Dr. Jeremy Siegel wants you to know that know is a great time to buy stocks. In fact, he says he’d be surprised if you didn’t get a 20% return on your investment in the next twelve months. Of course, Dr. Siegel’s crystal ball is proving to not be all that great. In 2007 he predicted that 2008 would be a great year for stocks and that financial stocks should do particularly well. So much for that prediction.

To understand his latest argument, Siegel is putting a fair market value on the S&P at 1380. Since the S&P closed today at 930, you can see why’d he think now was a great bargain, but how did he arrive at that 1380 number? Well he says that the long term fair market value for stocks is to trade at a PE of 15 and he then conjures up a figure for what the next 15 years of earnings for the S&P should be based on the past 15 or so- which is equal to $92 a share. $92 x 15 = 1380. Voila. I could almost hear Dr. Siegel add, “Wil-E Coyote. Super Genius!”

This article struck me as a bit fishy, and not just because I’m a bear. For one, having been a avid read of Bill Bonner, I knew from books such as Financial Reckoning Day: Surviving the Soft Depression of the 21st Century that the long term PE for stocks is to trade at 11, not 15. So I was curious as to how Dr. Siegel came up with such figure. It turns out, he made a mistake. Bonner and the bears are correct in saying that the average long term trailing PE for stocks is 11, 15 is the average PE for earnings from four years ago, not next year’s projected. Currently, stocks are trading at a PE of 18 compared to trailing earnings, as Dr. Siegel himself pointed out in the article where he calls stocks “dirt cheap”, and a PE of 18 is not cheap when the long term average is 11. The upshot is that Dr. Siegel made an error and that stocks are actually expensive on the order of 40% compared to their long term PE ratios, not 40% the cheaper as he claims they are.

The other thing that Dr. Siegel doesn’t seem to understand is that the long term average of stock PE is just that- a LONG term average. There are many bull market years where the PE is trading above 11 and many bear market years where it is trading below 11. Furthermore, these periods of over and under valuation tend to be grouped together in the time line: we see stocks priced well over the long term average through the 1920s and then under during the Great Depression of the 1930s. So if we are continuing the bear market slide that started in 2000, then we should expect stocks to be trading BELOW their long term average. Which means, if the trailing average is 11, we should expect to start seeing stocks trading at PE levels of 8 to 10 as they did in the 1970s. You’d have thought that the author of Stocks for the Long Run might have studied up on the market a bit to see just how long the “long run” can really be.

Of course, all of this bull market analysis is based on the notion that the next 50 years of American history should be more or less akin to the last 50 years or so, and that’s a claim I take issue with. American has dominated the last 50 years of world events as a titan with unmatched military, industrial and economic power. Looking forward 50 years into the future, do we really expect to see that continue? Which brings us back to Dr. Siegel; clearly he is wrong in his analysis, but it he simply mistaken or did he aim to reach for a conclusion that would make other parties happy.

Don’t get me wrong, we all make mistakes. Perhaps Dr. Siegel put less time and effort into his Yahoo columns that I put into this blog and just doesn’t get a chance to double check his math, but I don’t think so. I think Dr. Sigel fudged the numbers to arrive at a rosy outcome. If so, it wouldn’t be the first time a Macroeconomist has gone through a rather dubious trick of logic and math to reach the politically desirable conclusion. Indeed, John Maynard Keynes’s The General Theory of Employment, Interest and Money is nothing but a intellectual fraud filled with straw man arguments, shifting definitions, and math based on dubious assumptions, but it is heralded as a classic largely because it came to the desired conclusion of the day: the free market was inherently unstable unless assisted by the power of government. Macroeconomists are task masters at fudging their numbers to support the conclusions that they feel are popular. Why should we think Dr. Siegel is doing any different here?

In 1999 I plotted the trailing PE ratio for the DJ30 back to 1925. I have not updated it. But a quick look at the graph shows the average to be close to 15. Only two periods, once for 3 years and once for 4 years, had PE ratios below 10. So I think you are wrong.

I also made a correlation plot of PE ratio vs. following year market performance. There was not a significant correlation. In other words, forget about PE ratio when trying to decide what the market will do in the next year.

Thank you for your comment. I tried to answer it in my latest post.

Siegel actually makes another serious mistake. He simply multiplies S & P earnings of $92/yr x 15 to project the next 15 years’ earnings. The problem in that methodology is that there is no discounting of future cash flows in that model. it treats $92 of earnings in year 15 as worth the same amount of $92 in year one. That is simply incorrect. Every future cash flow must be discounted at a certain rate to arrive at a present value – that is economics 101. The “discount rate” used is usually based on the risk free rate of return (i.e. 90d T bills) + a risk premium. Historically this has been about 7%. Maybe today, because of low rates it is around 4%. To discount $92 some years from now we need only the net present value formula, namely; NPV=FV/(1+r)^n, where r = the discount rate, and n = the number of time periods (in this case years). So a cash flow of $92 15 years from now is worth $92/1.04^15 = $51.08. To calculate the net present value of the entire 15 years of earnings you need to do this calculation for each year or use a financial calculator. If you run the numbers you find the NPV of 15 years of $92 cash flow discounted at (a very generous) 4% is worth $1023. A far cry from $1380. If you use a discount rate of 5% that number drops to $955. If you use the historical discount rate of 7% then the S&P is fairly valued at $837.

Now these calculations are based on two assumptions – what the discount rate is and what future cash flows are, neither of which can be predicted over the course of a year or two. One thing is likely and that is that the earnings of the next 15 years are unlikley to be the same as the last 15 years. Another thing you can say is that the market is using a discount rate of about 5% since currently the SPX is about $930. If inflation is inflation is 2% that means the “risk premium” for holding stocks in this valuation is only about 3%. Keep in mind that in previous bear markets investor have “demanded” risk premiums of 8, 9, 10% or higher. Those sorts of numbers would value the SPX closer to half of what it is.

Excellent calculations, but I think Siegel may be getting a pass on this one. If he were making the argument that the fair market value of the S&P would be it’s present value after discounting for interest rates for the next 15 years, then you would be correct. He’s not saying that.

Siegel is arguing that stocks historically trade at 15 times future earnings, and that’s a different argument. He is not trying to say that the present value of the S&P is the next 15 years worth of earnings, but rather that historically stocks have traded at a price to earnings ratio of roughly 15 for next years earnings. So if next years earnings were $92, then 15 would be the math as he suggested.

Where he goes awry is that stocks have historically traded at 11-12 of last year’s earnings not 15 of next year’s projected earnings.

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