LogFAQs > #943409874

If you get a 30% gain every 2 months, in a year that's a 383% gain. In 2 years it's 23x. In 3 years it's 112x. In 5 years it's 2620x. In 10 years it's more than 6.8 million x. If you start with $10,000 and get 30% gains every 2 months for 10 years, you end with over $68 billion.

Now let's run that again with a 10x gain every 2 months, except that 50% of the time, you lose 90%. From an EV point of view, this works out to an average gain of more than 400% in 2 months - more than 13x better than the 30% gains discussed above. So if we just use compound multiplying on 400% every 2 months, after 10 years we should multiply our money by 8.67x10^41. That's our EV. But wait, before we celebrate, let's look at our median return:

After 10 years, on average you'll hit an average of 30 drawdowns - that's 50%. And you'll hit 30 gains of 10x - also 50%. Your return with 30 drawdowns of -90% and 30 multiples of 10x is... ZERO! That's right, you end up where you started, with no gains at all.

Now, you ask, how can that be, when each trade, measured by EV, was more than 13 times better than the 30% every 2 months trades above, and those were enough to turn 10k into 68 billion? The answer is, with the 10x gain/90% loss strategy, almost all of that massive EV is locked up in the universes where you don't hit many drawdowns. For instance, if you hit your 10x 45 times and hit the -90% only 15 times, your gain is now 10^30. That turns an initial 10k investment into 10 decillion dollars, which is orders of magnitude greater than the total amount of wealth in the world. Practically, of course, by this point money is meaningless and there's no way you could continue making trades with such high EV by the time you are putting billions into each trade, much less decillions. And yet that 45/15 gain/loss world is still lower than the mean result which produced a gain of over 10^41.

In other words, with calls the variance is not a bug, it is a feature. But the greater the variance, the greater the disparity between the mean return and the median return. A trading strategy that can produce a 10x gain half the time and 90% loss half the time is obviously insanely profitable from an EV point of view. If you could do that people would pay billions to have you manage their money. But if you actually use this strategy, 50% of the time you won't make anything at all. Almost all the benefits of your research are locked up in the worlds where you accumulate more wealth than the entire planet.

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September 1, 2003; November 4, 2007; September 2, 2013
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