Cutting Beta Inside a Hard Derivatives Cap
A registered commodity trading advisor manages a $12,000,000 equity separate account whose current beta to the S&P 500 is 1.15. The client's investment policy statement limits aggregate derivatives notional to 10% of account value at all times, measured at trade date. The adviser expects equities to fall over the next three months and has been instructed to reduce the account's effective beta to 0.60. December E-mini S&P 500 futures trade at 4,400 with a $50 multiplier; initial margin is $26,000 per contract and maintenance margin is $21,000. The account holds $250,000 of cash that the client refuses to have invested in securities but will permit to be used as futures margin. The adviser intends to lift the hedge before year-end.
1. Calculate the number of futures contracts required to bring beta to 0.60 and determine whether the adviser may execute that trade.
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Contract count
N = (β_target − β_current) × Account value ÷ (Index × Multiplier)
N = (0.60 − 1.15) × 12,000,000 ÷ (4,400 × 50) N = (−0.55) × 12,000,000 ÷ 220,000 = −30 contracts (short 30)
Test against the IPS
- Notional of 30 contracts = 30 × 220,000 = $6,600,000
- 10% cap = 0.10 × 12,000,000 = $1,200,000
The required hedge is 55% of account value; the mandate permits about 10%. The adviser cannot execute the trade as specified. Note the cap is tested on notional, not on margin - the $250,000 of available cash is irrelevant to the constraint, which is a common source of error.
2. Given the cap, what beta is actually achievable, and what alternatives should the adviser present to the client? State the trade-offs.
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Maximum permitted position
1,200,000 ÷ 220,000 = 5.45 → 5 contracts (rounding up to 6 would breach the cap)
Beta reduction = notional ÷ account value (futures beta = 1.0) = 1,100,000 ÷ 12,000,000 = 0.0917
Achievable beta = 1.15 − 0.0917 ≈ 1.06
That is roughly one-sixth of the de-risking requested. The gap must be documented, not silently absorbed.
Options to present
- Amend the IPS to raise the derivative notional limit or to define notional net of offsetting positions - the only route to a true 0.60 beta with futures.
- Restructure the physical portfolio - rotate into lower-beta sectors, raise cash, or add low-volatility holdings. This is not a derivatives position and is therefore unconstrained by the cap; it is usually the cleanest answer.
- Long index puts - check how the IPS measures option notional. If notional is premium- or delta-based, a put position can deliver meaningful downside protection well inside the cap; if the IPS counts full strike notional, puts are worse than futures, not better.
- OTC swap - same notional problem plus counterparty credit exposure and possible ISDA documentation delay.
Recommendation: execute the 5 contracts for partial cover, disclose that the 0.60 objective is unattainable under the current mandate, and obtain written instruction on which alternative the client prefers.
3. The index rallies 9% before the hedge is lifted. Quantify the margin experience on the 5-contract position versus the 30-contract position and assess the $250,000 cash buffer.
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Variation margin (futures loss)
- 5 contracts: 5 × 220,000 × 0.09 = $99,000
- 30 contracts: 30 × 220,000 × 0.09 = $594,000
Liquidity analysis at 5 contracts
- Initial margin posted: 5 × 26,000 = $130,000
- Free cash remaining: 250,000 − 130,000 = $120,000
- Adverse move of 9% consumes $99,000 of that $120,000
So the permitted position just survives a 9% rally without a cash call the client cannot meet. A further 2% move would exhaust the buffer and force a partial unwind at the worst moment.
At 30 contracts the $594,000 loss is more than double the entire cash reserve; daily settlement would have generated margin calls the adviser could only meet by selling the very equities being hedged - the classic failure mode of an oversized cash-settled hedge.
Note the offset: the physical equity portfolio rises roughly 9% × 1.15 ≈ $1.24 million, so the hedge cost is an opportunity cost, not an economic loss. The constraint that actually binds is daily cash settlement timing, not the P&L. Recommend pre-funding at least a 15% adverse-move reserve and setting a written trigger for partial unwinds.