to -4 -4 to -3 -3 to -2 -2 to -1 -1 to 0 0 to 1 1 to 2 2 to 3 3 to 4 4 to 5 5 to 6 6 to 7 7 to 8 8 to 9 > 9

Russell 1000 Russell MidcapRussell 2000 Russell 3000

≠≠


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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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“Let’s assume we have a can opener!”


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Are possible small model errors compounding to result in 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 investorsOct 25th 2007From The Economist print edition


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Nine standard deviations? Really?

Let’s look at a curve that can be considered accepted as normal: human height

Nine deviations from assumed average =

1 in 8,900,000,000,000,000,000Source: Nassim Taleb, The Black Swan, pg 231


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Illustration of financial crisis rarity.

Source: Bloomberg. Used with permission. Link: http://www.bloomberg.com/apps/news?pid=20601109&sid=acw1G8iS8oXc&refer=home

-4.04%As of 2/13/09

For Financial Advisor One on One Use OnlyPlease read important disclosures at end of presentation.. Graphs are for discussion purposes only.

Number of standard deviations

2323

“If it doesn’t fit, you must acquit.”

- Johnnie Cochran

“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.

The “Fatter” the distribution tails, the less reliable the

statistics!


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So what?

“Tail risk” may be a significant contributor to unexpectedly large market events.


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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

Not

=

=

Large Growth Manager Russell 1000 Growth Index

Large Growth Manager Russell 2000 Value IndexSmall Value Benchmark

Large Growth Benchmark


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R-Squared: Where is the “validity zone?”

70 -75Below 70 75 - 100

==

Statistics Unreliable.

Tip off is that statistical results appear strange.

Statistics Valid.


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In Summary

Risk can take many forms. Standard deviation may not be the best

way to measure risk. Most risk models assume a normal

distribution of returns in order to generate probabilities of downside risk.

Be aware that “fat tails” may exist in assumptions used to gauge risk. Thus, risk may be more extreme than originally assumed.


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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.

2. Data is subject to change over time.

3. Data has been obtained from sources believed to be reliable but there is no guarantee of completeness or accuracy.

4. 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.

Disclosures

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