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One Possible Model of VIX Stock Market Timing

(Guest Commentary by Bill Rempel September 13, 2007)

Dear Subscribers and Readers,

For those who had wanted to learn more about individual stocks, the art of stock selection, and model-based trading/investing, it is again time to see what one of our regular guest commentators, Bill Rempel, has to say.  Bill is a prolific writing on the stock market and individual stocks and is the author of a very active market blog at:

In this commentary, Bill is going to discuss the VIX, including a breakdown of the VIX into three different (and important) components, what historical volatility means, and finally, show us the model he is currently using/refining to make long-term timing moves in the stock market.  Moreover, all the necessary data is available on the web (and the statistical functions are available via Excel), so one can duplicate this study with relative ease and test out new and modified strategies based on the VIX should you want to. Without further ado, following is biography of Bill:

Bill Rempel (aka nodoodahs) is an active poster on the MarketThoughts forum as well as a few others around the web. Bill is a regular, monthly guest commentator on our website (see Bill Rempel on Potential Buying Candidates Part II for his last guest commentary). Bill graduated from Caddo Magnet High School (a high school for nerds) back in 1985 and proceeded to learn the hard way when he drank his way out of a scholarship to Tulane later that year. After a few years of sweating for a living, he decided to go back to school, and graduated from LSU-Shreveport in 1995 with a Bachelors in Mathematics - all the while working the overnight shift stocking shelves in a grocery store.

Post-college, Bill has been in the P&C insurance industry as an actuary, product manager, and pricing manager. Bill and his wife Millie are amateur investors with a variety of holdings, but they prefer to buy and hold value investments. In typical "value" style, they live cheap, driving old cars and preferring to save or invest instead of buying fancy "stuff."

Disclaimer: This commentary is solely meant for education purposes and is not intended as investment advice.  Please note that the opinions expressed in this commentary are those of the individual author and do not necessarily represent the opinion of MarketThoughts LLC or its management.

I actually started re-examining the VIX a few months ago, and I feel it has led to a useful model for longer-term stock market timing.  I think it has the potential to yield good returns on shorter timeframes, but I will leave that exercise to the reader.  In terms of "timing" systems, unless the total return is close to, or exceeds, "buy and hold," I'm generally not interested, and generally speaking, shorter timeframe systems don't provide total return (although some do provide strong risk-adjusted returns).  Since I haven't posted on the subject before, I'll start with an explanation of previous efforts, and then move on into the model.

If the VIX is high, does it really mean there is inordinate fear in the market?  I would suggest that the valid comparison is most likely "is the VIX high (low) compared to what I would expect given recent volatility and returns?" and not "is the VIX high (low) compared to historical or recent norms?" The "error term" between modeled and actual VIX is apt to give us better insight than just the VIX itself.

Any time we want to talk about "deconstructing" something (like the VIX), it helps to know what that something is.  Here's a good definition.  Probably the key concept is that index options are sampled and calculations based on them become the VIX.  This is also a good definition link because it includes the misnomer "investor fear gauge."

Some months back, I had been having a conversation with Bill Luby of VIX and More about this topic.  My distaste for using the VIX can be summed up by its easy model-ability based on price action; if we already have price action in our model, VIX adds comparatively little useful information.  VIX, regardless of actual construction methodology, can be described in terms of three contributors:

1) Actual, historical volatility

2) Some predictable measure of fear/greed resulting from recent price momentum

3) An error term.

Now, if we assumed that a modeled VIX, based on volatility and momentum in the S&P 500 index, contains no useful information outside of that in the price data itself, then the deviation of actual from expected VIX could be said to contain "pure sentiment data" that corresponds to the pricing biases of market participants.  That was my starting point, the expectation of modeling a VIX based on historical volatility and stock market short-term returns, and comparing it to the actual VIX to derive the "error term" or actual sentiment.

This leads to the next obvious question, "what is historical volatility?"  The pricing models in vogue for options almost invariably use the standard deviation of closing price over some range of time as the basis for defining the "historical volatility," but I have a bias towards using the ATR (Average True Range) as my measure.  If one were to pursue the regression model path to fruition, one also would need to define their shorter-term momentum measure to discuss relative fear/greed.  In April, I went down the path of developing a model for VIX that used the 45-day ATR divided by the 45-day simple moving average of the S&P 500 close for "historical volatility" and the 20-day Rate of Change on the close for momentum.  If you're interested, you can see the charts and regression output at my blog post, One Possible Model of the VIX.  The R-Square of 79.8% is pretty nice.

Simplicity, however, can sometimes rule the roost.

From 1/2/1990 to 7/20/2007, when regressing only the 45-day ATR divided by the close at the end of the period, to the VIX for that day, we find an R-Square of 78.1%.  The momentum term and the use of a simple moving average for the close, didn't really help all that much.

The formula could be approximated by

PredVIX = 1132 * ATR(45)/Cls + 5.

One could look at the error term in two different ways, either additive or multiplicative.  Since my previous work had determined the error increased as predicted VIX increased (reference the first graph on this post), I went with a multiplicative approach to control for that increased error.

As a quick double-check, I calculated daily returns for the day following a close where the VIX/[ATR(45)/Cls] ratio was very high(low).  These are close-to-close returns, which would be appropriate if one was buying at the close ... or if one was holding for a long period during which the ratios were in a range.  The general trend is unmistakable, if not terribly smooth buy fear and sell complacency.

If one were to use the 1st and 10th decile readings as the starting point, and simply buy the S&P when the VIX to ATR(45)/Cls ratio went over 1,975 and hold until it fell to 1,290 or below (rinse, repeat), ignoring repeat signals, the results are fairly nice.  The time in market is 59.2% and the CAGR is 8.74% annualized, assuming no return for out-of-market periods.  This compares to an 8.62% return for buy and hold over the same time period.  Neither return number includes dividends or adjusts for taxes.  This "system" generates 25 trades in 17.5 years. 

Here's a chart of the comparative returns.

The results are fairly robust for a wide range of entry and exit signals; risk-adjusted returns are good even with entry on 9th decile and exit on 2nd decile (although absolute returns aren't as good),

and the optimal (some would argue the "curve fit") setting generated CAGR of 9.95% while being in market 66% of the time. 

Because this is a "system" with very low trading frequency (25 trades per 17 years), there's no way of guesstimating what the exact "best" setting is; it may (or may not) be the optimal historical values of 1,950 and 1,250.  However, knowing that risk-adjusted returns are robust for a range of points around the optimal point gives me confidence that this is a real phenomenon that can be capitalized on.

The "real phenomenon" is that spikes in VIX, relative to where it should be based on actual historical volatility, tend to mark intermediate-term bottoms. 

It's also true that "clusters" of spikes tend to occur, meaning that buy-ins are often at very scary times, it the market can get worse before it gets better.  One "to do" could be examining those clusters for even better buy-ins.  Another "to do," and one that I probably won't be doing, might be an examination of short-term trades, perhaps buying a reversion from a high level once it has already started calming down.

Possible applications include changing portfolio weights to lower beta in stock holdings, or underweight stocks during the "sell" periods, add a hedged index option position like Hussman's funds do, or even add small hedging position short in stocks with poor fundamentals or in an inverse index fund.  Another alternative would be to add leveraged index ETF positions during "buy" periods, or limiting active trading in some short-term methodology (CANSLIM, anyone?) to "buy" periods.

"Be fearful when others are greedy. Be greedy when others are fearful."  This method does that.

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