Level III Core · Swaps, Forwards, and Futures Strategies

Futures for Asset Allocation and Equity Overlay

Updated 9 October 2026 · Fact-checked

You use stock index and bond futures to change a portfolio's exposure without trading the underlying assets. Contracts needed = (target beta − current beta) ÷ futures beta × portfolio value ÷ (futures price × multiplier). Positive means buy, negative means sell. Synthetic cash and synthetic equity combine futures with the cash or equity position.

Understand Futures for Asset Allocation and Equity Overlay

A futures overlay changes risk exposure quickly and cheaply. Instead of selling shares and buying bonds, you add a futures position on top of the existing portfolio. The underlying holdings stay in place. This avoids trading costs, market impact, and sometimes taxes or manager disruption.

The key idea is that a futures contract has almost no upfront value but carries the full price exposure of its underlying. Buying stock index futures adds equity exposure. Selling them removes it. The same logic holds for bond futures, where exposure is measured by basis point value (BPV), which combines duration and market value.

To change beta, you compare the portfolio's current beta with the target beta. The gap, scaled to money, is what the futures must cover. If the futures are not a perfect match to your portfolio, you divide by the futures' own beta.

To shift between asset classes, you use two positions. Selling equity futures reduces equity exposure. Buying bond futures adds bond exposure. Exposure is measured in money terms, so you convert the money you want to move into contracts.

Synthetic cash means holding equities and selling futures on the same exposure. The result earns the risk-free rate, because the equity risk is hedged away. Synthetic equity means holding cash and buying equity futures. The result earns the equity return. In the exam, always tie the choice to the client's objectives and constraints, such as a short time horizon, a liquidity need, or a rebalancing target.

Key rules to remember

Contracts to change equity beta: N = [(β_T − β_S) ÷ β_f] × (S ÷ (f × multiplier)); β_T is target beta, β_S is current portfolio beta, β_f is the futures beta (often 1 for an index future on the same index), S is portfolio value, f is futures price. Positive N is buy, negative N is sell.
Contracts to move equity allocation: N = (Target equity − Current equity) ÷ (f × multiplier); Work in money amounts. The money gap divided by the contract value gives the number of contracts. Apply a futures beta adjustment only if the question explicitly gives a futures beta that differs from the asset class. In that case β_f scales the money exposure each contract delivers, so divide the result by β_f. If β_f = 1, it drops out. A negative N means sell futures, which cuts equity exposure synthetically while the holdings stay in place. A positive N means buy futures to increase equity exposure. Pair with the bond leg below for the other side of the shift.
Bond leg of an allocation shift: BPV_T − BPV_P = (Target bond value × MD_T − Current bond value × MD_P) × 0.0001, then N_f = (BPV_T − BPV_P) ÷ BPV_f; Size the bond leg from the target and current bond allocations. MD_T and MD_P are the modified durations of the target and current bond exposures. If only the money moved is given, treat it as signed: positive into bonds, negative out of bonds. Then BPV_T − BPV_P = Money moved × MD × 0.0001, where MD is the duration of the exposure being added or removed. Divide by BPV_f, the BPV of one bond futures contract, to get contracts. Positive means buy bond futures. Negative, for a fall in bond exposure, means sell.
Contracts for bond exposure (BPV method): N_f = (BPV_T − BPV_P) ÷ BPV_f; BPV is basis point value, the money change per 1 bp. BPV_T is the target portfolio BPV and BPV_P is the current portfolio BPV. BPV_f is the BPV of one futures contract, found from the cheapest-to-deliver (CTD) bond's BPV divided by its conversion factor. All BPVs are for the same yield move. Positive means buy bond futures.
Synthetic cash: Equity portfolio + short futures ≈ risk-free asset; Fully hedged equity (beta of zero) earns about the risk-free rate. Short futures are sized so total beta is 0.
Synthetic equity: Cash + long futures ≈ equity portfolio; Buy futures with notional equal to the cash held. Cash earns the risk-free rate and the futures give the equity return.

How to solve Futures for Asset Allocation and Equity Overlay questions

Use the same sequence for any futures overlay question. It keeps the sign and units right.

1Read the client's objective and constraint first. Decide the direction: more or less equity, or higher or lower beta, or a shift between equity and bonds.
2Write down the current exposure in money terms, or the current beta or BPV. Write down the target in the same terms.
3Compute the gap: target minus current. Keep the sign.
4Find the exposure of one futures contract: price × multiplier for equity, or BPV of one futures contract for bonds. Note the futures beta if it is not 1 and you are adjusting beta.
5Divide the gap by the exposure per contract. For a beta change, also divide by the futures beta.
6Interpret the sign: positive is buy, negative is sell. Round to a whole number of contracts if asked.
7For a two-sided shift, repeat for the other asset class. For synthetic positions, state the resulting return, risk-free for synthetic cash and equity return for synthetic equity.
8Show each line of working. A correct number alone can earn full credit for a calculation, but working protects you if the setup is wrong.

Quickest way: Gap in money, then divide by one contract

When to use it: Use when the question gives clear current and target figures and you have limited time. Works for beta, allocation shifts and bond exposure.

Convert everything to one number: the money exposure to add or remove. For beta, that is (β_T − β_S) × S ÷ β_f.
Compute contract value: futures price × multiplier.
Divide and attach the sign. Negative is sell.
Sanity check: raising beta or equity means buying, cutting it means selling. If your sign disagrees, recheck.
For synthetic cash, the target beta is 0, so N = −β_S × S ÷ (β_f × contract value).

Common mistakes in Futures for Asset Allocation and Equity Overlay

Getting the sign wrong and buying futures to reduce beta.
Students compute the size correctly but forget that a negative gap means selling.
Fix: Always compute target minus current. Negative means sell. Check against intuition: reducing risk means selling.
Forgetting the futures multiplier.
The futures price alone looks like the contract value.
Fix: Contract value = price × multiplier. Underline the multiplier in the question before calculating.
Ignoring the futures beta when it is not 1.
Students memorise the formula with β_f omitted.
Fix: In a beta-change calculation, include β_f in the denominator whenever it is given. If the futures track the same index with beta 1, it drops out.
Mixing up synthetic cash and synthetic equity.
Both use futures and the names sound alike.
Fix: Synthetic cash is equity plus short futures and earns the risk-free rate. Synthetic equity is cash plus long futures and earns the equity return.
Using portfolio duration or beta where money amounts are needed for an allocation shift.
Students blend the beta formula with the allocation formula.
Fix: Allocation-shift calculations are based on money amounts. Adjust for the futures beta if the futures do not track the asset class one-to-one. Use portfolio beta only when the question asks you to change beta. For the bond leg, convert the money moved into BPV first.
Writing a recommendation without tying it to client constraints.
Students focus on the arithmetic only.
Fix: Add one line: for example, futures avoid selling holdings, keep the manager's stocks intact and reduce trading costs, which fits the client's need.

Worked examples

Example 1

A portfolio is worth $80,000,000 with a beta of 1.10. The manager wants to raise the beta to 1.30 using stock index futures. The futures price is 4,000, the multiplier is $250, and the futures beta is 1.00. How many contracts should be traded?

Show the solution

Gap in beta = 1.30 − 1.10 = 0.20.
Contract value = 4,000 × 250 = $1,000,000.
Contracts = (0.20 ÷ 1.00) × (80,000,000 ÷ 1,000,000) = 0.20 × 80 = 16.
Sign is positive, so buy.

Answer: Buy 16 stock index futures contracts.

Example 2

A client holds an equity portfolio worth $50,000,000 with a beta of 1.20. The client wants to move to a zero-beta position for a short period without selling any shares. The index futures price is 2,500, the multiplier is $200 and the futures beta is 1.00. How many contracts are needed, and what return should the position earn?

Show the solution

Target beta is 0, so the gap = 0 − 1.20 = −1.20.
Contract value = 2,500 × 200 = $500,000.
Contracts = (−1.20 ÷ 1.00) × (50,000,000 ÷ 500,000) = −1.20 × 100 = −120.
Negative sign means sell 120 contracts.
With beta of 0, the position is synthetic cash, so it should earn about the risk-free rate, before costs and basis effects.

Answer: Sell 120 contracts. The hedged portfolio behaves like synthetic cash and earns approximately the risk-free rate.

Exam tips

Write the formula and every input. A correct number typed alone earns full credit for a calculation, but a wrong number with working can still show your method.
Respect command words such as calculate, determine, and justify. If asked to justify, give a short reason linked to the client's objective or constraint, such as lower trading costs or keeping existing managers.
Watch for the futures beta and multiplier. Exam writers often give both to test whether you use them.
In item sets, check the sign before choosing an option. Distractors often have the right size but the wrong direction.
Answer only the number of responses requested. Extra answers are not evaluated, and only the first ones in the order given count.

Futures for Asset Allocation and Equity Overlay: frequently asked questions

How do I calculate the number of futures contracts to change beta?

Use N = [(β_T − β_S) ÷ β_f] × (S ÷ (f × multiplier)). The sign tells you whether to buy or sell. Use the contract value, which is price times multiplier.

What is synthetic cash in futures?

Synthetic cash is an equity portfolio combined with short futures sized to bring the beta to zero. The combination earns about the risk-free rate. It lets you de-risk without selling the holdings.

What is synthetic equity?

Synthetic equity is cash plus long equity futures with notional equal to the cash. It gives equity-like returns while the cash earns the risk-free rate. It is useful when you want fast exposure without buying many stocks.

Why use futures instead of trading the underlying assets?

Futures are usually cheaper and faster to trade, and they leave the underlying holdings and manager mandates untouched. They are useful for tactical shifts and for overlays across several managers.