Janet Yellen made headlines last week with her comment that stock market valuations "generally are quite high." The market took note, driving down prices.

Is she right? Are stocks overvalued?

It certainly feels that way to most investors. Stocks are trading at all-time highs and are in the midst of a bull market that has seen the S&P 500 move up more than 200% since mid-2009 lows.

However, investing based upon feelings isn't usually a very good idea. That's why we rely so much on statistical models to help us be objective about where market valuations stand at any given point in time. Let's see what we can uncover.

**The Average P/E Says… Stocks Overvalued**

It is most likely that Yellen was referring to the price-to-earnings (P/E) ratio in her speech. Stock market pessimists have been promoting doom-and-gloom for years now. The #1 argument they make is that the P/E ratio is higher than its long-term average.

Below is a chart showing the S&P 500's P/E ratio going back to 1962, as represented by the red line. The blue line is the S&P 500's long-term average P/E of 15.

The current P/E of 18.5 is higher than the long-term average. Taken at face value, this would indicate that stocks are frothy. However, this argument has several critical flaws.

1. *Stocks seldom trade at average P/Es*.

Since 1962, the S&P 500 spent virtually no time at its long-term average of 15. In many years, it traded at a P/E far from its long-term average.

2. *A "fair" P/E ratio is impossible to determine in isolation.*

What is a "fair" P/E ratio? Is 15 fair? If so, what makes it fair? The point is that P/E ratios mean little in isolation. There are other factors that we must consider to get the entire picture.

**The Missing Link: Inflation**

What is the most important factor in determining fair P/E ratios? We have looked at correlations between P/E ratios and all kinds of variables. We do not find strong relationships between any of the widely followed indicators such as interest rates, GDP growth or earnings growth. We have found that inflation is the best predictor of P/E ratios at any given point in time.

To make this more intuitive, we've converted the P/E ratio into E/P, which is known as the "earnings yield". In other words, if the S&P 500 paid out 100% of its earnings as a dividend, what would the yield be?

The chart below compares the S&P 500 earnings yield and the personal consumption deflator, which is what the Fed uses as its inflation measure.

As you can see, there is a clear visual relationship between the two. To measure the relationship mathematically, we created the scattergram shown below. On the left axis is earnings yield and the bottom axis is inflation. Drawn through the middle is a linear regression line.

The correlation between inflation and earnings yield is not perfect, but it is there. Using this regression, we arrive at the formula shown in the bottom right corner. That formula is:

y = 0.9048x + 0.0366

In the above formula, "y" represents the estimated earnings yield and "x" represents the current inflation level. If we plug in today's level of inflation, the formula will predict where today's earnings yield should be based on the historical relationship between inflation and earnings yield over the past 212 quarters.

In the chart below, we've applied this formula to each quarter going back to 1962. The blue line represents the "predicted" earnings yield and the red line represents what the actual earnings yield was.

Most people aren't used to looking at charts of earnings yield, so we converted the earnings yield (E/P) back into P/E. That chart is shown below.

The chart above clearly has more predictive power than the "average" P/E. If you were simply following this chart, you would have predicted that stocks were about fairly valued in most periods except the following:

- Overvalued from 1968 to 1973
- Undervalued in 1985
- Overvalued in 1987 (right before the market crashed by 25%)
- Significantly overvalued from 1992 through 1994
- Significantly overvalued from 1998 through 2001
- Undervalued from 2009 through today

**What does this mean for today's market?**

This model tells us a few things:

1. *Stocks are not overvalued.*

Far from it. According to this model, the appropriate earnings yield is roughly 4.7%, which translates to a P/E just over 21. If the personal consumption deflator were to hold around 1.1%, the market would likely continue P/E expansion.

2. *The stock market can handle some inflation.*

The Fed has stated that their target inflation level is 2% vs. today's 1.1%. If inflation does rise to 2%, our formula estimates that the fair P/E would be about 18.5, which is exactly where we are now. The stock market appears to be pricing in the expectation that inflation will rise.

3. *The Fed isn't going to wreck the stock market*.

Investors across the globe are concerned that stocks will be hurt when the Fed starts to raise rates. According to our research, however, this just isn't the case. Inflation is twice as correlated with P/Es as interest rates. In our judgement, a gradually rising Fed funds rate won't bring down the market. As long as the Fed does not aggressively raise rates, signalling that they see a significant risk to higher inflation, stocks can handle a period of rising interest rates.

The Great P/E debate will surely rage on for decades to come, but we believe many investors - including our own Fed chairwoman - have completely missed the point. Average P/Es have no predictive ability for future P/Es without taking inflation into consideration.

Unless inflation rises above 2%, the S&P 500 will be driven primarily by the future growth of earnings and dividends. In this regard, there is plenty of good news. Wall Street analysts are currently projecting double-digit growth in both earnings and dividends over the next 12 months.

If Fed chair Janet Yellen jawbones inflation worries higher, that could derail stocks. If she focuses her attention on containing inflation rather than forecasting stock market valuations, we would all be better served.