Expectancy & Drawdown
Expectancy is (Pw * Aw) – (Pl * Al). In the example data given:-
(0.6666 * $464) – (0.3334 * $295) which yields $210.95.
This means, I can expect on average every trade to yield $210.95.
So, after 134 trades, do I have an additional $28,267.30 in the account attribuatble to trading activities?
Drawdown is a function of losses or more correctly, the order and sequence of losses. Reality clusters. That is, you’re likely to get ungainly random clumps of consecutive strings of losses (and wins) rather than equally spaced out according to the Pw
l ratio. While 2 wins followed by a loss would be nice and orderly, it’s not that likely to occur in practise.
Doesn’t matter which method you use to calculate consecutive losses, for a system with the profile stated it’s going to come in at around 7. That is, statistically, you should expect clusters of 7 consecutive losses. Before you go running off to work out what you can increase your risk to as you’re only ever going to a max of 7 losers in a row, stop. This is just statistics – you could have an infinite number of losses in theory. Of course, a (not the) big question is, what do most traders when, for the first time faced with this very unappealing situation, do? Do they sit tight and trade on through it, as it’s part of the plan? Separate issue and another one we’re not going to deal with on this thread.
As another aside, this system should generate you a series of 13 consecutive wins and you shouldn’t be overly surprised, you wouldn’t need to raise an eyebrow – though you probably would. (I’m not a betting man, but I reckon you’d pull the plug and scupper yourself long before you allowed 13 consecutive wins to favour your account…LOL).
It’s interesting that Captain Currency went with a figure of 5 ‘based on gut’. That tells me a number of things. CC doesn’t use formulas to work out potentially winners/loser ahead of time for his system. Smart man. He intuitively expects the same run of consecutive losers as winners. Also smart man, as that’s how it turns out mostly and he wont be psychologically wrong-footed with Expectation Failure. It also tells me how 3 Ducks is performing….
So having found the max (statistically) number of consecutive losses, what else do we need to know? We need to know how often that is likely to occur. Well, for this system’s profile, it’s (statistically) going to occur every 2184 trades. Now, where shall we place this event? At the beginning, when it’ll drain your energy and (relative) account the quickest? At the end when it’ll take the most absolute lump out of your dosh? We’ll use the statisticians cop-out and stick in half way at trade 1088. It’s AS likely to occur anywhere, if at all, in your trading sequence in reality. Are you beginning to get a picture of where I’m leading with all this yet?
We’ve only had 134 trades so far. Well, there’s another little formula we can use to work out how many consecutive losers we’ve had (or are likely to have had) given this system’s performance profile for any given number of trades. For this system we can expect: 1 losing trade every 3. 2 consecutive losing trades every 9. 3 consecutive losing trades for every 27. 4 consecutive losing trades every 81. 5 consecutive losing trades every 243. So, for our purposes right now, we can calculate a worst case of 5 consecutive losing trades just occurred in the last 5 trades, taking out the biggest absolute slice of our trading moolah. So, what was/is our max drawdown.
Before I do that calculation (in fact, I’m NOT going to do it for reasons that are just about to be explained), there’s something you should know. Expectancy and drawdown and all the other formulas relating to this side of the business and completely useless. At every point from trade 1 to trade 134, your Aw, Al, Pw, Pl and by derivation your expectancy, max drawdown and consecutive losers (and winners) are potentially different. They potentially change with every trade. All I’ve given you is the data as a snapshot at the end of trade 134. That’s all you’ll ever have – the status as of NOW.
As you move further into your system and do more trades, you may imagine it will ‘settle down’ and the values wont move around too much. Well they may and they may not. All depends on a number of factors. Such as the standard deviation of your winning and losing amounts, the clustering of winning and losing sequences and some non-Gaussian analysis of your system against higher level derivatives of the instrument(s) you are trading.
