## Summary

- The S&P price/sales ratio is a particularly relevant way of sorting through disparate arguments currently held between today's market participants.
- We can break the market down into its log-linear component (sales) and its cyclical components (P/Es and profit margins).
- Varying sales CAGRs and P/S ratios over differing horizons do not indicate attractive forward-looking returns for S&P investors.

At any given time, there are people who believe the S&P 500 (NYSEARCA:SPY) is trading too cheap, too rich, or just right. All of us are prone to citing anecdotal reasons when offering our opinion. Today's bull might point out the record amount of cash on the sidelines, while a bear may point to margin debt as a percentage of GDP. While these stories are good to know, they're not particularly helpful in grasping the long-term return prospects an investment faces.

I currently find myself in the bear camp, believing the S&P to be meaningfully overvalued. Before I go further, however, I want to establish that I am by no means a "perma-bear," someone who is always waiting for the market's demise. Every argument needs a starting point. I begin mine with two graphs. The first is from Doug Short, who conducts a 140-year trend analysis on the real returns offered by the S&P Composite Index. I have read many of Short's articles on Seeking Alpha, and I find his work to be top notch.

The main observation I want to make from this chart is not where we are, but where peak insanity lay. On March 24, 2000, the S&P reached what was then its all-time closing high of 1527. At that time, the S&P Composite Index stood 152% above its long-run trendline. By contrast, the Index found itself furthest below trend in 1932. So, what the bottom of the Great Depression was in terms of pessimism and cheapness, the 2000 peak was to richness and "irrational exuberance." One may disagree with the particular statistical methodology Short uses in establishing this trend line. However, regardless of the precise degree of overvaluation, I doubt the final result would much change that the S&P was furthest stretched at this point.

The second graph I reference is from the Feb. 17, 2014, weekly commentary issued by mutual fund manager Dr. John Hussman. His work demonstrates that a bevy of metrics confirms what Short's trend-line graph displayed: that the 2000 zenith marked peak optimism. The zero-line in Dr. Hussman's graph indicates the long-run average for each metric dating back to 1947:

I propose to use one of these indicators as a gauge for asking what kinds of returns we can expect looking further into the future. I argue that price/sales ("price/revenue" in the chart above) offers particular insight to our current situation. To explain why, I offer the following formula:

Mathematically, share price equals EPS times the P/E ratio. But we can expand on this point:

This is to say that EPS is equal to per share sales times profit margins.

Substitution of Equation 2 into Equation 1 yields this final identity:

In other words, share price is a function of sales *levels*, as well as profit margins times P/E ratios. Another conclusion is that share prices rise if and only if the product of sales growth rates, profit margin expansion and multiple expansion is greater than 100%. We all know that P/E ratios are cyclical. They rise and fall with changing market views on interest rates, risk factors and growth prospects. Over the last year or so, many commentators have sought to remind us that profit margins are also cyclical, at least at the broad economy level. Another of Dr. Hussman's graphs (from his March 4 commentary) illustrates this concern well:

The blue line displays that after-tax corporate profits as a percentage of GDP have never been so high as they are today. If you accept the implicit conclusion, then you are anticipating a dramatic annualized drop in profits over the next four years (the trend appears to predict 15% annualized -- a 48% total spill).

My view is that earnings will be lower four years from today than they are now, but that's fodder for a different article. Today, I'm only here to argue one thing from the graph above: profit margins (as a percentage of GDP, or just generally) are indeed *cyclical*, just like P/E ratios.

So P/Es and profit margins run in cycles, while sales levels (which are also cyclical, but not nearly as volatile) are the log-linear driver of share price levels. Sales levels today really are higher than they were 10, 20, 50 years ago, etc. While arguments do exist for secularly higher P/Es or margins, these cyclical factors do not drive the long-term destiny of the stock market. *Sales growth drives share prices*. Again:

This is why the price/sales (P/S) ratio is so interesting here and now, because it removes the long-run determinant of share prices and leaves us only with the two cyclical components. To see this, divide both sides of the above equation by "sales/share."

You're left with the following:

If margins and valuations are both low, P/S will be low, and vice versa. If one is low and the other high, then we will likely obtain an average P/S metric. Margins today are more or less at all time highs, and the *current P/S ratio stands at 1.67x, well into the upper historical range*.

Today, the market is engaged in two continuing discussions. First, are valuations (P/Es) cheap or rich? Second, what do we make of these profit margins? The P/S ratio conjoins the two and asks what the metric has to say about overall cyclical cheapness or richness in the market, and concludes that we are cyclically rich. As we noted from the earlier graphs, we reached peak optimism (and peak P/S) in 2000. On March 24, 2000, the S&P 500 reached an all-time closing high of 1527.

Standard & Poor offers quarterly sales data going back as far as Q1 2000. Year 2000 revenue per share was $745.70. Ideally I'd have annual sales through Q1 2000 to give you, but I do not. My calculation is that Q1 2000 trailing 12-month Sales notched in the neighborhood of $700/share. So the March 24, 2000, P/S ratio was approximately 2.2x, which we can think of as an all-time high for broad cyclicality.

Standard & Poor's reports Sept. 30, 2013, trailing 12 per share revenues at $1,115.38, 59.3% higher than the estimated $700 from Q1 2000, which corresponds to 3.51% annualized growth over the 13.5-year time span. The graph below demonstrates how the actual S&P (red line) has compared to a theoretical S&P (blue line) that held a constant peak P/S level of 2.2x. The green line (see right axis) shows what percent of "peak value" the S&P was trading.

Notice how much less wobbly the blue line is than the red line. This is because the only thing driving the blue line is per share revenues, which are relatively stable. The red and green lines are much more volatile, because P/S is allowed to swing; they'd be even more wobbly if monthly rather than quarterly data were used. Also note how little ground the blue line has made since Q4 2008. This is because revenues have increased only modestly over the last five years. Because these are reported on a per-share basis, this includes the impact of share buybacks. With the S&P at 1870 as I write this, it is trading at about 77% of its peak P/S valuation level.

Suppose S&P sales growth continues at 3.51% as it has over the past 13.5 years or so. Next, suppose we are determined to reach peak P/S ratios once more. What kind of nominal annualized price-only returns would a dollar invested today achieve if the S&P were to reach those levels of gullibility again (and hence be set up for another devastating fall)? The table below reports this in the right-most column.

Here's an example for how to read the above chart. If in 25 years the S&P P/S ratio were 2.2x, and if the per share Sales CAGR (compound annual growth eate) was 3.51% over that horizon, today's investor will *necessarily* realize a nominal price-only return of 4.70%. I have enlarged the columns 0.8-1.2x because these hold the majority of historical observations.

What if you accept a more robust sales growth figure, say 5%? Here's what the data have to say:

If we found P/S ratios 50 years from now trading at the foolish 2.2x P/S level, *and if* you assume 5.0% annualized S&P per-share sales growth, the market's price return will be 5.6%. Of course, the stated returns include neither dividends nor inflation.

The other columns tell us what the returns would look like for alternative P/S ending points. For example, if in seven years the S&P trades at a P/S of 1.00x (and a 3.5% sales CAGR), then we will achieve a -3.6% annualized growth rate.

My reading of these tables lands me squarely in bear territory. First, while nobody knows which sales CAGR will prevail, or what the P/S will be over a given time frame, I am not impressed with the return prospects in the short *or* the long run under any but the rosiest of outcomes for both P/S and CAGRs. Note that you need CAGRs well above 5.0% to get anything like historical returns even over a very long time horizon. If these are the returns today's market has on offer, I think I'll wait.

Second, some may argue that today's P/S is driven by high margins rather than high valuations, and so the higher figure is more justifiable. But the flip side to that argument is if you have a P/S ratio with low margins, there's room for margin to expand. Remember, P/Es are a function of interest rates (lower is better), risk (lower is better), and earnings growth (higher is better). But with cyclically high margins, most, all, or even greater than 100% of future earnings growth depends upon revenue growth. So I don't buy that spiked margins give you a "higher quality" high P/S, at least not at the index level.

Third, I believe that we remain in a deflationary environment where lofty Sales CAGRs have been and will continue to be difficult to achieve. Deflationary cycles and inflationary cycles last a long time. This chart from the Bureau of Economic Analysis shows that our nation's total debt burden in relation to GDP has skyrocketed since around 1980. I do not believe that we will enjoy high revenue growth rates as past debts are repaid and increased borrowing becomes increasingly difficult. Does it look like we're closer to the bottom of the long-term debt cycle, or the top? While I concede that this chart ends in Q1 2011, I have seen recent estimates still in the neighborhood of 330%-350%. Regardless of the precise level, we do not look ready to re-lever the economy anytime too soon. Because one person's "debt-fueled" spending is some corporation's revenue, reductions in indebtedness meaningfully hinder sales CAGRs.

We've seen the proof of this over the last several years. Between Jan. 1, 2009, and Dec. 31, 2013, S&P data show that total per share sales have increased by a meager 7.6%, a CAGR of 1.48%. This is bad enough, but approximately half that sales growth came through share buybacks. S&P revenue growth absent buybacks over the last five years has been .67% annualized, for a total of 3.4%. Remind me once again why we're at all-time highs? That's right, the explosive sales growth is on it's way; it'll be here any decade.

The graph below demonstrates that much of the revenue growth that occurred in the 2000s (and which by the way are included within the 3.51% CAGR I used for the above analysis) was financed by debt growth. The FRBNY chart below shows that household debt financed much of the five-year 9.15% sales CAGR realized between Q3 2003 and Q3 2008.

Consider the graph below in retail sales growth composed by Princeton University economics professor Atif Mian. Revisit the total-debt-to-GDP visual above and ask yourself whether we should blindly use past sales CAGRs as a guide to the future.

Whatever the actual sales CAGR has been over the last 30 years, I do not expect it to be as high over the next 30 or even 50 years. That's an opinion, and we are each enamored of our own opinion. But I'd love to hear the opposing argument that setting the growth rate high is the more appropriate view.

In conclusion:

- The market peaked in its deviation from trend as well as its valuation in 2000.
- Among the metrics that demonstrated the foolishness of that 2000 peak was the P/S ratio
- P/S takes away the long-run driver of share growth, leaving us only with the product of the two cyclical components: profit margin and P/E.
- The P/S ratio peaked at approximately 2.2x in March 2000, has averaged in the neighborhood of 1.00x, and currently stands at 1.67x.
- We can apply a CAGR to sales to determine future price-only nominal returns based on time horizon and closing P/S to determine what returns an investment in the S&P would achieve.
- Many of the price-only nominal returns we observe from this methodology do not appear to adequately compensate equity investors for risk, even at a loftier 5% annual sales growth rate.
- An argument can be made that we are closer to the early stages than the late stages of a U.S. de-levering, which would hamper sales CAGRs.

While the argument above centers on the S&P, I imagine it is also highly relevant for tech stocks (NASDAQ:QQQ), the Dow (NYSEARCA:DIA), and small-cap stocks (NYSEARCA:IWM).

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