Position sizing for stock trades: a worked calculation

Risk tolerance, trade risk and position value

Three different numbers get mixed up when people talk about risk. Risk tolerance is personal: the decline in the whole account its owner could accept, financially and emotionally, which depends on goals, income and time horizon rather than on a formula. Trade risk is the planned loss on one idea if the stop is reached. Position value is the money committed to the shares, and it is usually several times the trade risk.

Sizing connects the three. The trade risks of positions that could lose together have to fit inside the account-level limit: with 1% at risk per idea, eight ideas stopped out together cost about 8% before any gap or slippage. This guide uses an example account of $25,000 risking 1% per idea throughout; both numbers are illustrations, not suggested levels.

Risk per share: the distance from entry to stop

Risk per share is what one share loses if the position is closed at the stop. For a long position it is the entry price minus the stop price; for a short position, the stop price minus the entry price. The stop comes first, at the price that would show the idea is wrong; the share count is then derived from it, instead of moving the stop to fit a share count.

Risk per share (long) = entry price − stop price
Risk per share (short) = stop price − entry price
Stop distance (%) = risk per share ÷ entry price × 100

The dollar distance, not the percentage, drives the share count. Setup B has the narrowest stop in percent but the largest risk per share, so it allows the fewest shares.

The fixed-fractional position size formula

Fixed-fractional sizing risks the same fraction of the account on every idea. Multiply the account value by the risk per idea to get a dollar risk budget, divide the budget by the risk per share, and round down to whole shares. Rounding down keeps the planned loss at or below the budget.

Risk budget = account value × risk per idea (%) ÷ 100
Shares = floor(risk budget ÷ risk per share)
Planned loss = shares × risk per share
Position value = shares × entry price

• If the stop equals the entry, the risk per share is zero and the division has no answer: a stop needs a real distance from the entry before a size can be calculated.
• If the risk per share is larger than the risk budget, the formula gives 0 shares: at that stop, the idea does not fit the chosen risk.
• Where a broker offers fractional shares, the rounding step can be skipped, but the gap and slippage risks described below stay the same.
• The account value behind the budget can be updated as equity changes, so the dollar risk shrinks after losses and grows after gains.

Worked example: a $25,000 account risking 1% per idea

Take setup A from the table above: an entry at $48.50 and a stop at $45.20 in an example account of $25,000 that risks 1% per idea. The first column ignores costs. The second sets aside $2.00 of commissions for the entry and exit orders and $0.10 per share for slippage on the stop exit, so the planned loss includes both.

Check: 75 × $3.30 = $247.50, and 72 × $3.40 + $2.00 = $246.80, both under the $250.00 budget. Commission schedules differ by broker, and some charge nothing for online stock trades; the $1.00 per order here only shows where a fee enters the arithmetic.

Rounding matters most when the share price is high and the share count small. For setup B, a 12th share would put $268.80 at risk, 7.52% over the budget, which is why the formula rounds down.

A volatility-based variant using ATR

A stop placed a multiple of the average true range below the entry ties the risk per share to how far the stock usually moves in a session. The same formula then gives fewer shares for a stock with a wide range and more for a calm one, so the dollar risk stays level while the position value changes. The multiple is a parameter of the plan; two ATRs is only an example.

Risk per share = k × ATR(14)
Stop price = entry price − k × ATR(14)
Shares = floor(risk budget ÷ (k × ATR(14)))

Both positions lose about the same amount at their stops, but the calmer stock ties up three times the capital. In TradeClever, CleverScan rules can use ATR(14) and atrPct14 (ATR as a percentage of the close), and the results table can show an ATR% column, so the stop distance of each candidate can be estimated before the chart review.

Position value, gaps and losses beyond the plan

The planned loss assumes the exit happens close to the stop. A stock can open far below a stop after news released outside regular trading hours, and a stop order then fills near the opening price, so the realized loss can be a multiple of the plan. In the worst case the loss is bounded by the position value, not by the risk budget.

Some plans respond to gap risk by lowering the risk per idea when an earnings release or another scheduled event falls inside the expected holding period, or by capping the position value, as in the next section. Neither removes the risk; both limit how large it can get. Stock price gaps explains how gaps form, and the stop-loss guide shows how stop and stop-limit orders behave when one occurs.

Measuring portfolio concentration

Concentration measures how much of the account sits in one position or in one group of related positions. Divide each position value by the account value, positions plus cash, to get its weight, and add the weights of positions that share a sector or industry. A tight stop can create a heavy position: at a fixed risk per idea, the position weight equals the risk per idea divided by the stop distance.

Position weight (%) = position value ÷ account value × 100
Group weight (%) = sum of the position weights in the group
Weight at a fixed risk (%) = risk per idea (%) ÷ stop distance (%) × 100
Effective number of positions = 1 ÷ Σ (position value ÷ invested value)²

Concentration limits are parameters, not laws. With an example cap of 20% per position and 35% per sector, every position fits, but the Technology group exceeds the sector cap by 10.20 percentage points.

When the risk-based size breaks a cap, a plan can take the smaller of the two sizes. With an entry at $40.00 and a stop at $39.20, 2% away, a 1% risk budget allows 312 shares worth $12,480.00, or 49.92% of the account. An example cap of 20% ($5,000.00) allows 125 shares, which put $100.00, or 0.40% of the account, at risk.

Correlated positions and portfolio risk

Positions that tend to move together behave more like one large position than like separate bets. If several stocks in one industry fall on the same news, their stops can be hit in the same session, and the account loses several risk budgets at once. Correlation of daily returns runs from −1 to +1, and a value measured over past sessions can change; it can rise when the whole market falls sharply.

Combined volatility of n equal positions = σ × √(n + n × (n − 1) × ρ)

At zero correlation, five positions swing only about 2.24 times as much as one; at 0.9 they swing almost as much as a single position five times the size. The stop-based view gives the same warning in dollars: five positions that each risk $250 and share one driver can lose $1,250, or 5% of a $25,000 account, in one session, and more if the move is a gap.

In TradeClever, the results table can show each candidate’s sector, and Symbol Comparison places up to twelve compact daily charts side by side, which makes moves on the same sessions easy to spot. The correlation itself can be computed in a spreadsheet, for example with a CORREL function over two columns of daily percentage changes.