## Wednesday, 16 January 2013

### The myth of the harmlessness of 'taking profits'

Thee percentage of winning trades - in the broadest sense of the word -  is something every trader ought to be familiar with in his own trading.  Let's call this percentage (on a 0-1 scale, so that it also doubles up as a probability of winning) $p_w$.  0.5 is the score a coin tossing machine gets.  Anything consistently lower than that, then you're really on to something - just start doing the opposite of what you are doing and soon untold wealth will be yours.  0.6 I think is a decent batting rate.  0.7 and 0.8 very good.  I doubt many human beings have ever consistently achieved 0.8.

So, given all that, in the following analysis, let's consider an extraordinary trader who scores 0.9.  Unbelievable, I know, but 9 out of 10 of all his trades win, in the technical sense of return > 0.  One out of ten returns <= 0.

Next, let's take a principle you see mentioned in a lot of books on trading: don't risk more than 1% of your total capital on any one trade.  Let's assume mister 9-out-of-10 sticks to that rule religiously, and indeed is happy to stay in the position on the downside as long as he isn't stopped out at a level which triggers a stop, closing the trader for a loss of 1%.  I will call the monetary value of a failed trade as $0.01 P$, or 1% of AUM.

So the set up is in place - our trader wins nine times out of 10, and has a 1% of AUM stop loss.  Sound plausible?  Happy?  Even more so, let us force him to only put on is best trade at any given time.  That is, a maximum of only 1 trade on at any moment.  He can be holding no positions if he likes, for as long as he likes.  Nothing forces him to open a position unless he feels compelled to.

The point of all this set up, which sounds rather wonderful, is to show that it all comes to nothing if you set your trades to get you out of the trade on a +10 basis points profit.  That is, if you close your winners, all 90% of them, for a 10 basis point gain, you've effectively imposed a rule on yourself which prevents you from making any money at all, since $(p_w \times 0.001 \times P) + (1-p_w \times - 0.01 \times P)$.  I assume your 1 win out of 10 comes on average at any point in a series of trials, and isn't clustered and otherwise exhibits no informational characteristics within the series.  On average this set up will bleed 1 basis point of your AUM every time.  You will go bust.  You can't abandon the 1% stop loss, due to the more violent downside of many markets (equities, bonds) on occasion, so get rid of the safe-sounding 'sell out on a 10 basis point profit' rule.

With a more realistic 6 or 7 out of 10 batting average, you need to make them all count by at least 20 basis points for a break even strategy.  That's a lot.  And if you're thinking 1% AUM can be tightened to a smaller loss, then remember that this transformation of a fraction of AUM into a stop loss on a specific market leaves you open to the volatility of that market.  If your trading account is under-capitalised, then that stop loss is way too close to the market, meaning there's not much chance at all that you'll hit your winning out-target price before you hit your loss making out target price.  Strictly speaking, it is a function of the minimal trade size and the deposit requirement of that market.  Additionally, the outcome is partly a function of the volatility of tick-by-tick returns.  A handy rule of thumb is: if your ideal place to put a stop means you could lose 1% or more of your capital, then you're under-capitalised.