*NOTE: This is an update to the valuation post from November 2020. I'll reference that article throughout this piece, but you can also read the original here.*

Over the last 5 years, I’ve read a nauseating number of articles suggesting that the stock market was wildly overvalued. The underlying logic of their argument was the regurgitated “analysis” of current price-to-earnings (P/E) ratios compared with long-term averages.

They all go something like this:

“The average P/E ratio for stocks has been 16 over the past 20 years. Today the P/E ratio is 22. Therefore, the stock market is extremely expensive right now.” -Every valuation article. Ever.

That’s the worst excuse for “analysis” I’ve ever heard.

A 12-month period can be completely irrelevant to the long-term picture. In April 2009, the inflation-adjusted P/E ratio for the S&P 500 reached 123.7 [1]. At the moment when the P/E ratio was the highest it has ever been, yet it was a historically good time to buy stocks.

Stocks can also appear artificially cheap in good times, when profit margins and earnings may be unsustainably high. In this scenario, the “E” part of the equation would be artificially high; therefore, the P/E ratio would be artificially too low.

### Multi-year Earnings > Single Period Earnings

Consider a scenario where you owned a business. That business generated between $100,000 and $0 from year-to-year. When doing your budget, which number would you use as your expected income?

You wouldn’t use the high number or the low number, would you? Neither one provides you with an accurate picture of the business profits. You would probably use the average, which is $50,000. By smoothing out earnings over a longer-term, you eliminate both the abnormally high earnings and the abnormally low ones.

We can do the same with the stock market.

To really effectively understand what the current earnings power for businesses looks like on a longer-term basis, we must smooth out the earnings across many years. This is the method first promoted by Benjamin Graham and popularized by Robert Shiller. Graham initially suggested 7 to 10 years in his classic book “Security Analysis.”

To illustrate why multi-year earnings are superior, check out the chart below. It compares the rolling 12-month earnings (green line) with the rolling 10-year average earnings (blue line). Which appears to provide the most helpful information about business earnings?

Rather than using the 12-month earnings as the “E”, it is far more useful to use the 10-year rolling number. This results in much more accurate extreme market points. Remember, the rolling 12-month P/E ratio spiking to 123.7 in April 2009? If you were looking at a smoothed 10-year earnings number, the P/E ratio would have been 8.88. [2]

Despite its improvements over trailing 12-month P/E ratios, the Shiller P/E is still used in comparison to the long-term averages. The Shiller P/E is over 37 [3], which is way higher than its long-term average. So analysts and investors (wrongly) conclude that stocks must be overpriced.

The reality is far more nuanced than simple comparisons to past averages. We’re missing a very important part of the equation: interest rates.

### Interest Rates: The Key That Unlocks the Valuation Door

How do you know if you’re overweight? You could calculate your weight in relation to the average person. That would be a start, but it wouldn’t be the entire picture. It would be more reasonable to compare your weight to the average person of the same gender and height. Then you would have a better assessment.

Now, what happens if you’re on the moon? Does it make sense to compare your weight on the moon to the average weight of your gender and size on Earth? Of course not.

**Comparing P/E ratios to historical averages without considering interest rates is like measuring weight without gravity.** It’s like someone going from Earth to the Moon and thinking they’ve lost weight. They haven’t lost any weight; their environment has just changed.

The only way to properly value stocks or any asset is in relation to other assets. If you can earn a guaranteed 20% return somewhere, then why would you accept a 10% return that involved risk? You wouldn’t.

So it is with stocks. If we can make 5% in Treasury bonds, we need to make more than 5% in stocks because they are riskier. If we only make 1.62% in Treasury bonds (like today), then we may be quite pleased to earn “only” 5% in stocks. And the lower return investors as a whole are willing to accept, the more they will be willing to pay for $1 of earnings.

Low-interest rates make P/E ratios, in general, increase as well. The higher the P/E ratio, the lower the future returns; however, stocks could still be fairly priced in relation to other assets that are also likely to produce lower returns.

### Bringing Interest Rates Back Into the Picture

To evaluate whether the P/E ratio right now is appropriate or not, we must introduce interest rates into the equation. To do that, I’m going to be using a regression model with data from 1960 to 2020. Smoothed earnings [4] will be used in addition to the 10-year US Treasury yield. We’ll use this data to predict the price. [5]

The model tells us that, over the time frame measured, each variable has something to add to the valuation equation. Earnings should have a positive impact on price. For every additional $1 of earnings, stock prices should generally go up. Interest rates, on the other hand, should have a negative impact on price. Higher interest rates will compete with stocks and, in general, drive prices lower.

The model incorporates all of the past data and makes its best assessment of what “fits” the overall environment best.

### Last Update

I last wrote about valuation in November 2020. At the time, we were still coming out of COVID-19 and there were (and always are) people screaming that the market was overvalued and destined to crash.

Here was the valuation prediction at the time:

If the appropriate earnings number is $111 and interest rates remain at 0.79% on the 10-year US Treasury rate,

the model suggests the fair value for the S&P 500 is 3,709. Based on Friday’s close of 3,509, that would be approximately 5.5% higher.

And then I gave a range using 1 standard deviation:

...the S&P 500 should trade between 2,824 at the low end and 4,868 at the high end.

The conclusion from November 2020?

The biggest takeaway here is that stocks are not necessarily cheap, but

they also aren’t overly expensive. And they certainly aren’t in a “bubble” as so many are currently proclaiming.

Since that article was written, the S&P 500 is up another 20% and is starting to push above my predicted fair valuation from about 6 months ago. So where are things today?

### June 2021 S&P 500 Valuation Update

The 7-year average earnings are up to just under $118 from $111 last time. If we assume interest rates remain at today's levels at 1.62%, the model suggests **the fair value for the S&P 500 is currently 3,470**. That is lower than the 3,709 estimate from November.

How is that possible if earnings are up from $111 to $118?

*Interest rates.*

**For every 1% increase in the 10-year US Treasury rate, it seems (based on my data) that stocks decline about 10%.**The 10-year US Treasury bond is now at 1.62%, which is up nearly a full percent from the 0.79% it traded at back in November. If we assume a 10% decrease in value for that alone, the model would suggest the S&P 500 should be trading around 3,330. Since we also boost earnings a bit, we end up higher than that.

Below is an image of the model going back to 1960. The predicted value is in blue with the actual S&P 500 price (adjusted for inflation) in red. The scale is logarithmic, so ignore the values on the left. The shaded grey cloud is the statistical noise at one standard deviation (more on that in a minute). [6]

### Statistical Noise

Before we get too carried away with this, let’s keep in mind that this is a model. It takes the data you give it and spits out an answer. As humans, we love precision. We love exact predictions. It’s essential to remember that **stock prices cannot be modeled like other areas.** We’re dealing with complex interactions between human emotions, economic progress, government interventions, and all kinds of other variables that cannot be known.

To account for the statistical noise that any model naturally has, we must expand the midpoint to include a larger window. To do that, we can ask the statistical software to give us a range of historical values that would capture a certain percentage of the observations.

For my analysis, I did 1 standard deviation. That simply tells us that given our current inputs (earnings and interest rates) we would expect the stock market to trade within a certain range 68% of the time. Using this more broad measurement, **the S&P 500 should trade between 2,652 at the low end and 4,545 at the high end**.

### Bottom Line

Stocks are not cheap, but **they also aren’t overly expensive**. And they certainly aren’t in a “bubble” as so many are currently proclaiming.

Still, it's clear how powerful rates are. If we assume rates stay at 1.62%, then I think you could make a reasonable argument for the market to continue to do well and push towards that upper limit around 4,545 (or even higher).

If rates go up another 1%, however, I think stocks would start to have trouble from a valuation perspective. **A 10-year US Treasury bond at 2.50% or 3% would start to provide a bit of competition for stocks. **That would almost certainly pull the market down; I would think at least a correction would be warranted if that happens.

If you believe interest rates are likely to stay under 2%, there’s no reason why stocks can’t remain at their elevated P/E ratios. In fact, it would be abnormal for them *not* to. Stocks are the only place that offers a reasonable rate of return for investors. As long as that continues, I'm not too worried about valuations here.

*Disclaimer: This article is for educational purposes only. I’m not your financial advisor. I’m not giving you investment, legal, or tax advice. The data I’ve shown here cannot be guaranteed to be accurate. You should always do your own research before making investment decisions. Past performance is no guarantee of future returns.*

Using Shiller data from Yale accessed on November 6, 2020. http://www.econ.yale.edu/~shiller/data.htm. ↩

Using Shiller’s data downloaded from Yale’s website. http://www.econ.yale.edu/~shiller/data.htm. File name “ie_data.xls”. Accessed on November 7, 2020. ↩

Shiller data. Accessed June 8, 2021. http://www.econ.yale.edu/~shiller/data.htm ↩

I’m using 7 years. ↩

Using S&P 500 price adjusted for inflation to today’s dollars ↩

Keep in mind that the model uses data from 2020, so it is not quite fair to look back at, say, January 2000, and see how clearly overvalued stocks were. To know that for sure, we would have to run the analysis ending in the month we were trying to predict and see if the out-of-sample data would confirm it. ↩

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