Session 21 of 30 70%
Chapter 7 · Risk, probability, and survival
How much to risk on any single trade
· · · 18 min read
Narration is coming later. For now the course is text, and the text is complete.
Here's the arithmetic that costs individual investors the most, and it comes from a confusion of words: "risking 1%" doesn't mean "investing 1%". They're completely different figures, and anyone who mixes them ends up taking risks twenty times larger than they think.
Investing 1% and risking 1% aren't the same thing
It's the chapter's most important distinction and the one almost no material clarifies.
The two figures
What's invested is how much money you put into the position.
Risk per trade is how much you can lose if it goes wrong, which depends on where your exit point sits.
With an example: you have €10,000 in the account and buy €2,000 of a stock, having decided to sell if it falls 5%.
- You've invested €2,000, 20% of your capital.
- You've risked €100, 1% of your capital.
Both statements are true at once and describe different things. When this chapter talks about risking 1%, it always means the second.
Why the confusion is so expensive
Anyone reading "risk 1%" as "invest 1%" does one of two things, and both are bad.
Either they invest absurdly small amounts, putting €100 of €10,000 into each idea, and no trade moves the needle enough to justify the effort.
Or, far more commonly, they invest 20% believing they're risking 20%, when in reality — without a defined exit point — they're risking the full 20%. If that stock falls 60%, they've lost 12% of their capital on one idea.
The difference between the two readings isn't a nuance: it's a factor of twenty.
And from here comes the question that orders everything else
If risk depends on where you'll exit, then you can't decide how much to buy until you've decided where you'll sell if you're wrong.
That's the correct order and it's the reverse of what nearly everyone does, deciding first how much to buy and only then, if at all, where to put the stop.
How to calculate position size
With one division. Once you know how much you're willing to lose and how far away your exit is, the size falls out on its own.
The formula
Position size = (capital × risk per trade) ÷ distance to exit point
Here are the numbers.
Capital of €10,000. Chosen risk: 1%, meaning €100. You buy a stock at €50 and decide to exit if it drops to €47.50, which is €2.50 per share of distance.
€100 ÷ €2.50 = 40 shares.
Forty shares at €50 is €2,000 invested. If the stock reaches €47.50 you lose exactly €100, which is the 1% you decided.
The detail that makes it useful: distance governs
If the exit sat further away — say at €45, five euros of distance — the same €100 risk would allow buying only 20 shares, meaning €1,000.
Notice what happens: the further away your exit, the less you buy. The position adjusts itself so the money at stake is always the same, regardless of how volatile the asset is.
That's where the ATR (Average True Range) from the previous chapter fits. Setting the exit at a distance measured in multiples of that asset's ATR means a calm stock and a very active one end up with different position sizes and identical risk. It's exactly the problem that tool solved.
An exit point doesn't have to be an order
Worth clarifying because it causes confusion. That level can be a stop order placed at your broker, or it can be a decision of yours written down somewhere: if this reaches €47.50, I sell.
Both work for calculating size. The order has the advantage of executing without you and the drawback that, as we saw in the guide to order types and how they execute, it doesn't guarantee the price. The written decision depends on you following it.
What doesn't work is having neither, because then the formula can't be applied and the position's real risk is "everything you invested."
What risk of ruin is and why it isn't linear
Risk of ruin is the probability of losing enough capital that you stop being able to trade. You don't need to reach zero: falling far enough that recovery stops being realistic is sufficient.
Why doubling the risk does far more than double the danger
Here's the part intuition misses.
Many people assume risking 2% per trade is exactly twice as dangerous as risking 1%. It isn't: it's considerably more than twice, because losses accumulate by multiplication rather than addition.
With a run of ten consecutive losses:
- Risking 1% per trade, your capital sits around 90% of the original.
- Risking 2%, around 82%.
- Risking 5%, around 60%.
- Risking 10%, around 35%.
From 1% to 2% the damage nearly doubles. From 2% to 10% it multiplies. And those gaps worsen the longer the run, which is what the next session, on drawdowns, streaks, and sample size, covers.
The anti-martingale principle
There's a design decision that helps on its own, and it consists of calculating risk on current capital rather than starting capital.
Start with €10,000 and risk 1% and that's €100. After a bad run leaves you at €8,000, that 1% becomes €80. Bet size reduces automatically when capital falls.
Van Tharp called this the anti-martingale principle, in opposition to the casino strategy of doubling your bet after each loss to win it all back at once. That strategy feels logical and leads to ruin with mathematical certainty, because it demands a winning run precisely when capital is smallest.
Setting risk as a percentage of current capital does the opposite without you deciding anything.
What percentage to choose
The usual reference is between 1% and 2% of capital per trade, and it's worth saying where it comes from and what its limits are.
Where it comes from: it's the figure that lets you absorb a long run of losses — ten, fifteen trades in a row, which happen — without leaving the account in a state it can't come back from.
What its limits are: it treats everyone identically. One percent can be too conservative for someone with a proven edge and too aggressive for someone who doesn't yet know if they have one. It isn't a law of physics, it's a reasonable starting point.
And a caveat almost nobody mentions: for long-term buy-and-hold investing, this arithmetic doesn't apply the same way. It's designed for someone opening and closing positions with a defined exit. Anyone buying an index fund for twenty years has no stop, and their risk management is Chapter 2's: horizon and emergency cushion, and diversification.
What the Kelly criterion is and why nobody uses it in full
You'll hear about it, so here's the honest version.
A formula published by John Kelly in 1956, in the Bell System Technical Journal, calculating what fraction of capital maximises long-term growth given a known edge. Mathematician Ed Thorp later popularised it.
Its logic is the chapter's: with an edge, betting too little wastes the growth and betting too much ruins you before the edge can act. Kelly looks for the point between the two.
Why nobody uses the full formula
For one specific reason: Kelly is optimal only if you know the true probabilities exactly, and you never do. They're estimates drawn from a limited, backward-looking sample, and errors in those estimates get amplified by the formula.
The result is that full Kelly, even with a genuine edge, produces drawdowns capable of exhausting anyone's patience before the mathematics has time to work.
The solution used by those who use it
Betting a fraction of the result: half, or a quarter. Thorp used half.
And there's a mathematical property making that trade very favourable: the growth curve is flat near its optimum. Betting half what Kelly says retains most of the theoretical growth while sharply reducing volatility and the depth of drawdowns.
Translated into this session's practical lesson: staying below the optimum costs little and protects a lot. Overshooting costs enormously. The asymmetry isn't in your head, it's in the formula.
Why five correlated positions are one bet
You can hold five positions risking 1% each and believe you're risking 5% spread out. If the five move together, you're risking 5% on one thing.
The example
Someone opens five positions in five different technology companies. Five names, five lines in the portfolio, 1% risk on each.
News arrives affecting the whole sector — a rates figure, a regulation, results from the group's largest company — and all five fall together.
They haven't had five bad trades. They've had one bad trade five times.
It's exactly what we saw in Chapter 2 discussing how much diversification you need and when it stops helping: thirty tech stocks aren't diversified. Here you see the same idea from the other side, applied to size rather than composition.
The check that takes a minute
Before opening one more position, one question: if what I'm considering goes wrong, how many of my current positions suffer too?
If the answer is "nearly all of them," your portfolio's real risk isn't the sum of individual risks: it's far larger, and it appears nowhere.
The sources of correlation people see least
Sector is the obvious one and nearly everyone spots it.
Currency is less obvious. Hold five US stocks from a euro account and all five share the exchange-rate risk we saw in Chapter 2, on top of their own.
A common factor is the most invisible. Companies in different sectors can share dependence on the same thing: energy prices, interest rates, discretionary spending. Two companies that appear unrelated can fall together every time oil rises.
And your own income, as we saw: work in the same sector you invest in and your salary is one more correlated position.
Your risk sheet
This chapter produces the second of the three documents you take from the course. Like the first one, which closed Chapter 2, these are decisions written down before money is at stake, for the same reason: the worst moment to decide how much to risk is while you're losing.
Five fields, and it's worth understanding what each one asks before filling it in.
How much you're willing to lose on a single trade. It's a percentage of your capital, not the amount invested. The usual reference sits between 1% and 2%, and below that is perfectly reasonable while learning. This figure is what divides afterwards to give you each position's size.
How many losses in a row you expect to sit through. It isn't a prediction, it's an expectation written down, and it exists so that a normal streak doesn't get read as a sign the method has stopped working. The next session measures it: at a 55% hit rate, five losses in a row show up about twice per hundred trades. Anyone who hasn't written that down beforehand reads them as a failure of the method.
What drawdown within the month makes you stop trading. It's the month's, not the account's whole life: a floor that resets, and that cuts a bad run short before it turns into a hole. Setting it in advance avoids the situation where you decide to push on precisely when you're thinking worst. Remember a 25% drop requires a 33% rise to get back to where you started, and a 50% drop requires 100%.
How many positions open at once. Each one adds risk and none adds attention: the time you can spend following them is the same. A small number decided in advance is worth more than "however many come up."
Whether you check correlation before opening another. It's a yes-or-no box, and its value isn't in the answer but in the question existing before you hit the button.
If you've got this far and filled in the sheet, keeping it makes sense: it's what you'll want to reread in six months, after three bad trades running and about to decide something in a hurry. Saving it to a free account means it's still there if you switch devices. Continuing the course doesn't require it.
What to remember
- Investing 1% and risking 1% are different figures that can differ by a factor of twenty.
- Position size comes from dividing what you're willing to lose by the distance to your exit point: the further the exit, the less you buy.
- Doubling risk per trade does considerably more than double the danger, because losses accumulate by multiplication.
- Five positions that move together aren't five 1% risks: they're one 5% risk on a single thing.
Related: what "risk" really means · order types and how they execute · what each indicator measures and how people fool themselves
Sources
- Van Tharp, work on position sizing and the anti-martingale principle: setting risk as a percentage of current equity automatically reduces size after losses
- Kelly, J. L. Jr. (1956), 'A New Interpretation of Information Rate', Bell System Technical Journal: origin of the Kelly criterion
- Literature on fractional Kelly (Thorp, MacLean and Ziemba): the growth curve is flat near its optimum, so betting half retains most of the growth while sharply reducing volatility and maximum drawdown
- Standard drawdown-recovery arithmetic and stop-distance position sizing
What you keep
Your maximum-loss sheet
Five decisions about how much you are willing to lose and when you stop. All in percentages: amounts are never asked for.
It asks for no amounts, balances or specific holdings. Only percentages and decisions.