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The Significance of the Equity Put-to-Call Ratio

(Guest Commentary - July 28, 2005)

Dear Subscribers and Readers,

As I mentioned in our discuss forum earlier today, I have brought back a very active poster, Bill R. (a.k.a nodoodahs) to be a guest commentator for this Thursday morning’s commentary. A significant number of you have expressed interest in hearing more from Bill. For those of you who missed his last commentary – “The Art of Value Investing” – I would encourage you to go back and check it out. Bill is also a great stock picker, and in his last commentary, he gave us a very good basic run-down on how he typically screens for individual stocks.

Here’s a short update on some of Bill’s picks since his last guest commentary: OSG is up just over a dollar, while RE is up over 7%, and IMKTA is up over 15%. For a further discussion of his picks, you can either post your question on our discussion forum or email him at NODooDahs@aol.com.

Before we begin, I will again give you a very brief introduction of Bill. Like I had mentioned before, Bill is a very modest guy, indeed: “Bill R. drank his way out of a scholarship to Tulane in 1985, and went back to college for his math degree years later, graduating in 1995. Since then, Bill R. has been in the P&C insurance industry as an actuary, product manager, and pricing manager. Bill and his wife are amateur investors with a variety of holdings, but they prefer to buy and hold value investments." 

In this commentary, Bill will be discussing the significance of the equity put-to-call ratio (something I have discussed on and off – mostly in our discussion forum) and its usefulness in predicting the future trend of the market. In doing so, Bill leaves no stones unturned.


Today I’d like to talk about two of my favorite things, stock market timing and mathematics. Yes, I know that I’m mentally ill. I must preface my discussion by stating that I am primarily a value investor in the stock market, and my market timing is, in practice, usually limited to infrequent switches to cash or bonds in times of great instability. But that doesn’t mean I haven’t given short-term market timing a great deal of investigation, some of which I’ll share with you now.  Be forewarned, this gets kind of technical in a math nerd sort of way.

One of the most commonly used contrarian indicators of market sentiment is the “put to call ratio” (PCR for the remainder of this piece). A “put” is an option play similar to a short, in that buying a put will profit me if the item falls in price. Similarly a “call” is an option play whereby I profit if the item increases in price. In either case, there is a time specified wherein the option would expire, and if unexercised, become worthless. Several sites have information on options, from the general to the specific. Here’s one I’ve found useful: http://www.investopedia.com/articles/optioninvestor/default.asp

If there are more puts than calls in place for any particular day, one might say that market sentiment is negative or bearish, as there are more negative bets than positive ones. This is a high PCR. A low PCR indicates a positive or bullish market sentiment. [Just to confuse everyone totally – every put or call has a buyer and a seller – what PCR measures are buyers, so it is a measure of option buyer sentiment, which is the opposite of option seller sentiment – now I’m confused, too!] Few people use the “total put to call ratio” (TPCR) to measure sentiment, because institutional traders will often place puts or calls on indices as a hedge, and their money is considered to be smarter than that of the retail investor’s. So in practice, we use the “equity put to call ratio” (EPCR) as a measure of market sentiment. We use it as a contrarian indicator because studies have shown that 90% of puts and calls expire worthless, meaning that the buyers of puts and calls, by and large, have wasted their money. Therefore, measuring market sentiment through the EPCR should pay off, as long as we do the opposite of the market sentiment. A high EPCR indicates a bearish sentiment, which means the contrarian reaction is to be a bull, and vice versa. In the following chart, we clearly see the relationship between one broad measure of the market (S&P 500 Index) and the market sentiment for the last month (20 trading days) as measured by the EPCR. 

S&P500 vs 20 Day Avg EPCR

Note the bearish sentiment peaks in May of 1997, October of 1998, March and September of 2001, October of 2002, and February of 2003. Each of these peaks is clearly the mark of a short term bottom and a subsequent move upward in the index, indicating the contrarian value of the EPCR. Even the smaller peaks and many of the valleys seem to be indicative of future behavior for the index. Unfortunately, while the relationship is evident, it is not obvious how we can use this relationship to our advantage. There are some relative peaks that don’t seem to mean much to the index, and others that seem to mean an awful lot. And is it just my imagination, or did the bull market up until late 2000 just have a plain old low EPCR? Average sentiment was much more bullish then it was in say, January of 2004, but the index just kept on rising, whereas in Jan ’04 it responded to the same levels of EPCR by flattening out.  Hmm …

Being a math nerd, I just can’t wait to quantify this relationship! To do that, we will break up the time periods as described by the black arrows (in the above chart), into the ultra bull market period from 1997 through August 2000, the ultra bear market from September 2000 through February 2003, and today’s market through July 2005. Following is a chart which describes the relationship between the readings of the 20-day EPCR and the return of the S&P 500 over the subsequent 21 trading days from 1997 to August 2000:

relationship between the readings of the 20-day EPCR and the return of the S&P 500 over the subsequent 21 trading days from 1997 to August 2000

By convention, many investors use the four-week average EPCR to smooth out our measure of market sentiment. For this analysis I used a 20 trading day weighted average ratio, but for all practical purposes the simple averages you get from any charting site will do just fine. I measure the stock market return as the change in the S&P 500 Index over the next 21 trading days (approximately one month).

Looking at the bull market ending in 2000, we see that average sentiment is to the left of the chart – very bullish. But when sentiment was to the far left, returns were lower in the following month. And when sentiment was (at least, relative to the market at that time) bearish, the subsequent returns were higher. The formula in the graph is a mathematical representation of the relationship, known as linear regression, and is represented by the red line through the distribution of red dots. The R2 number is known as “r-squared” and is a statistical measure of the formula’s accuracy. The multiplier on the x term is the slope of the line, in this case, 0.1543. Generally speaking, the slope indicates the power of the relationship, and the R2 indicates the accuracy of the formula. Ideally when we develop a linear model, we want it to have both a high accuracy and a large slope, because having both will lead us to a profitable use. I am lucky enough to have a mathematics degree, and I get to use regression analysis on a regular basis at work. Hooray! But others may not be so lucky, so for more on linear regression, see the sites listed below, or Google the phrase “linear regression” and keep going until you find one that’s user friendly enough for you.

http://www.sportsci.org/resource/stats/linreg.html

http://www.mste.uiuc.edu/patel/amar430/intro.html

http://davidmlane.com/hyperstat/index.html 

Now let’s look at the ultra bear market of 2000 to 2003.

bear market of 2000 to 2003

The scale on both charts is the same for easy comparison. The first thing that jumps out at me is the range for the EPCR. All the points on this Bear Market chart are further to the right, indicating that the average EPCR was higher from 2000 to 2003, than it was in 1997 to 2000. Visually, it looks like the Bear Market distribution is tilted to the left. That leftward tilt in the Bear Market distribution is confirmed by the regression multiplier on the x term. Here in the Bear Market, it is 0.2620, whereas it was 0.1543 in the Bull Market. Finally, the Bear Market distribution appears to be tighter to the blue line than the Bull Market was to the red line. Mathematically this is confirmed by the R2 number of 0.1191, indicating that this Bear Market formula is twice as predictive as the previous Bull Market one.

What have we learned so far? That:

(1) EPCR is predictive of future returns in both periods,

(2) The range of EPCR was bullish in the Bull Market, and bearish in the Bear Market,

(3) A relatively high or low EPCR for the Bear Market is more predictive than it was in the Bull Market, and

(4) We can’t use the same expectations for EPCR to predict returns in different types of markets.

I think point (4) is especially important for traders and market timers to note. If you successfully traded on the EPCR in 1999, you would find that by the end of 2000, your signals didn’t work anymore. What you thought was an overly bearish sentiment in early 1999 is now the norm.

Let’s take a look at today’s market:

current market

What an amazing difference! The distribution of EPCR is in the same range as during the Bear Market – obviously the average sentiment hasn’t changed much since 2003. What has changed is the accuracy of the predictive formula, the slope of the line / strength of the relationship, and the range of returns, which is very compressed. All of those have changed for the worse.

Bull, Bear and Current

While I think using the EPCR to predict short-term returns in the stock market is a game that can be played, it is obvious that the rules change over time, as should our game plan. Or do we need a more complex plan that fits all periods, or accounts for the recent market’s bull/bearishness?

Borrowing a cue from our technical analysis friends, let’s take a peek at the relationships between the moving averages. Below is a chart that shows the EPCR over time, with the 20 day average, the 100 day average, and the 20/100 day average.

EPCR

The switch from a bullish sentiment in the 1990’s to a bearish sentiment ever since shows up in both the 20 and 100 day averages for the EPCR. Once we control for this sentiment shift by dividing the 20 day average by the 100 day average, however, we get a much more useful graph. This 20/100 EPCR floats around 1.00 when the average sentiment for the last trading month is close to the average sentiment for the recent market. When the last month’s sentiment is more bearish than it has been recently, we get numbers above 1.00, and vice versa. Now let’s overlay the 20/100 with the S&P500.

SP500

Here the inverse relationship is even clearer. Before we move forward with this moving average approach, let’s revisit the EPCR conceptually, and see if we can’t add more to the party.

The EPCR measures the sentiment of option buyers. But what makes them bullish or bearish? To a large degree, they become bearish when the last month’s return is significantly less than the prior month’s return. Similarly, when the more recent month has outperformed, the sentiment is bullish. After the bust from July to September of 1998, note how bearish the EPCR got. Conversely, after the recovery, the EPCR quickly regained its bullishness. Clearly we’ve got something else going on here. So if the EPCR is, to some extent, defined by the market’s recent return, are we really just seeing regression to the mean, i.e., trend consolidation or things “evening themselves out?” http://www.ruf.rice.edu/~lane/hyperstat/B153351.html

Defining last month’s performance in context of the prior month’s, and next month’s performance in context of last month’s, we get the following.

Regression to the Mean

When we have a really, really high-returning month, we can expect one that really really reeks next month. And vice versa. Unfortunately, the options buyers don’t seem to see it that way. 

Ratio of 20 Day Average EPCR to 100 Day Average EPCR

The better performing that last month was relative to the prior month, the more likely options buyers are to have a bullish sentiment (low EPCR ratio). Similarly the worse performing the last month was, the higher (bearish) the EPCR is. Their sentiment for the future is exactly the opposite of the future result, which is the regression to the mean shown above.

Putting it all together now:

(1) EPCR is a moderately accurate predictor of next month’s market return, but

(2) The signal values for EPCR change with the markets (bull/bear), so

(3) We use the ratio of 20 day average EPCR to 100 day average EPCR and get a better predictor, but

(4) Last month’s relative market performance is a driver of sentiment, so

Are the two measures (last month’s outperformance and the EPCR 20/100 ratio) really just the same thing?

In a word, no. And that answer surprised me.

I ran a multivariate linear regression in Excel and obtained the following results.

Regression Statistics

Combining the 20/100 day EPCR ratio with the relative outperformance of the prior month yielded a very accurate prediction of the next month’s outperformance. Statistically speaking, next month’s S&P outperformance can be defined with 41% accuracy, and there is basically zero chance that the relationship could be defined by random chance (see highlighted areas).

The predicted relationship is 0.21 * ( 20 day EPCR / 100 day EPCR) – 0.424 * ( last month’s gain minus prior month’s gain ) – 0.214 = next month’s gain minus last month’s gain.

EPCR and past performance as predictors of future performance

The strategy applications of a model like this are left to the reader. One obvious strategy is to short or go long on an ETF tracking the S&P500, or for the brave, to use a leveraged fund like one from Rydex to get 2x the market gain or loss. Development of buy or sell signals are left to the reader as well. Unfortunately I could not get adequate data for the EPCR before 1997 and this has limited my back testing. Ideally I would like to back test over a period of 20-25 years, develop buy and sell signals and determine their alpha, but for now I think I’ve stretched my brain enough for one week. Time for a nap …

Note on the regression tools used: none of the above work required anything special. I use Excel ’97 at home, and Excel 2000 at the office, and either one has powerful statistical tools waiting for you to unleash them. Lotus and QuattroPro have these capabilities as well, but I am not familiar with them. Those of you with MS Works or StarOffice, or similar, may be left out in the cold. Anyone looking for help on unlocking the statistical tools in MS Office can consult MS Office Help on the Web, visit the appropriate statistical websites, or (last resort) drop me a line at NODooDahs@aol.com, or PM me on the forum (www.marketthoughts.com/forum).

Thanks, Henry, for asking me to do this! I hope it’s not too technical and that someone gets some use out of it!

Bill R.

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