Dow 100^100

During the 90s there were two books predicting the Dow would go to insane levels of valuation. Dow 36000 and Dow 40000. While there certainly is much to criticize in these books, I was thinking about when inflation would make their dreams come true. The Dow Jones Industrial Average closed at 12650 in the end of January. According to Global Financial Data, the DJIA earnings were 260.86 at the end of January implying a PE of roughly 48.49. I suppose this number isn't exactly fair since the number jumped up in July (a nice signal to get out of the market) when GFD has earnings going from like 800 to like 200 or so. It looks like the data is quarterly and they just have the numbers in the months spots multiple times. So, I'll just use the PE and earnings data from before the ratio goes from 20 to 50 since 20 is closer to the historical average. For that quarter GFD has earnings at 824.65 and with 13409.3 as the number for the DJIA. I'll average those two with the most current numbers so that I don't totally throw off my estimates of the growth rate (giving 542.76 and 13029.65). That gives a PE estimate at 24 that I'll assume could be a long-term number.

I'll split the difference of 36k and 40k (38k) and use that a future price target. Since PE=P/E, That leaves 24 on the left side and 38000 in the denominator. The earnings value I want to use is 542.76*(1+r)^n where r is the rate of growth for earnings and n is number of years to achieve 38k in the Dow (what I want to solve for). GFD has the June 2005 earnings number at 571 which would give a 44% increase in earnings to June and a similar negative decrease to use January's number. It would probably be more appropriate to run a Monte Carlo simulation using all of the data and put together a complicated model (since I am at a library with limited user rights I can't do that right now). Another long-term estimate would look at the average growth rate over the paste twenty years (the 1976 number is 95.81) which gives a number of about 9% growth a year. This number includes inflation (which is important) so you could consider the real number at about 5 or 6% a year depending on your estimate of inflation.

Plugging in the numbers and solving for n (ln 2.912/ln 1.09) gives 12.42 years. This would seem like a few number of years. I agree. This number is incredibly sensitive to the PE ratio or the growth rate. A one point change in the PE ratio would change n by (-1/24)/(ln 1.09) or roughly 6 months (granted the effect changes as you change the start date and decreasing the PE means lengthesns the time it takes to reach 36k). However, a one point change in the growth rate has an even larger effect, -ln(2.912)*(1/1.09)/(ln 1.09)^2 or (-132.3/100) or decreasing by 1.3 years for each percentage point increase in the growth rate. Certainly there are huge uncertainties with this analysis and calibrating the proper numbers. If actual earnings growth is comes in at 6% (3% inflation, 3% real GDP growth) with a long-term PE of 15 (not historically uncommon), then it might take (4.5+3.9) or 8.4 longer than originally planned at almost 21 years.

The Dow may reach 36000 (or 38000 or more) with a sound valuation over the next 10-20 years by pretty reasonable assumptions and 20-30 years from when the author's book was published. However, this does not imply anything about what the Dow will do tomorrow, next month, or next year (or even the next five years). It is a simple estimation that anyone who has taken high school math and introductory finance could figure out. I suppose the author's main flaw was not looking at a longer-trend of earnings growth and PE ratios. Saying the Dow will go to whatever 20 years from now doesn't save you from a Standard deviation that's twice as large as the yearly expected return if you're retiring in five years.

Furthermore, when the earnings growth for the Dow is a number as low as 6% or 9%, inflation will destroy half of the increase in value. If you only looked at real earnings, real Dow Prices, and the real PE, it would be unlikely to see real Dow going to 36000 by the end of the 21st century and it is mathematical impossibility with positive inflation for it to double in value when the nominal Dow doubles in value. For the average long-term investor, country and sector analysis combined with tactical rotation can provide much stronger returns in an inflationary environment.