How Understanding Variance Can Change History

Occasionally you stumble across an article on the old ‘worldwide web sphere’ (to borrow a phrase from Gordon Brown) that helps you articulate something you already knew but needed spelling out. And once it’s right in front of you, your trader brain (that bit right next to the lizard brain, just below the neo cortex) hopefully starts the process commonly known as lateral thinking. Well that happened to me the other day while pursuing one of my hobbies, reading military history. I stumbled across this little gem of an article: “How the Allies guessed the number of German tanks using serial numbers”. Of course, Churchill, tied by the official secrets act, did not spill the beans in his memoirs as to how exactly they outsmarted the Germans, so sometimes you have to dig a bit deeper… And then one thing leads to another…

If you trade in options or manage a portfolio of assets, the concept of variance is part and parcel of your daily toolkit. It’s the number that tells you by how much stuff moves, and it is one of the fundamental concepts behind risk measurement. So, if you want to get an idea of how much data points deviate from their mean, it yields you exactly that information about the past. And as we all know, the past can be a pretty good predictor for the future.

When you sample a random set of data points with the intention of extrapolating the reality for the whole population, you want this sample to be unbiased. That means that in statistics, just as in real life, you should avoid the daily newspaper coverage, an analyst, or your uncle Bob influencing you.

Achieve this and you come close to what is called an unbiased estimator. With that you can obtain variance readout that is as small as possible for the data set you surveyed.

But Why Would You Want To Take On This Much Number Crunching?

Well the potential profits are huge: history has proven this could even help win you a war.

During WWII the British couldn’t be sure how many of the mighty German Panthers were leaving enemy production lines. The Panther was fast, had powerful armament and solid armour. Additionally, it was more rapidly produced and cheaper than the German Tiger tank – a real menace on the eastern and western front – and the allies had at this point in time no real answer to this weapon system if it was ever churned out in large numbers.

Her Majesty’s Secret Service estimated that the Germans were producing roundabout 1,400 tanks a month. Here you have a biased estimator. Why? Well, that information was obtained through spying, intercepting and decoding transmissions, and interrogating captured enemies. So, much of it was deliberately misrepresented, provided under duress, or incorrectly recorded. And to many that number simply seemed absurdly high.

But the statisticians in Bletchley Park asked their fellow warriors on the frontlines to provide them with the serial numbers of destroyed Panthers in their possession. The idea being that although there is a certain degree of randomness in war, because the Germans produced these numbers for their tanks, it would be possible to estimate from this sample size (which can now be described as unbiased), the minimum variance of the whole population of battle-ready Panther tanks. And the statistician’s estimates differed substantially from those figures that intelligence obtained.

Instead of 1,400 a month, their Minimum Variance Unbiased Estimator (MVUE) – I didn’t come up with the term – gave them a figure of, on average, 245 tanks that were leaving the production facilities each month.  After the war, the accurate German production figures were obtained. Between 1940 and 1942 the Germans produced on average 246 tanks.

So what’s the use of this for us? Well, take for example the never-ending conversation about whether Elon Musk is actually fulfilling his production targets and rollout figures predicted by market pundits, or whether Apple is selling enough Apple watches or mobile phones to satisfy its earnings multiples. Even though Tesla won’t let you sniff around their mega factories and Apple doesn’t publish the number of units sold (anymore), to my knowledge neither of these corporations has an army (yet!) to stop you from counting the serial numbers of the vehicles on the road, or the wristwatches and handsets adorning fashion-aware hipsters, and then plugging those into a formula so simple that it doesn’t even have an exponent or a sigma sign.

If you want to take it a step further, and that’s what the boys and girls at Bletchley park did, you can even estimate growth rates by comparing samples over time.

Start counting.

Thorsten Roland Wegener spent twenty years trading equity derivatives and was a partner at Bear Stearns. Currently, he teaches as well as cooking, driving, and cleaning lots.

(The commentary contained in the above article does not constitute an offer or a solicitation, or a recommendation to implement or liquidate an investment or to carry out any other transaction. It should not be used as a basis for any investment decision or other decision. Any investment decision should be based on appropriate professional advice specific to your needs.)