Borrowing costs in futures pricing: how financing is embedded in futures prices and what it means for returns
When you buy an equity index ETF, you pay the full price upfront. When you buy the equivalent futures contract, you pay only a margin deposit—a fraction of the notional value. That difference is not free. The futures market prices the financing cost directly into the contract, creating a premium to spot that decays over the contract's life. Understanding how that pricing works explains why futures and ETFs on the same underlying do not behave identically, and why leveraged investors almost universally prefer futures for large index exposures.
What the cost-of-carry model is
The cost-of-carry model for futures pricing was formalised by Black (1976) in The Pricing of Commodity Contracts, Journal of Financial Economics. Black showed that in the absence of arbitrage, the futures price must equal the spot price adjusted for the net cost of carrying the underlying asset to the contract’s expiry—incorporating financing costs, storage costs, income received, and convenience yield. The model provides the theoretical foundation for understanding why futures prices differ from spot prices across maturities.
The cost of carry is the net cost of holding a position in the underlying asset through time. It has two components: what you pay to finance the position (the risk-free rate, r) and what you receive for holding the underlying (dividends or yield, d). For equity index futures, the theoretical fair price is approximately:
F ≈ S × (1 + r − d) × T
where S is the current spot price, r is the annualised risk-free rate, d is the annualised dividend yield on the index, and T is time to expiry in years. For a three-month S&P 500 E-mini contract (ES) with a spot level of 5,000, a risk-free rate of 5%, and a dividend yield of 1.4%, the fair value of the futures contract is approximately 5,000 × (1 + (5% − 1.4%) × 0.25) ≈ 5,045. The premium of 45 points represents the net financing cost for one quarter. At the ES contract multiplier of USD 50 per point, that premium equals USD 2,250 per contract—a cost that recurs every quarter for as long as the position is maintained.
What the premium means in practice
The futures premium to spot is not a profit opportunity—it is the market's way of making two things equivalent: owning the underlying directly and holding a futures contract. If the premium were too high, arbitrageurs would sell futures and buy the index, earning a riskless profit. If it were too low, they would buy futures and sell the index short. Arbitrage keeps the futures price close to its theoretical fair value under normal market conditions.
For an unleveraged investor comparing a futures position to an ETF on the same index: the total cost is approximately the same. The futures holder earns interest on the cash they do not need to deploy (collateral yield), which offsets the financing premium embedded in the futures price. The ETF holder pays no premium but puts all their capital to work at the index level.
For a leveraged investor, the calculation is materially different. Someone borrowing to invest in an ETF pays the borrowing rate explicitly, as a margin loan charge—typically prime rate plus 1–2%. Someone using futures achieves the same leveraged exposure by posting only initial margin, with the financing cost already embedded in the futures price at close to the risk-free rate. On a USD 1 million notional exposure, the difference between a 7% retail margin loan rate and a 5% risk-free rate embedded in futures pricing saves approximately USD 20,000 per year in financing costs. This is why professional systematic managers, hedge funds, and leveraged strategies use futures rather than margin borrowing for large index exposures.
Dividends and the carry calculation
Dividends reduce the cost-of-carry premium because the holder of the underlying receives them while the futures holder does not. The futures holder does not collect dividends—those accrue to the actual holder of the shares underlying the index. The dividend yield therefore subtracts from the financing cost in the carry formula. When interest rates fall near or below the dividend yield, the cost-of-carry premium narrows or turns negative, and the futures curve can flatten or invert. In the post-2008 environment, when central banks held rates near zero and dividend yields on major indices were around 2%, equity index futures sometimes traded at a slight discount to spot.
Limitations
The cost-of-carry relationship holds cleanly under normal market conditions but breaks down in periods of stress. During liquidity crises, futures can trade at significant discounts to theoretical fair value because sellers in the futures market outnumber arbitrageurs who would otherwise close the gap. In March 2020, S&P 500 futures briefly traded well below their theoretical fair value as market participants sold futures faster than the arbitrage mechanism could correct. The divergence corrected within days, but during the dislocation the spread was large enough to matter.
For physically settled futures (commodity contracts), the carry formula must incorporate storage costs rather than simply the risk-free rate minus yield, and the relationship between futures and spot becomes more complex and less mechanically reliable.
Borrowing costs in pfolio
pfolio's continuous futures chain builder embeds actual transaction prices into the constructed price series, including the cost-of-carry premium at each roll. Historical performance series for any futures-based strategy in pfolio therefore already reflect the financing costs as they were at each point in time—not a hypothetical fair-value calculation. Users can compare a futures-based strategy directly against an equivalent ETF-based strategy in the platform's backtesting view to observe the net cost difference across different rate environments.
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