**Introduction to the S&P 500 price regression trend line**

There is a large market (pun intended) for metrics that give a gauge of the relative valuation of the stock market. Among them are the Shiller PE, the Buffett Indicator, and the S&P price regression trend line.

Many analysts use these indicators to make determinations about the relative valuation of the stock market. The general process is to compare the current reading of the metric to the long-term average, which is true for the Shiller PE and the Buffett Indicator. And for the S&P price regression, a price regression line is drawn, which essentially reflects the long-term mean price appreciation, and then the current S&P price index level is compared against it. So, all these metrics essentially compare current market data to the long-term averages.

However, the comparisons are problematic when the current data is systematically different from long-term averages. I’ve highlighted how this is the case for the Shiller PE and for the Buffett Indicator, but the same appears to be true for the S&P price regression.

This metric has merit to the extent it identifies whether the S&P is deviating from long-term trends

The S&P price regression can be developed by using long-term S&P 500 data, for example from Shiller’s database. Then, a best-fit exponential curve is created to fit the data as best possible, essentially a regression, which seeks to minimize the squared error of all the actual data points to the regression line.

Once the regression line is developed, its usefulness relies on the assumption that the stock market should rise in price at the same level throughout all history, since the trend line is based on historical data back to 1870.

### The assumption that the market will rise at the same rate over time is not valid, so this metric is problematic

The issue arrives with the assumption of a constantly rising rate of increase in the stock market. The data series used is from 1870 to present. In the 1870-1930 period, there was no persistent inflation and the dividend yield on the S&P 500 index was much higher. Using the Shiller data, the CPI index used was essentially at the same level from 1870 as it was in 1932. Therefore, without inflation, the S&P 500 did not need to rise as fast to negate the impact of inflation. Also, the average dividend yield from 1870-1932 was about 5.3%, so to provide the long-term average real return of 6.5%, since the stock market had an average dividend yield of 5.3%, it only needed to appreciate 1.2% over the period.

Flash forward to the present day, where the recent inflation readings are in the 2% range, which is also the Fed’s own target. The S&P 500 dividend yield is about 1.8%, so to get the 6.5% long-term real return, a total return of 8.5% is needed, which means the stock market must appreciate 6.7% per year in conjunction with the 1.8% dividend yield to provide the 8.5% total return, or 6.5% in real terms. Even if one believes the long-term real return is now lower, like say 5%, that still requires price appreciation of 5.2% per year, which is well above what was needed in the 1870-1932 period.

### Buybacks Over Dividends

The main reason why the required stock price appreciation is greater now than decades ago is the shift to buybacks over dividends. The average payout ratio from 1871 to present is 61%, but the most recent payout ratio reading is 46%, which indicates much more of the earnings are being retained or are used for buybacks than dividends. The lower dividend rate means more of the return must come from appreciation, which makes the long-term price regressions invalid, since they are based on older periods which required less stock price appreciation, given there were more dividends.

*Uses Shiller data from Yale.edu*

Further emphasizing the point is the look at the buyback yield. As we can see, the buyback yield for the last decade has been about 3% on average, but no such buybacks really existed before 1982, when the SEC issued a safe harbor provision that protected use of buybacks. To the extent the buyback yield persists at 3%, we would expect the stock market to rise 3% faster on an annual basis, over the long term, than it did in the past. This assumption is not overly optimistic, because the 3% rise in price is negating the lower dividend yield, since the current 1.8% dividend yield is about 2.5% below the long-term average from 1871 to present of 4.4%.

### Conclusion

Investors who relied on misleading indications from the Shiller PE, Buffett Indicator, and S&P regression line may have missed out on the bull market, since these indicators all have falsely signaled overvaluation compared to long-term averages since the year 2012.

Like the Shiller PE and the Buffett Indicator, the S&P price regression line is flawed in that the recent readings have different expected means than the historical data. As a result, recent price appreciation appears unsustainable by the regression line metric, since recent appreciation has occurred in excess of the long-term averages. However, the recent price appreciation in excess of long-term averages merely reflects lower dividend payouts in recent years than older years, so greater price appreciation is required to provide a total return in line with historical averages. The increased price appreciation component is also consistent with the shift to buybacks over dividends.

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**Additional Disclosure****:** The information contained in this article is an opinion and constitutes neither actionable investment advice nor a recommendation to trade any security.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.