Compounding Short Stories – A King, Columbus And Indians by Investment Master Class
The Investment Masters understand that losing money inhibits the power of compounding and that is why they focus on avoiding the permanent loss of capital as opposed to beating an index.
Below are some of my favourite excerpts on the power of compounding. The story of the 'Peasant and the King' comes from the book 'Classics - An Investors Anthology' while the story of Columbus, the Mona Lisa and the Manhattan Indians come from Warren Buffett's early partnership letters. The final short extract comes from a 2011 letter from Jeremy Grantham.
The Peasant and the King ['Classics - An Investors Anthology']
And then there was the king who held a chess tournament among the peasants- I may have this story a little wrong, but the point holds- and asked the winner what he wanted as his prize. The peasant, in apparent humility, asked only that a single kernel of wheat be placed for him on the first square of his chessboard, two kernels on the second, four on the third-and so forth. The king fell for it and had to import grain from Argentina for the next 700 years. Eighteen and a half million trillion kernels [18,500,000,000,000,000,000] or enough, if each kernel is a quarter inch long, to stretch to the sun and back 391,320 times That was nothing more than one kernel's compounding at 100 percent per square for 64 squares.
[This story really does highlight the absurdity of achieving 100% returns a year. Assume a 20 year old lives to 84 years [equivalent to 64 chess board squares of investing years] and starts with $1. Doubling his stake every year the old man would end up with $18,500,000,000,000,000,000]
Columbus's Journey - The Joys of Compounding [Buffett Partnership Letter 1962]
I have it from unreliable sources that the cost of the voyage Isabella originally underwrote for Columbus was approximately $30,000. This has been considered at least a moderately successful utilization of venture capital. Without attempting to evaluate the psychic income derived from finding a new hemisphere, it must be pointed out that even had squatter's rights prevailed, the whole deal was not exactly another IBM. Figured very roughly, the $30,000 invested at 4% compounded annually would have amounted to something like $2,000,000,000,000 (that's $2 trillion for those of you who are not government statisticians) by 1962. Historical apologists for the Indians of Manhattan may find refuge in similar calculations. Such fanciful geometric progressions illustrate the value of either living a long time, or compounding your money at a decent rate. I have nothing particularly helpful to say on the former point.
The following table indicates the compounded value of $100,000 at 5%, 10% and 15% for 10, 20 and 30 years. It is always startling to see how relatively small differences in rates add up to very significant sums over a period of years. That is why, even though we are shooting for more, we feel that a few percentage points advantage over the Dow is a very worthwhile achievement. It can mean a lot of dollars over a decade or two.
Mona Lisa - Joys of Compounding - Part II [Buffett Partnership Letter 1963]
Now to the pulse-quickening portion of our essay. Last year, in order to drive home the point on compounding, I took a pot shot at Queen Isabella and her financial advisors. You will remember they were euchred into such an obviously low-compound situation as the discovery of a new hemisphere.
Since the whole subject of compounding has such a crass ring to it, I will attempt to introduce a little class into this discussion by turning to the art world. Francis I of France paid 4,000 ecus in 1540 for Leonardo da Vinci’s Mona Lisa. On the off chance that a few of you have not kept track of the fluctuations of the ecu 4,000 converted out to about $20,000.
If Francis had kept his feet on the ground and he (and his trustees) had been able to find a 6% after-tax investment, the estate now would be worth something over $1,000,000,000,000,000.00. That's $1 quadrillion or over 3,000 times the present national debt, all from 6%. I trust this will end all discussion in our household about any purchase or paintings qualifying as an investment.
However, as I pointed out last year, there are other morals to be drawn here. One is the wisdom of living a long time. The other impressive factor is the swing produced by relatively small changes in the rate of compound. Below are shown the gains from $100,000 compounded at various rates:
It is obvious that a variation of merely a few percentage points has an enormous effect on the success of a compounding (investment) program. It is also obvious that this effect mushrooms as the period lengthens. If, over a meaningful period of time, Buffett Partnership can achieve an edge of even a modest number of percentage points over the major investment media, its function will be fulfilled.
Some of you may be downcast because I have not included in the above table the rate of 22.3% mentioned on page 3. This rate, of course, is before income taxes which are paid directly by you --not the Partnership. Even excluding this factor, such a calculation would only prove the absurdity of the idea of compounding at very high rates -- even with initially modest sums. My opinion is that the Dow is quite unlikely to compound for any important length of time at the rate it has during the past seven years and, as mentioned earlier, I believe our margin over the Dow cannot be maintained at its level to date. The product of these assumptions would be a materially lower average rate of compound for BPL in the future than the rate achieved to date. Injecting a minus 30% year (which is going to happen from time to time) into our tabulation of actual results to date, with, say, a corresponding minus 40% for the Dow brings both the figures on the Dow and BPL more in line with longer range possibilities. As the compounding table above suggests, such a lowered rate can still provide highly satisfactory long term investment results.
Manhattan Indians - The Joys of Compounding Part III [Buffet Partnership 1964]
Readers of our early annual letters registered discontent at a mere recital of contemporary investment experience, but instead hungered for the intellectual stimulation that only could be provided by a depth study of investment strategy spanning the centuries. Hence, this section.
Our last two excursions into the mythology of financial expertise have revealed that purportedly shrewd investments by Isabella (backing the voyage of Columbus) and Francis I (original purchase of Mona Lisa) bordered on fiscal lunacy. Apologists for these parties have presented an array of sentimental trivia. Through it all, our compounding tables have not been dented by attack.
Nevertheless, one criticism has stung a bit. The charge has been made that this column has acquired a negative tone with only the financial incompetents of history receiving comment. We have been challenged to record on these pages a story of financial perspicacity which will be a bench mark of brilliance down through the ages.
One story stands out. This, of course, is the saga of trading acumen etched into history by the Manhattan Indians when they unloaded their island to that notorious spendthrift, Peter Minuit in 1626. My understanding is that they received $24 net. For this, Minuit received 22.3 square miles which works out to about 621,688,320 square feet. While on the basis of comparable sales, it is difficult to arrive at a precise appraisal, a $20 per square foot estimate seems reasonable giving a current land value for the island of $12,433,766,400 ($12 1/2 billion). To the novice, perhaps this sounds like a decent deal. However, the Indians have only had to achieve a 6 1/2% return (The tribal mutual fund representative would have promised them this.) to obtain the last laugh on Minuit. At 6 1/2%, $24 becomes $42,105,772,800 ($42 billion) in 338 years, and if they just managed to squeeze out an extra half point to get to 7%, the present value becomes $205 billion.
So much for that.
Some of you may view your investment policies on a shorter term basis. For your convenience, we include our usual table indicating the gains from compounding $100,000 at various rates:
This table indicates the financial advantages of:
(1) A long life (in the erudite vocabulary of the financial sophisticate this is referred to as the Methusalah Technique)
(2) A high compound rate
(3) A combination of both (especially recommended by this author)
To be observed are the enormous benefits produced by relatively small gains in the annual earnings rate. This explains our attitude which while hopeful of achieving a striking margin of superiority over average investment results, nevertheless, regards every percentage point of investment return above average as having real meaning.
Finally, an extract from Jeremy Grantham's 2011 Letter..
I briefly referred to our lack of numeracy as a species, and I would like to look at one aspect of this in greater detail: our inability to understand and internalize the effects of compound growth.
This incapacity has played a large role in our willingness to ignore the effects of our compounding growth in demand on limited resources. Four years ago I was talking to a group of super quants, mostly PhDs in mathematics, about finance and the environment. I used the growth rate of the global economy back then – 4.5% for two years, back to back – and I argued that it was the growth rate to which we now aspired. To point to the ludicrous unsustainability of this compound growth I suggested that we imagine the Ancient Egyptians whose gods, pharaohs, language, and general culture lasted for well over 3,000 years. Starting with only a cubic meter of physical possessions (to make calculations easy), I asked how much physical wealth they would have had 3,000 years later at 4.5% compounded growth.
Now, these were trained mathematicians, so I teased them: “Come on, make a guess. Internalize the general idea. You know it’s a very big number.” And the answers came back: “Miles deep around the planet,” “No, it’s much bigger than that, from here to the moon.” Big quantities to be sure, but no one came close. In fact, not one of these potential experts came within one billionth of 1% of the actual number, which is approximately 10^57, a number so vast that it could not be squeezed into a billion of our Solar Systems. Go on, check it. If trained mathematicians get it so wrong, how can an ordinary specimen of Homo Sapiens have a clue?
Well, he doesn’t. So, I then went on. “Let’s try 1% compound growth in either their wealth or their population,” (for comparison, 1% since Malthus’ time is less than the population growth in England). In 3,000 years the original population of Egypt – let’s say 3 million – would have been multiplied 9 trillion times! There would be nowhere to park the people, let alone the wealth. Even at a lowly 0.1% compound growth, their population or wealth would have multiplied by 20 times, or about 10 times more than actually happened. And this 0.1% rate is probably the highest compound growth that could be maintained for a few thousand years, and even that rate would sometimes break the system.
The bottom line really, though, is that no compound growth can be sustainable. Yet, how far this reality is from the way we live today, with our unrealistic levels of expectations and, above all, the optimistic outcomes that are simply assumed by our leaders. Now no one, in round numbers, wants to buy into the implication that we must rescale our collective growth ambitions.