🎯 In 30 seconds: Position sizing answers "how many shares?" The best-known method starts from how much you are willing to lose, not from how much you want to make. Decide your dollar risk (say 1% of the account), decide where you will get out if wrong (the stop), and divide: shares = (account x risk%) / (entry - stop). Everything else in this chapter, from R-multiples to the Kelly criterion, builds on that one line.
Three ways to size a trade
A position is the amount of one stock you hold. Position sizing is the rule you use to pick that amount. There are three common approaches.
1. Fixed dollar amount. You put the same amount, say $1,000, into every trade. It is simple. The problem is that the risk changes from trade to trade. If one trade has a stop 2% below entry and another has a stop 15% below, the second risks seven and a half times as much.
2. Percent of account. You put a fixed share of the account, say 10%, into each position. This grows and shrinks with your account, which is good. It still ignores where your stop is, so the risk per trade still varies.
3. Risk-based sizing. You fix the amount you are willing to lose on each trade, then let the distance to your stop decide the share count. It is widely taught because it makes every trade cost about the same when it fails.
The risk-based formula
Here is the formula:
shares = (account x risk%) / (entry price - stop price)
- Account is the value of your trading account today.
- Risk% is the share of the account you accept losing if the stop is hit. 1% is a common starting point (see Risk comes first).
- Entry minus stop is the loss per share if you are wrong. For a short sale it is stop minus entry.
Always round the result down to a whole share, unless your broker offers fractional shares and you want to use them.
Worked examples
All of these are hypothetical.
Example 1: the basic case.
| Account | $10,000 |
| Risk 1% | $100 |
| Entry | $50.00 |
| Stop | $47.00 |
| Risk per share | $3.00 |
| Shares: 100 / 3 = 33.3 | 33 |
| Position size: 33 x $50 | $1,650 |
| Loss if stopped: 33 x $3 | $99 |
Example 2: a smaller account and a tighter stop.
| Account | $5,000 |
| Risk 2% | $100 |
| Entry | $20.00 |
| Stop | $19.20 |
| Risk per share | $0.80 |
| Shares: 100 / 0.80 | 125 |
| Position size: 125 x $20 | $2,500, half the account |
Notice what happened. A tight stop produced a large position. Half the account sits in one stock, even though the planned loss is only $100.
Example 3: when the formula asks for more than you have. Account $10,000, risk 1% ($100), entry $100.00, stop $99.50. The formula says 100 / 0.50 = 200 shares, which is a $20,000 position. You do not have $20,000 without borrowing, and a stop that tight can be hit by ordinary noise.
This is why the formula needs a second rule: a maximum position size. A common choice is no single position above 20% to 25% of the account. With a 25% cap, Example 3 becomes 25 shares ($2,500), and the real risk is only 25 x $0.50 = $12.50. That is fine. The risk rule is a ceiling, not a target.
R-multiples: measuring trades in units of risk
R is the dollar amount you planned to risk on a trade. In Example 1, R = $99. Every result can then be written as a multiple of R.
| Sold at the $47 stop: -$99 | -1R |
| Sold at $56: +$6 x 33 = +$198 | +2R |
| Stock opened at $44 after bad news: -$6 x 33 = -$198 | -2R |
| Sold at $51.50: +$1.50 x 33 = +$49.50 | +0.5R |
Why bother? Because R lets you compare trades of different sizes and different accounts. "+2R" means the same thing whether you trade $1,000 or $100,000. It also makes problems obvious. If your losses keep coming in at -1.5R or -2R, your stops are slipping or you are not honoring them.
The third line matters. A stop order becomes a market order when triggered, and the SEC warns the fill "can deviate significantly" from the stop price. Overnight gaps are the usual cause. Stop losses covers this in detail.
R-multiples are also the language of expectancy, which tells you whether a set of trades makes money on average.
Sizing by volatility
Some stocks move $3 a day. Others move 50 cents. If you use the same dollar stop on both, the quiet one rarely gets stopped out and the jumpy one gets stopped out by noise.
Average True Range (ATR) measures how much a stock typically moves per day, including gaps. It is explained in Volatility tools. A common approach is to set the stop a multiple of ATR away, often 1.5 to 3 times, and then size with the same formula.
Two hypothetical $60 stocks, $100 of risk each, stop at 2 x ATR:
| Stock A (jumpy) | Stock B (calm) | |
|---|---|---|
| ATR (typical daily range) | $2.50 | $0.80 |
| Stop distance (2 x ATR) | $5.00 | $1.60 |
| Shares: $100 / stop distance | 20 | 62 |
| Position size | $1,200 | $3,720 |
| Loss if stopped | $100.00 | $99.20 |
You own fewer shares of the jumpy stock and more of the calm one, but each trade risks about the same $100. That is the whole point: volatility decides the share count, not your excitement.
The Kelly criterion
In 1956 a Bell Labs scientist, John Kelly, published a formula for how much of your money to bet when you have an edge, to grow it as fast as possible over the long run. Traders adapted it. For a trade that either wins W of the time with an average win of R times the average loss, or loses:
Kelly fraction = W - (1 - W) / R
The result is the share of the account to risk (lose if wrong) per trade.
| Wins 55%, wins equal losses (R = 1) | 0.55 - 0.45 / 1 = 10% |
| Wins 45%, wins twice losses (R = 2) | 0.45 - 0.55 / 2 = 17.5% |
| Wins 50%, R = 1 (no edge) | 0.50 - 0.50 / 1 = 0% |
Those numbers are far above 1% to 2%. So why does almost nobody trade full Kelly?
Reason 1: the curve is lopsided. For the 55% system above, risking 10% grows the account about 0.50% per trade on a compounded basis. Half Kelly (5%) grows it about 0.38% per trade, three quarters as much. But double Kelly (20%) grows it about zero, and 25% shrinks it. Betting too little costs you a little. Betting too much can cost you everything.
Reason 2: you do not know your real win rate. If you think you win 55% but the truth is 52%, the true Kelly fraction is 4%. Betting 10% then shrinks your account over time. Win rates measured over 30 or 50 trades are very uncertain, as Risk/reward and expectancy shows.
Reason 3: the ride is brutal. Using exact probabilities for the 55% system over 200 trades, the chance of falling to half your starting money at some point is:
| Quarter Kelly (2.5% risk) | 0.2% |
| Half Kelly (5% risk) | 7.9% |
| Full Kelly (10% risk) | 38.2% |
| Double Kelly (20% risk) | 78.5% |
Real trading is also messier than the formula. Results are not neat wins and losses of fixed size, trades are not independent, and gaps can produce losses bigger than planned. So traders who use Kelly at all usually treat it as an upper limit and take a quarter or half of it, and many skip it and stick with a fixed 0.5% to 2%.
Putting it together
- Pick your risk per trade (start at 0.5% to 1%).
- Find the stop from the chart or from ATR, before thinking about size.
- Compute shares = dollar risk / (entry - stop), rounded down.
- Check the position against your maximum position size and cut it if needed.
- Check total open risk across all positions, called portfolio heat. See Diversification and correlation.
- Record R for the trade so you can measure the result in R later.
Update the account value you use for sizing at a regular time, such as every Monday. Sizing off a stale, larger number after losses means you are risking more than you think.
Try it
Pick three stocks on your Watchlist. For each, choose a sensible stop below a recent low, then compute the share count for a $10,000 account at 1% risk. Check whether any position would exceed 25% of the account, and cut it if so. Place the trades in the paper portfolio, and when each one closes, write the result in R. After ten trades, look at your average loss in R. If it is worse than -1R, find out why.
- What is the risk-based position sizing formula? Answer: Shares = (account x risk%) / (entry price - stop price), rounded down.
- Account $10,000, 1% risk, entry $100.00, stop $99.50. The formula says 200 shares ($20,000). With a 25% maximum position size, what do you buy? Answer: 25 shares ($2,500). The real risk is then only $12.50, which is fine: the risk rule is a ceiling, not a target.
- You planned to risk R = $99 on 33 shares bought at $50. The stock opens at $44 after bad news. What is the result in R? Answer: -2R (a $198 loss).
- For a system that wins 55% with wins equal to losses, what is the Kelly fraction, and why do most traders use less? Answer: 10%. The growth curve is lopsided (betting too much can cost everything), you do not know your real win rate, and the drawdowns are brutal.