Using Forward Prices to Infer Rates When Carry Costs Are Small

Summary

The document considers estimating a riskless interest rate from spot and forward or futures prices using the relationship between the forward price, spot price, rate, and time to maturity. Rearranging that relationship gives an implied rate from the logarithm of the forward-to-spot price ratio divided by maturity. This inference is valid only when other sources of carry are absent or negligible.

The author notes that dividends affect equity forwards, while commodity forwards also reflect convenience yield and storage costs. These factors must be estimated or accounted for before interpreting the price difference as a riskless rate. Precious metals are suggested as a possible case with relatively modest net storage costs, and non-dividend-paying stocks are mentioned as a less common equity example. The document is a question seeking further candidates, not a comparative study; it gives no contract list, data, or evidence that any suggested market reliably satisfies the assumptions.

Key ideas

• The forward pricing relationship can be rearranged to infer an implied rate from spot and forward prices.
• The inference assumes dividends and other carry effects are absent or small.
• Commodity convenience yields and storage costs complicate rate estimation.
• Precious metals and non-dividend-paying stocks are raised as possible cases, without supporting analysis.

Tags

# Forward/futures contracts that satisfy $F=S\exp(rT)$


# Forward/futures contracts that satisfy $F=S\exp(rT)$












I am interested in estimating riskless rates from forward/futures data. The standard forward pricing formula is given by

$$F=S\exp(rT).$$

From this we can solve the interest rate used in pricing as a function of the spot and forward prices:

$$r=\frac{1}{T}\log(F/S).$$

Now the issue is that the formula assumes no dividends and in the case of commodities, no convenience yields and storage costs. These modify the formula in well-known ways, but complicate the issue as they need to be estimated separately.

My question is: for which contracts is this formula approximately correct, i.e. the underlying pays (approximately) no dividends and the convenience yield and storage costs are small?

Precious metals are often thought to have relatively small net storage costs. Some stocks have never paid dividends but this is rare for mature firms. Do you have other ideas?

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