VIX options investors expect, with an 80% probability, the S&P 500 index price to range between 1024 and 1184 (roughly +/- 7%) around its Friday close of 1104 for the period ending 30 days later.

Let’s see how to draw that inference from the VIX.

## What VIX Measures:

CBOE VIX is an estimate of expected (implied) volatility of the S&P 500 index based on SPX option bid/ask quotes for the nearby and second nearby options with at least 8 days left to expiration for out-of-the-money options, weighted to yield a constant, forward looking, 30-day measure of the expected volatility of the S&P 500 index.

Options investors don’t have a corner on analysis, wisdom or judgment, but they are putting their money where they mouths are, and they are more exquisitely focused on the BY WHEN question than most long investors in the underlying index funds such as SPY, IVV and VINFX.

Examining what they “think” by analyzing VIX is potentially useful to S&P 500 investors.

## Statistical Price Inference With Volatility:

Let us state at the outset, that statistical inferences are far from perfect, but they are better than nothing, and can complement other non-statistical analysis. How much weight an investor places on statistical inference, chart analysis, fundamental bottom-up analysis, fundamental top-down analysis, wishful thinking or reading chicken bones tossed on the ground, is a matter of personal choice. This is about the statistical inference approach and is not presented as a panacea or a method that should be used to the exclusion of others. It is only one tool of several that investors might consider using.

## Managing Expectations:

No volatility indicator can be used to predict a specific price, just a range within which a price is expected to be found. Volatility indicators do not suggest direction of price movement — trend indicators are separate tools.

What volatility does well is help set limits on expectations, to set stop loss points, to decide if a stock is potentially suitable or it could be useful for a particular purpose in terms of price variation.

For example, volatility measures can help you determine if your price objective is too high, or if the potential decline in price is outside of your risk tolerance, or to help you set a stop loss point.

Volatility-based statistical inference is only one of several tools that investors may consider for their total decision aids tool box.

## Volatility Factor:

The annualized volatility figure for the VIX can be translated into the expected volatility for shorter periods, such as quarterly and monthly by dividing the volatility by these factors:

- quarterly divisor = 2.000
- monthly divisor = 3.464

Since VIX is about the next month, the monthly divisor 3.464 is of interest to us here. The quarterly divisor would be used with VXV, which measures the 3-month expected volatility.

For those curious about the derivation of those factors, standard deviation varies over time based a square root function. To translate annualized volatility to shorter periods divide the annualized volatility by the square root of the ratio of the number of days in the year by the number of days of the period in question. For example, finding the divisor for 30 days in Excel would be done with this function:+SQRT(360/30) = 3.464.

## Probability Factor:

Remember that by convention, volatility is expressed for one standard deviation, which accounts for a range of values encompassing approximately 68% of the expected prices. Two standard deviations are expected to encompass approximately 95% of the likely range of prices. Three standard deviations are expected to account for almost 100% of expected prices, but as we all witnessed in 2008, the unknown unknowns can and sometimes do create those nasty Black Swans that push prices way out past three standard deviations into the “fat tails” of the price distribution.

Because volatility is expressed as one standard deviation, and because that covers only a specific “width” (probability range) of likely prices, investors may want to create their own “width”, such as 70%, 80% or 90%.

To use a statistical inference for those probability ranges over one of the time periods listed above, pick one of these multipliers to be uses as the probability factor in the formula discussed below:

- 70% – 1.04
- 80% – 1.28
- 90% – 1.64

## Price Probability Range Calculation:

For example, if you wanted to make an approximate statistical inference about the likely price range of the S&P 500 (or its proxies SPY, IVV or VINFX) over the next 30 calendar days at 80% probability, and with the last VIX reading at 19.50 (= 19.50%), you would do this calculation:

- select the monthly Volatility Factor (”VF”) from the list above
- select the 80% Probability Factor (”PF”) from the list above
- divide the VIX level by 100 (”V”)
- obtain the SP 500 market price (”MP”)

Probable Price Range = MP +/- { [ (V /VF) * MP ] * PF }

As of Friday February 27, that calculation for the VIX-based statistical inference of price range for the S&P 500 for the next 30 calendar days would be:

Probable Price Range = 1104 +/- { [ (0.1950 / 3.464) * 1104 ] * 1.28 }

= 1104 +/- 80

= 1024 to 1184

Conceptually, the extremes of that range are more likely to be achieved closer to the end of the 30 days than the beginning.

## Other Volatility Information:

There are other CBOE volatility indexes that may be of interest to some investors in the corresponding underlying securities.

The CBOE VXV is the percentage volatility expected by options investors for the next 90 days. The VIX and VXV are often nearly equal, but they do diverge as well. When the VIX is higher, for example, options investors expect volatility to be higher over the next 30 days than over the next 90 days.

Other 30-day volatility indexes now available are:

- VXD for DIA (Dow Jones Industrial Average)
- VXO for OEF (S&P 100)
- RVX for IWM (Russell 2000)
- VXN for QQQQ (NASDAQ 100)
- OVX for USO (crude oil near futures)
- GVZ for GLD (gold bullion)
- EVZ for FXE (USD/EURO)

You can apply the same formula to these volatility indexes as for the VIX (except that for VXV you would use the quarterly volatility factor divisor 2.00).

## VXD

## VXO

## RVX

## VXN

## OVX

## GVZ

## EVZ

**Holdings Disclosure:** As of February 27, 2010, we do not have current positions in any securities discussed in this document in any managed account.

**Disclaimer:**

*Opinions expressed in this material and our disclosed positions are as of February 27, 2010. Our opinions and positions may change as subsequent conditions vary. We are a fee-only investment advisor, and are compensated only by our clients. We do not sell securities, and do not receive any form of revenue or incentive from any source other than directly from clients. We are not affiliated with any securities dealer, any fund, any fund sponsor or any company issuer of any security. All of our published material is for informational purposes only, and is not personal investment advice to any specific person for any particular purpose. We utilize information sources that we believe to be reliable, but do not warrant the accuracy of those sources or our analysis. Past performance is no guarantee of future performance, and there is no guarantee that any forecast will come to pass. Do not rely solely on this material when making an investment decision. Other factors may be important too. Investment involves risks of loss of capital. Consider seeking professional advice before implementing your portfolio ideas.*