Brutal lessons: Expectancy and Risk

Over Christmas I digested a few trend following investment books. I found the O'Neil CANSLIM bible to be very interesting, particularly the lessons on entering on reduced volatility pullbacks and relative strength metrics across the market and higher timeframes (weekly with daily).

Following on similar themes,and again very useful and interesting, was Minervini "Trade Like a Stock Market Wizard". Perhaps a bit too much hype at times, but I found myself re-reading his section on risk over and over. Now I've read (and thought I understood) the need for risk control, stops and what Brooks calls "a positive trader's equation". Minervini seemed to get through to me where others have failed.

The penny dropped one day when I realised I was making a fundamental beginners probability error. If you have 3 winning trades interspersed with 3 losing trades, each winning and losing the same amount (say 50%) you end up even? WRONG, of course! The probability for each event is multiplied not added. If you lose 50%, it takes more than 50% to get that back.

Minervini firmly recommended a value of 7.5% maximum risk, particularly for traders with less than 50% winning trades (he calls this the "batting average"). Wanting to explore this further I did a series of spreadsheet pages on what happens when you have 10 consecutive trades with increasing probabilities of gain and loss.

Below is a plot for 2:1 win/loss for "batting averages" from 25% to 55%. Total predicted return after 10 trades is on the Y Axis in %. The optimal return after 10 trades is not intuitive (to me!). Minervini is quite right to suggest trend trading beginners, frequently only achieving 40-45% batting averages, should stringently aim for losses to never exceed 7.5% - which easily ends up at 10% in real life.

Similar plots are possible of course for different win/loss ratios - this is only a summary for the specific situation of win/loss = 2. I'd be happy to put the spreadsheet up for general reference and people to check if all this babble interests anyone!


The take home lesson for me is what experienced traders have learned the hard way and know intuitively - and try to bang into our beginner heads all the times! That is, stringently contain your losses, but aim to let your winners run (or at least regularly exceed losses).

Newt said:

Minervini firmly recommended a value of 7.5% maximum risk, particularly for traders with less than 50% winning trades (he calls this the "batting average"). Wanting to explore this further I did a series of spreadsheet pages on what happens when you have 10 consecutive trades with increasing probabilities of gain and loss.

Below is a plot for 2:1 win/loss for "batting averages" from 25% to 55%. Total predicted return after 10 trades is on the Y Axis in %. The optimal return after 10 trades is not intuitive (to me!). Minervini is quite right to suggest trend trading beginners, frequently only achieving 40-45% batting averages, should stringently aim for losses to never exceed 7.5% - which easily ends up at 10% in real life.

Click to expand...

Good on you for exploring these relationships in detail... nothing paints a picture better than some charts on Excel done by yourself.

However... your charts look wrong and don't actually make any sense. If you have a 2:1 win/loss and "batting average" of 55%, the expected outcome after 1 trade is simply 0.55x2-0.45x1 = 0.65. And over 10 trades... 10x0.65 = 6.5. There are no other parameters required to describe the expected outcome. The probabilities of gain and loss doesn't change (it's already defined by your 2:1 win/loss and batting average) so it's not clear what your X-axis is doing.

Newt said:

The penny dropped one day when I realised I was making a fundamental beginners probability error. If you have 3 winning trades interspersed with 3 losing trades, each winning and losing the same amount (say 50%) you end up even? WRONG, of course! The probability for each event is multiplied not added. If you lose 50%, it takes more than 50% to get that back.

Click to expand...

Not entirely true. This only applies if you deploy 100% of your capital in every trade, and that you only have one trade at a time. With more conventional fixed risk, fractional position sizing, you do simply add the returns from each trade.

skc said:

Not entirely true.

Click to expand...

He also makes the common mistake of saying that a 50% needs a 100% gain to get it back, while true in % terms the 50% of the original capital and the 100% of the reduced capital are the same amount, so its comparing apples with oranges. The simple way to look at is a loss of $x requires a gain of $x to offset it.

It seems to be a very common mistake that people make, not sure whether its something our schools miss out teaching kids but %'s would be one of the most misunderstood areas of basic maths I see.

Thanks for thinking about it guys. Lies, damned lies, and statistics......!

Skc, you're perfectly right that these hypothetical calcs are based on the premise of TOTAL capital being reinvested each trade. That leads to a pretty huge "risk of ruin" in reality, but eventually a steady loss IS going to affect your capital, so let's live with that assumption. I won't disagree with your expectancy calculation either.

However, let me make a more serious attempt at describing the parameters of the exercise:

- Take $100k starting capital.
- 50% "batting average"
- 10 trades.
- Assume 5 losses and 5 wins (I know - big assumption, but if you repeat the exercise enough times that's what the averages will come out to).
- Invest all available capital each trade
- 2:1 win/loss. For this example, say win = 15%, loss = 7.5%

Each winning trade will result in 1+ % win x initial capital:
5 winning trades: $100,000 x 1.15 x 1.15 x 1.15 x 1.15 x 1.15 = $201136
5 losing trades: $201136 x 0.925 x 0.925 x 0.925 x 0.925 x 0.925 = $136207

Outcome after 10 trades is a 36.2% windfall, as per graph above. As you increase the %win and %loss, but maintain the 2:1 win/loss ratio you quickly become unprofitable, as per the graph above.

Likewise with other batting averages. For 60% assume 6 winning trades, 4 losses (long run averages).
I stand with my comment that many people would incorrectly think a 2:1 win/loss will always give the same outcome over a series of trades, when in reality you quickly become unprofitable for most realistic batting averages once %loss exceeds 10-15%.

Apples and oranges? Maybe.
Brutal if you think the outcome from a series of trades for 20/10 versus 40/20 should be the same, I would argue.

My point here was to explore non-intuitive maths that I suspect does eventually become internalised and intuitive for very experienced traders after they've experienced a HUGE number of trades. Those people learn to "feel" how much risk they and their account can tolerate, even if they haven't run the sums in this way. Most may not be able to explain to newbies why they "know" this based on experience, but they damned well know it hurts if you let you %loss creep up! The newbie might however look at risk win/loss differently, depending on their aptitude for some maths and spreadsheeting, if they succeeded in getting their head around the underlying math.

I expect I'll do very well to exceed a 50% batting average in trend trading, so therefore I will from now on be working hard to hold my long run average losses at 7.5% or lower. Its interesting you might actually be better off allowing large win/loss values if you do get a batting average of 50% or better.

Happy to put up the graphics for 3:1 if of value to anyone (or the full spreadsheet).

Newt said:

The take home lesson for me is what experienced traders have learned the hard way and know intuitively - and try to bang into our beginner heads all the times! That is, stringently contain your losses, but aim to let your winners run (or at least regularly exceed losses).

Click to expand...

And the people that make these claims are either people that haven't made a trade in their life or are the ones that are quick to fail.

It's more so about increasing your probability of success on entry (more winning than losing trades) and taking off winners when you can (not about letting them run - big mistake). Also, you should never be in a situation where you can lose 50% let alone 10% of you capital in one go. A good number is 2%.