Why Equity Futures Include Financing Costs in Their Price

Summary

The document explains why a positive-rate equity futures price can exceed the current spot price without implying that the futures buyer loses money on average. Under the stated zero-dividend assumption, spot-futures parity links the futures price to spot multiplied by the funding growth factor over the contract’s maturity. The question mistakenly compares the future delivery price with today’s spot value as if both were values at the same time.

The answer corrects the timing comparison: the current value, grown at the interest rate to the delivery date, is the relevant benchmark. If the expected future stock price were only today’s spot price, an investor could borrow or invest at the risk-free rate and exploit the inconsistency. The parity relationship prevents that arbitrage; it does not guarantee that the realized future stock price equals the futures price. The explanation assumes zero dividends and omits other carry costs and market frictions.

Key ideas

• With zero dividends, equity futures reflect the financing cost over the contract’s maturity.
• Compare values at the same date when reasoning about futures profit.
• Spot-futures parity is an arbitrage pricing relationship, not a guarantee of the realized future spot price.
• Dividends and other carry factors are outside the document’s simplified setup.

Tags

# Do equity futures contracts bleed money?


# Do equity futures contracts bleed money?












According to the spot-futures parity:

$$ F = S\exp^{rt}$$

where $F$ is the futures price, $S$ is the spot price, $r$ is the interest rate, and $t$ is the maturity. Dividends are assumed to be zero.

My question is, does the buyer of this contract not lose money on average, all else equal?

At time $t$, our best guess of the stock's worth is $S$ (due to the efficient market hypothesis).

So at time $t$, I will be paying $F$ and receiving $S$. So my profit is $$S - F = (1 - \exp^{rt})$$

So if $r > 0$, my profits are negative. And I am thus losing money?

## Answer by D Stanley (score 1)

https://quant.stackexchange.com/a/80783

> At time t, our best guess of the stock's worth is S

No, at time `t` the best guess of the stock whose current price is $S$ is $Se^{rt}$ due to the time value of money.

If your best guess on the future price of the stock was `S`, then instead of buying for `S` now, one would enter into a contract to buy the stock for `S` in the future, invest the funds at rate `r`, and wait, making an arbitrage profit. Therefore forward stock prices always are a future value based on a risk-free interest rate.

(There may be other ways to explain it to be more precise, but the market certainly prices stock futures with this principle)

It's not saying that the stock is guaranteed to be the future price, just used to prevent arbitrage scenarios.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.