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3/3/05
Yes, You Can Time the Market (Retrospectively)

Ben Stein, author of Yes, You Can Time the Market!, is a smart, funny guy, as evidenced by his role as the high school history teacher in Ferris Bueller's Day Off and as host of Win Ben Stein's Money. He's also supposed to be a savvy economist. Certainly I agree with most of his political opinions expressed. Despite all this, he's got the stock market all wrong.

The core of "Yes,.." is a series of tests in which Stein shows that over the last 100 years, you would have been best off buying when various valuation measures (e.g. price, price/earnings, price/dividend, price/book, Tobin's Q) are low . At first I was glad to see that Stein didn't make the mistake of assessing low -ness by choosing, say, the years with the 10 lowest PE s of the last 100. That would be using data from the future. For example, let s suppose that the lowest price to book ratio occurred in 1932. Well, that was a very good year to buy. But in 1932 we didn't know that that year s price/book was the lowest of the full 100 year period spanning 1900 to 2000. Knowing that in advance would have given us confidence that the market probably wouldn't go much lower.

Nevertheless, even though Stein doesn't peek at the future in the blatant way outlined above, he does peek in a more subtle way that I will show probably explains the effects he observes.

Let me review the first test that he does, based on price, and then I will show that much or all of the apparent effect that he observes results from his retrospective clairvoyance. At the close of each year, starting in 1901, Stein takes the closing S&P price and then divides it by the trailing 15 year average of the price. This gives him a number. I'll call it x, and we'll have values of x for each year, e.g. x(1901), x(1902), etc. Then he takes the 20-year forward return of the market. For 1901, that would be the return from 1901 to 1921. I'll call that number y , and again we'll have values for each year, e.g. y(1901), y(1902), etc.

Stein then takes the (x,y) pairs, sorts on x, and looks at the average of the y s for the four quartiles in x. Lo and behold, the y s for the lowest two quartiles (when price is low compared to the 15-year moving average) are higher than the y s for the highest two quartiles (when price is high compared to the 15 year moving average). The average forward 20 year return is 150% for the highest quartile, 220% for the next highest, 490% for the 3rd highest, and 560% for the lowest quintile. On this basis, Stein writes that THE LAST YEAR YOU WOULD HAVE BOUGHT STOCKS DURING THE TWENTIETH CENTURY WAS 1984. (caps added).

A typical spec's antennae are at this point on full alert. He might be thinking the following:

--In 100 years, there are only 5 non-overlapping 20 year intervals, and isn't it going to be hard to conclude anything?

--Should we trust a book that s telling us not to buy in any year from 1985 through (at least) 1999? Haven t we heard a lot of this before, from the first page of Barron's?

and my pet:

--Stein divided things up in quartiles at the END of the 100 year period. He wouldn't have been able to do that in 1929 or 1932 or 1945, because he wouldn't know all the 100 x values. Isn't he cheating by peaking into the future?

From now on I'll focus on this last concern, the concern about peeking into the future. I will show that significant differences in returns between these retrospectively assigned quartiles will occur even for a random walk model, with a drift term.

I modeled the market as a random walk, using this iteration:

Log(price in year n+1)=Log(price in year n)+R+epsilon(n).

Here R is the long term drift of the market, which I took to be 0.1 per year (corresponding to about 10% per year; in retrospect a bit too high). Epsilon is the random term. I obtained the epsilon s from Excel, using Excel s hard-to-find feature that generates random numbers from a normal distribution. The standard deviation that I used was 0.2, corresponding to about 20% annual variation in market returns.

Using this iteration method, I generated 116 market prices. Starting with price 16, I can compute the trailing 15-year moving average, and then I can calculate x for each year. For each year (except the last 20) I can also calculate y , the 20-year forward return. For 80 of these years I can get both x, the 15-year trailing moving average, and y, the 20-year forward return.

Following Stein, I sorted these 80 pairs into quartiles in x.

The results of the first run:

Whaddya know, if I do my retrospective sort on x (price/15-year moving average), the 20-year forward returns are highest for the lowest x values and lowest for the highest x values. And this is using a RANDOM WALK model in which we know that today s price and its relation to past prices has absolutely no predictive value. Apparently all our predictability came from retrospection.

I ran the same test eight more times to get some statistics:

Probably my first run was a bit of an outlier, but the full test with nine repetitions shows that on average the lowest x quartile beat the highest x quartile by 385%, and this difference was non-zero with a t-score of 1.8.

My conclusion is, don't wait 15 years to put your money to work.

3/3/05
Victor Niederhoffer Responds With a Real P/E Perspective

The results on p/e's of the Former Tennessean, the Yale Real Estate Expert, and others like the imitative switch hitting tennis player from the University of Chicago, and the chronic bears, all have a variation of lookback bias far more serious than the Professor's very sanguine overview. This is over and above the fact that anyone who believes that p/e's that occurred in 1905 or 1930 are relevant to today. And over and above the fact that people like most of the aforementioned don't seem to realize that the price of something that gives cash flows over time is its discounted value, and when interest rates decline by 1/2 the discounted value doubles. And this is over and above that when computing p/e's in those days, apparently the compilers didn't know how to divide by a negative number so if you look carefully they threw out all the negative numbers in computing p/e of individual issues. And this is over and above the fact that earnings they use are revised often and so are retrospectively adjusted.

The main problem is the announcement effect. In those days, they didn't have quarterly earnings so all the back figures are annuals. But the annuals were announced and compiled in March in those days. Let's assume that price is always 10 times earnings. And that the earnings as of 12-31-1904 for the calendar year ending 12-31-2004 are estimated to be $10.00 a share. Also, assume a p/e of 10 times the actual or best estimate. So that the Dow was selling at 12- 31-1904 at the famous 100 level that the Founder of Security Analysis always thought was too high because he went bankrupt by buying it above in the 1930's ( and then this Steinian reasoning got him out of the market in 1955 at Dow 700 for the rest of his life). Okay, assume that earnings actually came in at 12 a share. Price would advance to 120. But the actual p/e of was a low 8.5 in the kind of figures moves by the aforementioned. Similarly when the earnings came in at 8 a share, the actual p/e would go to 12.5 and price would decline to 80. Thus, the low p/e's were associated with a 20% artificial anomalous bias in favor of the above mentioned mumbo. This process repeated year after year is more than sufficient to account for the 0% correlations that a counting study actually shows.