Direct answer
Multiple position sizing typically uses a risk allocation formula built from a per-position “risk per unit” and a shared “total risk budget.” Conceptually, you start with a maximum total amount you are willing to lose (or hedge) across several positions, then compute how many units (often lots) each position may take so that the expected worst-case loss defined by the stop distance stays within that budget.
A commonly used structure is:
- Convert the stop distance into a monetary loss per unit: (\text{risk per unit} = \text{price move} \times \text{value per price move}).
- Convert the allocated risk into position size (units): (\text{position size} = \frac{\text{allocated risk}}{\text{risk per unit}}).
- Optionally ensure the sum of risks across positions equals the total risk budget: (\sum_i \text{allocated risk}_i = \text{total risk budget}).
Because “risk” depends on how you define price move and the instrument’s contract specifications, the exact numeric inputs vary by provider and instrument. The mechanics below stay stable: risk budget → risk-per-unit → position size.
Mechanism or definition
What “multiple position sizing” means
Multiple position sizing is the process of determining position sizes for more than one simultaneous position while keeping overall constraints in mind—most often a maximum total risk across the set.
Two common ways to distribute the budget are:
- Equal risk per position: each position gets (\frac{\text{total risk}}{N}).
- Weighted risk per position: position (i) gets (w_i) share of the budget, where (\sum_i w_i = 1).
Core formula (risk-based sizing)
For each position (i):
- (R_i) = allocated risk for position (i) (in account currency).
- (\Delta P_i) = stop distance measured as an absolute price change from entry to the stop (positive number).
- (V_i) = monetary value per one unit of price move for that instrument (account currency per price unit, given by contract/quote conventions).
- (\text{RPU}_i) = risk per unit = (V_i \times \Delta P_i).
Then:
[ \text{size}_i = \frac{R_i}{\text{RPU}_i} = \frac{R_i}{V_i \times \Delta P_i} ]
Allocating the total risk
Let:
- (R_{\text{total}}) = total risk budget across all positions.
- (N) = number of positions.
Equal allocation: [ R_i = \frac{R_{\text{total}}}{N} ]
Weighted allocation: [ R_i = w_i, R_{\text{total}},\quad \sum_i w_i = 1 ]
Units and sign conventions
- Use (\Delta P_i) as a positive stop distance magnitude. The direction (long/short) should be handled by how you define the stop, but the risk magnitude uses absolute distance.
- Keep the units consistent: if (V_i) is “account currency per 1.0 price unit,” then (\Delta P_i) must be in the same price-unit scale.
Evidence or example
Because there are multiple instrument conventions, use a generic “price move → value per price move” model.
Example setup (assumptions stated)
Assume:
- Two positions ((N=2)).
- Total risk budget (R_{\text{total}} = 100) account currency units.
- Equal allocation, so (R_1 = R_2 = 50).
- For position 1, stop distance (\Delta P_1 = 0.010) and value per price move (V_1 = 10{,}000) account units per 1.0 price unit.
- For position 2, stop distance (\Delta P_2 = 0.020) and value per price move (V_2 = 5{,}000).
Compute risk per unit:
- (\text{RPU}_1 = V_1 \Delta P_1 = 10{,}000 \times 0.010 = 100).
- (\text{RPU}_2 = V_2 \Delta P_2 = 5{,}000 \times 0.020 = 100).
Now compute position sizes:
- (\text{size}_1 = \frac{R_1}{\text{RPU}_1} = \frac{50}{100} = 0.5) (in “position units” matching your (V_i) definition).
- (\text{size}_2 = \frac{R_2}{\text{RPU}_2} = \frac{50}{100} = 0.5).
Total allocated risk check:
- (R_1 + R_2 = 50 + 50 = 100 = R_{\text{total}}).
Rounding example (whole-lot constraint)
Many markets require sizes to be rounded to allowed increments (for example, minimum trade size or step size). Suppose your calculated size for position 1 is (0.53) but the platform only allows increments of (0.10). You must choose a rounding rule.
A conservative validation approach is to round down (or otherwise ensure the rounded size does not raise risk beyond the intended budget when recalculated with the same stop distance model).
For instance, if (\text{RPU}_1 = 120) account units per size unit:
- Unrounded risk estimate: (0.53 \times 120 = 63.6).
- If rounded down to (0.50): risk becomes (0.50 \times 120 = 60), which does not exceed the model risk estimate.
Then you recalculate total risk using the rounded sizes: [ R_{\text{total, model}} = \sum_i (\text{rounded size}_i \times \text{RPU}_i) ]
Limitations and risks
1) Risk model depends on your stop-distance definition
If the stop distance is measured differently (for example, based on different quote conventions or different “pip” scales), the computed (\Delta P_i) changes, which changes risk per unit and therefore size.
Material failure mode: you can end up systematically oversizing because you used a (\Delta P_i) that is not aligned with the (V_i) used to compute monetary risk.
2) Instrument contract value (V_i) can be easy to mis-specify
(V_i) is the monetary value per price move for the contract size. Providers may express it using different conventions (and it can depend on quote direction). If you plug in the wrong (V_i), the formula still “works,” but it produces the wrong unit-to-currency conversion.
Material failure mode: mismatch between “price move units” and “value per price move units.”
3) Rounding can move risk away from the intended budget
Even if the mathematical formula targets the budget, practical constraints (minimum size, step sizes, margin requirements, leverage constraints) can force rounding.
Material failure mode: rounding up may increase the actual modeled loss beyond your risk budget.
4) Market costs and execution uncertainty are not included
The model above captures a worst-case loss defined by a stop distance magnitude, but real outcomes can differ due to slippage, spread, execution timing, and fees.
Material failure mode: assuming the stop distance translates to the exact realized loss in your account currency.
5) Correlated positions change what “total risk” means
If multiple positions move together (for example, because they are exposed to the same underlying drivers), the sum of independently computed risks may not reflect the combined outcome.
Material failure mode: using additive risk intuition when the true joint behavior is non-additive.
Verification or next question
To independently verify that you understand the multiple position sizing formula, you can do these checks using only your own assumed inputs: