Scaling Fallacy in Investing

December 17, 1903, was a momentous date in the history of human transportation. On this day, Wright brothers — Oliver and Wilbur — made the first controlled, sustained flight of a powered, heavier-than-air aircraft.

We all know, Wright brothers weren’t the first to attempt human flight. For centuries curious adventurers had been trying to decode this puzzle — how to fly. They looked at nature and noticed that birds fly by flapping wings. So do insects and butterflies.

But mimicking nature can be dangerous — this was a painful lesson that was learned by many early pioneers of human flight. There’s a long list of men who plunged to their death when they jumped from towers wearing large artificial wings.

In true sense, the history of man-made aviation goes back a few thousand years when kite flying was invented in China. Technically, a kite doesn’t fly. It more or less glides in the air like any other light object would in a strong wind.

Of course, manned flights have been in existence since the 18th century when hydrogen gas was first discovered, leading to the invention of hydrogen balloon which was soon followed by much safer hot air balloons. But flying a balloon is less about flying and more about sailing in the air. The promise of flying was in affording us faster travel. If a flying machine couldn’t take us from place A to place B faster than surface travel then it was just another fancy pursuit by a few crazy innovators.

Oliver and Wilbur figured that the problem of flying couldn’t be solved by copying birds or insects. The mechanism of flying works differently at different scales. At a very small and very large scales, flapping simply doesn’t work.

At microscopic scales, wings are too small to displace the air molecules. At very large scales, the effects of gravity are too great for flapping to work

This is called the scaling fallacy — a tendency to assume that a system that works at one scale will also work at a smaller or larger scale.

Some microscopic creatures like aerial plankton simply float in the air. At their size, flying is not a problem. Other bigger insects like many species of spiders use their web-like a parachute. And, of course, insects and birds flap their wings to fly.

The lesson is that strategies and solutions that seem to be effective at one scale can turn out to be utterly ineffective at a different scale.

I am sure you’ve heard of the trivia about an ant, how it can lift weights 50 times its own weight. Instead of feeling motivating, this ant-story always ends up astonishing me. Does it mean that if an ant was the size of humans, it could lift a few tons? If you understand Scaling fallacy, you can guess that a 50 kg ant would have a hard time just rolling out of bed in the morning, let alone lifting weights.

Here’s an excerpt from the wonderful book Universal Principles of Design —

Much is made of the relative strength of small insects as compared to that of humans. For example, a leafcutter ant can carry about 50 times its weight; whereas an average human can only carry about half its weight. The standard reasoning goes that an ant scaled to the size of a human would retain this strength-weight advantage, giving a 200-pound ant the ability to lift 10,000 pounds. In actuality, however, an ant scaled to this size would only be able to lift about 50 pounds, assuming it could move at all. The effect of gravity at small scales is miniscule, but the effect increases exponentially with the mass of an object. This underscores the basic lesson of the scaling fallacy—systems act differently at different scales.

So what does this have to do with investing?

Warren Buffett once said that he was managing a much smaller capital — a few million — he could compound that money at 50% CAGR. He foregoes hundreds of such opportunities today because at his scale — tens of billions of dollars — those bets are too small to move the needle. It’s like a man flapping the wings — it won’t generate any lift.

Investors often miss this point when they blindly copy what other big investors are doing in the market. Their reasons for buying and selling may not apply to small investors. In fact, it can be outrightly dangerous to mimic others without knowing exactly why they did what they did.

While studying any past decision (of your own and others), recognizing the context is very important. In investing, that context could be scale, time horizon, or something else.

Another way the idea of scaling fallacy has its implications in investing is how it applies to time. Just by changing the length of time, the outcome of an investment decision can vary widely.

Traders speculate on the price and their time scale could be in minutes, hours, days, or weeks. For a fundamental investor who is more concerned about the economics of the underlying business, the order of time scale is in years and decades. Wishing that a stock bought based on short term trading tip can generate a multibagger on the longterm is like a aerial plankton trying to compete with a pigeon flying from Africa to England. (Fun fact: Pigeons can fly between 600 and 700 miles in a single day, with the longest recorded flight in the 19th century taking 55 days between Africa and England and covering 7000 miles)

I hope you’ll think about scaling fallacy — both in terms of your time horizon and the amount of capital — when investing your hard-earned money.