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Are stocks cheap now?

That’s the question that investors inevitably ask after a drop like the one we’ve seen since the Standard & Poor’s 500 Stock Index hit a high at 1217 on April 23. From that high through the close on July 2 the index dropped almost 16%.

Attempts to answer that question almost always haul out historical comparisons. Stocks are cheap because they trade at a price-to-earnings ratio that hasn’t been seen since wooly mammoth futures traded on the LME (London Mammoth Exchange.) Or they’re expensive because in decades when interest rates are rising stocks have historically traded at a price-to-earnings ratio of the inverse of the second derivative of the change in the yield of 10-year Treasuries (or something.)

I think that kind of historical number will get you part way home. It will give you a probability that stocks in general are cheap or that a stock in particular is cheap. That’s not a guarantee that a stock won’t get cheaper tomorrow but it is a useful read on how likely it is that you buying somewhere in the neighborhood or “cheap” or “fairly valued” or “expensive.

To get you closer to a complete answer, though, I think you need to ask a second question: When we ask, Are stocks cheap? what exactly do we mean by cheap?

Put the two approaches together and I think you can actually come up with a pretty good answer to that question. Right now, I’d say, the answer is kind of mixed. Some stocks are cheap. Others are still moving in that direction. Let me see if I can explain how to tell which stocks are which.

The problem with attempts that use historical data to answer “Are stocks cheap?” is that the answer depends to a disappointingly large degree on what assumptions you make about the future.

So, for example, at the end of June Birinyi Associates, reported that over the last twenty years the average trailing price to earnings ratio for the S&P 500 is 20.3. On June 29 the trailing PE for the index was just 15.6.

Ergo stocks are historically cheap.

Absolutely true.  But not totally helpful. Stocks may be cheap if you look at trailing earnings—that is the earnings per share over the last twelve months—but that doesn’t tell us anything about whether they’re cheap on future earnings. And it is future earnings that will determine the price tomorrow of the stocks you buy today.

And that’s especially true right now when it’s fear that a slowing global economy is going to take a bite out of future earnings that’s driving stock prices down.

So what does data on future earnings (what’s called “forward earnings) and future price-to-earnings ratios tell us? Again that stocks are cheap. The forward four-quarter PE ratio for the S&P 500, according to Thompson Reuters, is just 12.7. That’s below the average forward PE ratio over the last year of 14.4.

But that data leaves us in exactly the same place. Stocks are cheap, if analysts’ projections of future earnings are correct. If the global economy is slowing, then the projections are wrong and so is the conclusion that stocks are cheap.

You can massage this data in lots of ways. You can take into account current interest rates—and the projected direction of interest rates. You can factor in where the market stands in the economic cycle. You can try to correct earnings numbers and projections to come up with what’s called “normalized” earnings that look at what a company’s earnings power will be once the current “unusual” economic condition is over.

All those are useful but they run into the same problem—they rest on some projection about the future. And it’s the current uncertainty about the future that is driving investors to sell and to wonder if they shouldn’t instead be buying.

I don‘t advise throwing out all these historically-based attempts to answer the “Are stocks cheap?” question. They can be very useful if you recognize that instead of giving you a concrete yes or no answer to your question, they give you a probability. Knowing that stocks trade at a trailing price to earnings ratio of 15.6 when the average over the last 20 years has been 20.3 doesn’t guarantee that stocks can’t get cheaper tomorrow or that they’re about to rally because of this low valuation. Instead it tells you that in the most common economic situations—those that occur, say, two-thirds of the time, buying now will be buying at a bargain price.

And that’s a useful context. Keep it in mind and then turn your approach to the question on its head by asking not “Are stocks cheap?” but “What do I mean by cheap?”

For example, on July 6 shares of Chevron (CVX) closed at $67.56. By many historically based measures this stock is cheap. The 52-week high was $83.41 so we’re looking at a stock that’s down 20% from its high. The projected PE on calendar 2010 earnings is just 10.2 and on projected 2011 earnings it’s an even lower 6.73.

This is a cheap stock on a historical basis—if you think that Wall Street analysts are correct when they project 80% earnings growth for Chevron in 2010. And if you forget about the fact that the stock traded about 10% lower at its 52-week low of $60.88 and that at their March 5. 2009 low the shares sold for $56.46.

But also ask yourself what do I mean by cheap when I’m talking about Chevron. Sure, if you can catch the stock at something near a low for this correction (or whatever it is), then the stock is cheap. Unfortunately, we don’t know that low in advance.

There is another way, though, that Chevron is cheap, one that is more ‘knowable.” Chevron now trades with a yield of 4.28%. As of July 6 that was 1.35 percentage points more yield than I’d get with a 10-year Treasury note. That kind of dividend yield on the shares of a company that I know will be around to pay its dividend—and probably raise it—for years and years and years meets my definition of cheap.

It’s not only stocks with dividends that can match my definition of cheap.

Contrast this pair of stocks, (CTRP), the largest online travel company in China, and Itau Unibanco (ITUB), the largest bank in Brazil. is an extremely volatile stock—it fell almost 14% on July 6. Despite that at a July6 close near $33 it still traded nearly 75% above its 52-week low. Given the volatility and the 52-week low, at roughly 30% off the 52-week high at $47 doesn’t strike me as cheap. Itau Unibanco, on the hand, is either cheap or getting there. The stock isn’t nearly as volatile; it traded at 20% below its 52-week high on July 6. Add that to the relatively lower risk in Brazil versus China right now and Itau Unibanco strikes me as cheap.

What I’ve done in the case of these two stocks is factor stock-specific risk into my definition of cheap. Risky stocks need have dropped by more than less risky shares to meet my definition of cheap.

Let me give you the names of three other stocks that strike me as cheap right now on the basis of my dual approach: Abbott Laboratories (ABT) with its yield of 3.8%, Yara International (YARIY) with a chart that looks like it has built a base for gains even as the rest of the market has faltered (and that despite that move was trading at just 25% above its 52-week low), and Teva Pharmaceutical Industries (TEVA) with a July 6 price just 10% above its 52-week lows.

I wouldn’t rush to buy any of these right now (although a nibble would be fine if you think you want to build a position in any of these stocks.) The individual shares may be cheap but the trend in the market is still down.

Remember back to my discussion on exactly what market history tells us about when stocks are cheap. I think that the probability is fairly high—say the two-thirds odds that I mentioned earlier—that current prices are cheap. But the last two years have been full of unusual events that fall outside the two-thirds band that defines business as usual.

So I think I’m going to be just a little cautious yet and wait to see if Brazil and China get their growth acts together (for more on how that schedule is unfolding see my posts and ) and how far the economy in the United States will backslide before I buy even the stocks that I’m pretty sure are cheap.

I’d like a little better odds than pretty sure right now as attractive as these five stocks are.(For more on how I see global markets developing over the next six months or so see my post )

After all my definition of cheap also includes a read on the volatility of the stock market as a whole.

Full disclosure: I don’t own shares of any company mentioned in this post.