At an occasion earlier this month, Warren Buffett, one of the profitable traders of all time, revealed his prediction that the Dow Jones industrial common (DJIA) might be "over 1 million" in 100 years.
With the DJIA at present sitting at about 22,400, is it even affordable to suppose that the inventory market may develop that a lot? Progress from the present worth of the Dow to 1 million would signify a rise of about 45 occasions over. My first impression was worth of 1 million for the Dow may be very excessive, and Mr. Buffett have to be both confused or overly optimistic to place forth such a prediction.
However since this prediction got here from somebody who clearly has a superb understanding of investments and the inventory market, I made a decision to take a look at the maths behind this prediction to see if it is smart.
An essential a part of Warren Buffett’s prediction is the "in 100 years" half. 100 years is a very long time, and though it might be shocking, Warren Buffett’s prediction of the Dow topping 1 million is definitely fairly affordable given the historic efficiency of the market. In reality, the prediction of the Dow reaching 1 million in 100 years might even be conservative.
Here is the maths
Let’s take a look at what sort of progress charge can be required for the Dow to succeed in 1 million in 100 years. As I discussed, the Dow would want to develop by 45 occasions its present worth. When fascinated about funding progress, it’s informative to take a look at the expansion by way of the variety of doublings that will be required.
2^{n} = 45
n ln(2) = ln (45)
n = ln(45) / ln(2)
n = three.81 / zero.693
n = 5.5
So the market worth would want to double 5.5 occasions from its present worth to succeed in 1 million. Let’s take a look at this within the type of a desk to verify it is smart:
# of Doublings |
Ensuing Dow Worth |
zero doublings |
22,400 (present Dow) |
1 doubling |
44,800 |
2 doublings |
89,600 |
three doublings |
179,200 |
four doublings |
358,400 |
5 doublings |
716,800 |
6 doublings |
1,433,600 (Dow over 1 million) |
From the desk above, you’ll be able to see that doubling the present Dow 5 occasions yields 716,800, and doubling six occasions yields over 1 million, so the variety of doublings for the Dow to succeed in 1 million have to be someplace in between. Our estimate of 5.5 doublings is smart.
So the Dow would want to double 5.5 occasions in 100 years — or in different phrases, it will have to double each 18.2 years: 100 years / 5.5 doublings = 18.2 years to double.
The following step to testing Mr. Buffett’s prediction is to determine what charge of progress can be required for the worth of the Dow to double each 18.2 years.
For a fast estimate, I turned to the "Rule of 72." The Rule of 72 is a useful approximation to seek out what number of years it’s going to take an funding to double — merely divide 72 by the annual charge of progress. I flipped the Rule of 72 method round to test the speed of progress required:
72 / progress charge = years to double
72 / progress charge = 18.2 years
Resolve for progress charge:
72 = 18.2 x progress charge
progress charge = 72 / 18.2 = three.96 p.c annual progress
So the "Rule of 72" approximation tells us that an annual progress charge of three.96 p.c can be required to double the Dow each 18.2 years, which is the speed of progress wanted for the Dow to hit 1 million in 100 years.
In the event you do not need to accept an approximation, or if you’re simply geeky in a cool kind of means, you are able to do a extra precise calculation:
2P = Pe^{Yr}
2P = Pe^{(18.2)r}
ln(2) = 18.2r
r = ln(2) / 18.2
r = zero.038 or three.eight p.c
The approximation from the Rule of 72 matches fairly carefully with the precise calculation, so it appears we’ve got nailed down the speed of progress that’s required for the Dow to succeed in 1 million.
It seems that that an annualized progress charge of three.eight p.c is effectively inside the historic progress charge of the inventory market over the previous 100 years. The common charge of return from the inventory market is often thought of to be as excessive as 7 p.c.
After all the inventory market doesn’t march steadily alongside at a mean charge of progress 12 months after 12 months. The market swings up and down from day after day and follows longer upward and downward traits throughout bull and bear markets. However over the lengthy haul, the typical development for the inventory market has been upward at a charge of effectively over three.eight p.c common progress over the previous 100 years.
Along with the mathematical consideration of the speed of progress required for the Dow to succeed in 1 million in 100 years, one other consideration is whether or not the world’s folks and pure assets will proceed to maintain financial progress over the subsequent 100 years. With improvement of thrilling new applied sciences and rising world markets to drive progress, it appears affordable that the inventory market may preserve going up.
So it appears like Mr. Buffett’s considering makes good sense as normal, and the prediction of the Dow 1 million makes good sense.