On Recent Equity Markets 'Volatility' & MFQ

Much is heard recently on the 'volatility' of US equity markets.

What is meant by this? My business partner and I discussed this topic yesterday over lunch.

Technically, volatility usually is inferred to mean something associated with a type of standard deviation measure, or some derivative thereof, such as variance (the square of a standard deviation).

On that basis, a graph of S&P monthly returns from 1990 to the present looks like this (click on the chart to see it in a larger version).

Optically, you can see that the S&P monthly returns became more dispersed in the middle of the period covered by the graph, but has calmed down noticeably in the past 3-4 years.

This next graph portrays the standard deviation of the S&P monthly returns over trailing 12, 24, 48 and 96 month period.

As you would expect, the standard deviations of the longer periods move much more gradually.

Even so, all four measures have been in notable and significant decline since early 2003. Only this month's current -6.6% S&P monthly return has disturbed this pattern in recent years. Even so, it isn't necessarily a bigger shock than those of mid-2004, which were only a brief exception to the longer-term, continuing decline of the standard deviation of S&P monthly returns.

If the S&P monthly returns, measured over various timeframes, aren't showing increasing 'volatility,' on what measure would the S&P, as the best broad US equity market measure, depict rising 'volatility?'

As my partner argued that my reference to this graph missed the point, we debated what would be relevant? That question led my partner and me to construct the following measure yesterday.

Begin with the daily adjusted closing price series of the S&P500, available, for free, from Yahoo's finance website. Calculate the first differences, i.e., a series of daily raw change in adjusted closing S&P500 price. From this series, identify each raw daily change as either positive, or negative in sign.

Then, construct a series which looks at each day's adjusted closing price difference sign, relative to the preceding day's closing price difference sign. The value for a day in this series will be "1" if the signs changed between daily adjusted close differences, and "0" they were the same.

In effect, each time the S&P close changes direction from the prior day, that day registers a "1." If the market records two consecutive up, or down days, the values for those second days would be "0" in this last series.

We call this last series, and its monthly total, the Market Fluctuation Quotient, or MFQ.

The nearby graph displays the S&P500's MFQ, on a monthly basis, from January of 2000 until yesterday.

The highest value we've seen for the MFQ was 17, in August of 2005. The lowest value was a 6, in September of 2001. However, that was affected by the market's close for a period during the week following the WTC attacks. Other than that datapoint, the series hit a low of 8 three times in the 95 months measured.

To more clearly understand the distribution of MFQ values during the 95 months of this decade, here is the same data arrayed in a histogram, by frequency of occurrence.

Two of the six MFQ values over 14, since January of 2000, have occurred since July of this year. If either today or tomorrow sees a closing S&P value lower than the preceding day, then November, 2007, will be the third over-14 MFQ value out of seven since the beginning of the measured period.

Since July of this year, no MFQ value has been below 11. The last similar period of elevated MFQs was from February to June of 2005, just prior to that year's hurricane season-affected equity markets.

If you are a frequent trader, than the MFQ is relevant. It clearly captures the recent, heightened day-to-day volatility, when that term means changes in closing market value direction.

We, however, are longer-term investors. Even in our equity options portfolios. As such, the MFQ doesn't really affect our investment decisions very much.

Still, it's interesting to note how divergent the two different perspectives on market 'volatility' can be- a series of standard deviations of month-to-month S&P returns, and a series measuring S&P daily close sign changes.

Clearly, volatility is in the eye of the beholder, and his/her frame of reference.