ANNANDALE, Va. (MarketWatch) -- I felt really old on Thursday.

The guest before me on a television talk show expressed astonishment that price/earnings ratios were so low currently. In fact, he pointed out incredulously, some stocks' P/Es had dropped so low that they were now even in the unheard of single digits.

To me, this just showed how little stock market history that this guest really knew. In fact, according to data collected by Yale University Prof. Robert Shiller, the stock market's P/E ratio has been below 10 in 17% of the months since 1871.

That's about one-sixth of the time.

Of course, most of those months came more than two decades ago. That's why those with short memories can get away with thinking that current P/E ratios are particularly low. The last time the market's P/E was below 10, for example, according to Shiller's data, was in 1984, some 24 years ago. Anyone younger than 45 or 46 was probably still in college at that time.

I was prompted by this talk show guest's incredulity to see how the stock market's current P/E ratio stacks up to long-term historical norms. I emerged from my analysis with incredulity, but of just the opposite variety: I was amazed at how high the stock market's current valuation is, even after the market's plunge over the past month.

Any analysis of stock market valuation has to carefully choose which definition of earnings to use when calculating P/E ratios. One can focus on operating earnings, as-reported earnings, and core earnings, for example. And then one can focus on these earnings over the trailing year, or as analysts are forecasting for the coming 12 months.

To be comparable with Shiller's database, I focused on as-reported earnings per share over the trailing 12 months. On this basis, the current PE ratio for the S&P 500 index SPX, -0.48% is 18.1.

Only 21% of the months since 1871 have had higher PE ratios than this, it turns out.

You read that right: Even after a year-long bear market, and especially even after the market's rout over the last month, the stock market's current valuation is still more expensive than 79% of the months over the last 138 years.

How, then, can anyone even think that the market's current P/E ratio is low? One way they can do so is by focusing on projected earnings over the coming year. But analysts are perennially optimistic, and any P/E ratios based on their projections are risky.

To be sure, P/E ratios sometimes are artificially high at the end of bear markets, when earnings are depressed. But I don't think that we can use this possibility to explain away the market's apparently high valuation right now.

Consider, for example, a modified P/E ratio that Shiller calculates; one of its virtues is that it overcomes the problems associated with artificially depressed earnings at bear market lows. The denominator of this modified ratio is average inflation-adjusted earnings over the trailing 10 years. Call this modified ratio "P/E10."

According to Shiller's data, the market's current P/E10 is higher than 80% of comparable readings over the past 130 years.

What does all this mean? For starters, it means that the stock market's current valuation is not abnormally low right now, much less even below average. If you have been basing your bullishness on the belief that it is particularly low, then you need to rethink your bullishness.

Secondly, this analysis suggests that any stock market low that happens at or close to current levels would be the springboard for only a so-called cyclical bull market, not a secular one.

Secular bull markets occur no more often than once a generation. At the beginning of the bull market in August 1982, for example, the market's P/E ratio was below 8. Now that's a secular bull-market valuation, and over the subsequent 20 years the stock market went up more than tenfold.

At the beginning of the bull market in October 2002, in contrast, the market's P/E ratio was 29.1, according to Shiller's data. That only could support a so-called cyclical bull market, and the ensuing bull market didn't even quite produce a double.