How Rates, Dividends, and Carry Affect Futures Basis

Summary

The document asks whether a futures price can fall below spot if interest rates turn negative, starting from the cost-of-carry relation for an asset with no dividends. The response points out that a negative futures basis does not require negative interest rates. If dividends exceed the financing rate, the basis may already be negative, and it can shift as dividends go ex and repo rates change. The answer cites real-estate index futures as an example that it says are often in negative basis.

This exchange highlights that futures and spot prices are linked by more than the risk-free rate: income from the underlying and financing conditions also affect the relationship. However, the response is incomplete in the supplied text: it raises the S&P 500 as another example but provides no accompanying data or conclusion. It does not develop the full pricing formula, distinguish futures from forward valuation, or quantify how a rate change affects the basis. The example therefore supports the possibility of negative basis, not a detailed forecast of when prices will cross.

Key ideas

• A futures price can be below spot even when interest rates are positive.
• Dividends can make the basis negative when their rate exceeds the financing rate.
• Repo rates and dividend events can cause the basis to change over time.
• The cited examples illustrate basis behavior but provide no full quantitative analysis.

Tags

# What happened to future price if rates become negative?


# What happened to future price if rates become negative?












Imagine the spot price of a non deliverable and not paying dividend asset is 100\$. With positive rate, the theoretical formula $F = S \cdot e^{rT}$ give us a future price higher, let's say 105.

If rate become negative before maturity, does the future price will 'cross' the spot price of the underlying asset? Because with negative $r$, $F$ will be reduce and could be lower than $S$, so at some point will there be a 'cross' of the two prices?

## Answer by JoshK (score 1, accepted)

https://quant.stackexchange.com/a/48618

Futures actually have a negative basis all the time without having to have negative interest rates. Dividends can have a rate that is higher than the interest rate and that makes the basis negative. Futures on the Dow Jones Real Estate Index are almost always negative.

Here are the DJUSRE Sep and Dec futures. The "Spread" column shows you the negative basis:

As dividends go ex and repo rates change the basis can, and does, swing form positive to negative to positive and all over again. Here is the basis for the SP500, a little niche index you might have heard of:

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.