June 8, 2013

The Notion of Drawdowns

It is often said that the worst drawdown is the one to come. However, no one seems to quantify the notion. You can't see if they are expressing these drawdowns on a percentage basis or on an amount basis. In most cases, these two views have major differences when looked at from a single trade perspective, at a portfolio level, or over a long term trading interval like 20 years or more.

Not to mention a kind of defeatist's view as if anything you might do will lead to your worst drawdown ever, as if stating that you will eventually lose no matter what you do.

A portfolio's return could be expressed as a multiplicative series of plus and minus returns: A(0)*(1+r(i))* .... *(1+r(n)) for the i to n successive returns over the life of the portfolio. Another way of expressing the same thing could be as compounded return: A(0)*(1+r)^t.

Giving, for example, a drawdown of 50% somewhere over the trading interval could then be simply represented as: 0.50[A(0)*(1+r)^t] which based on a positive r over the duration would give bigger and bigger amounts as time elapsed.

So yes, the more you progress in time and the higher your rate of return, the more your next future drawdown will be of a much larger amount.

A 50% drawdown is equivalent to 1 doubling time (the time required to double a portfolio). It's like going back and losing half of what ever you have made no matter how long it took to get there. For instance, a 15% compounded rate of return will require 4.97 years to double. A 50% drawdown will set up back this doubling time. A doubling time series: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024,.... The later the drawdown in the series, the more expensive it will be. A more elaborate view on doubling time is presented here:

Mr. Buffett has had 4 drawdowns in excess of 50% during his long and prosperous career. His last one (covering the financial crisis) was over $100B, now that's a drawdown. Should Mr. Buffett have taken a stop loss prior to his more than 50% portfolio decline? Personally, I don't think so. And there are many reasons for this. One of the simplest reasons, especially for Mr. Buffett, is that over the long haul, portfolio declines tend to recover. At least when you play the game the way Mr. Buffett plays it.

IMHO, one should not fear having his/her major drawdown going forward since it will happen. And if it does not happen, then you did not get there; meaning that you have not made enough to really make it matter. 

Created... June 8, 2013 © Guy R. Fleury. All rights reserved. 

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