A Volatility Cap Meets Whole Contracts

Freeze a wholly hypothetical budget

Start with $1,000,000 of reference capital, estimated annual volatility of 20%, a 10% annual target and a maximum exposure multiple of 1.5. Each fictional contract represents $100,000 of notional and requires an assumed $7,000 margin deposit. These inputs describe an educational budget, not an actual exchange contract, market estimate or account. Every exposure in this case is stipulated long; no price series determines direction.

The remaining assumptions are $2.50 commission per contract side, one tick of slippage per side, a $12.50 tick value, twelve round trips and a 2% adverse price move. Keep those inputs fixed while following the calculation. The twelve round trips are a cost multiplier, not a simulated schedule of trades. There is no changing volatility estimate, reinvestment process or historical account path in this static exercise.

Calculate exposure before counting contracts

Divide target volatility by estimated volatility: 10 divided by 20 equals 0.5. Apply the exposure cap by taking the smaller of 0.5 and 1.5, leaving 0.5. Requested notional is therefore $1,000,000 times 0.5, or $500,000. The cap does not bind in this version. Its presence in the specification does not mean it reduces every requested position.

Divide $500,000 by the hypothetical $100,000 unit notional and round down to whole contracts. The result is exactly five, so actual notional remains $500,000 and actual exposure is 0.5 times reference capital. No rounding residual arises here. This reconciliation matters because other inputs can produce fractional requested contracts, at which point actual exposure will fall below the capped continuous request.

Keep margin separate from the volatility target

Five contracts at an assumed $7,000 margin each require $35,000 under this simplified schedule. That is a collateral calculation, not a maximum-loss calculation and not the price paid to purchase $500,000 of assets. CME's performance-bond FAQ explains the obligation-supporting role of futures margin. The fictional $7,000 input is not taken from a current product requirement and should not be read as a broker quotation.

Likewise, multiplying 0.5 exposure by the supplied 20% estimate reproduces the 10% target only within the linear sizing approximation. It does not establish future realised volatility. A different realised path, an abrupt discontinuity or changing conditions can produce a different outcome. The budget has neither estimated a probability of loss nor shown that a particular target is suitable for anyone's actual capital.

Count both sides of every assumed round trip

The one-way per-contract cost is commission plus assumed slippage: $2.50 plus one times $12.50 equals $15. Twelve round trips for each of five contracts contain five times two times twelve, or 120 contract sides. Multiplying 120 by $15 gives an illustrative total of $1,800. Relative to $1,000,000 of reference capital, that is 0.18%, not 18% and not an investment return.

The calculation assumes the same quantity and the same per-side rate throughout. CME's clearing and trading fee page shows why actual fee categories require more context, including the product and participant's applicable status. The chosen commission and slippage inputs are teaching assumptions, not a complete current fee schedule. Additional charges, differing execution conditions and changes in size are outside this deliberately simple cost budget.

Interpret the cash illustration narrowly

Apply the assumed adverse 2% move to the $500,000 long notional. The illustrated loss magnitude is $10,000. Adding it to the $35,000 margin assumption produces a $45,000 cash illustration. This sum combines a collateral amount with one chosen adverse-move amount. It is not a probability-based risk limit, an estimate of the worst possible loss or a complete statement of required funding.

In particular, the $45,000 sum does not include the separately calculated $1,800 cost budget. It also omits potential margin changes, additional cash obligations, collateral haircuts, transfer timing and further adverse moves. Keeping those omissions visible prevents a tidy addition from becoming an unsupported liquidity guarantee. The fact that this limited sum is below reference capital does not certify that an actual account would remain adequately funded.

Change only volatility and the cap

For the second version, reduce estimated volatility to 2% and set the cap to 1.25, retaining the 10% target and the same capital and contract unit. Raw requested exposure becomes 10 divided by 2, or 5. The cap reduces that request to 1.25. Capped requested notional is $1,250,000, which corresponds to 12.5 fictional contracts before rounding.

Rounding down produces twelve contracts and $1,200,000 actual notional. Dividing by $1,000,000 capital gives actual exposure of 1.2. The residual is $1,250,000 minus $1,200,000, or $50,000 of unused requested notional. That residual is not automatically idle account cash: notional measures exposure rather than an asset purchase payment. Both the cap and indivisible contract size prevent the continuous request from being fully expressed.

Separate arithmetic completeness from risk completeness

The two versions answer a mechanical question: given specified inputs and downward whole-contract rounding, what exposures and budgets follow? They do not demonstrate that low estimated volatility warrants greater exposure in practice. A low input could reflect benign history, stale information or an unsuitable measurement. This case assumes a valid supplied number without claiming to have measured, forecast or independently validated it.

An auditable interpretation preserves every stage: raw ratio, cap, requested notional, whole-contract quantity, actual exposure, assumed margin, costs and adverse-move illustration. Do not rename the target as realised risk or the margin-plus-loss sum as complete cash needs. The case succeeds when another reader can reproduce the arithmetic and identify its omissions, not when its outputs are mistaken for a recommendation or a trading result.

Source record

1. CME Group: Performance Bonds and Margins FAQ
2. CME Group: Exchange Fees for Clearing and Trading