Forward Pricing for Consumption Assets Without Short Selling

Summary

The document considers whether the standard no-arbitrage forward-pricing argument can be adapted when the underlying is a consumption asset that investors may be unwilling or unable to sell short. It assumes no yield or storage cost and compares a long forward with borrowing the spot price to buy the asset immediately. Under continuous borrowing and lending at rate r, the author argues that investors’ relative preference between these ways of acquiring the asset would push an underpriced forward upward and an overpriced forward downward.

This is an intuitive demand-based argument for the familiar financing relationship between spot and forward prices. The text raises the broader idea that equivalent future payoffs may be compared using portfolios that both involve long positions, avoiding a short sale. It is posed as a question and provides no formal proof, market-clearing model, or treatment of transaction costs, credit constraints, liquidity, or differences in asset access. Thus it motivates a pricing intuition but does not establish that the proposed adjustment argument alone guarantees the no-arbitrage bound.

Key ideas

• The usual forward-pricing argument may depend on the ability to short the underlying asset.
• The proposed comparison is between buying the asset with borrowed funds and entering a long forward.
• Investor preference is argued to exert upward or downward pressure on the forward price relative to financing cost.
• The discussion suggests comparing long positions with equivalent future payoffs as an alternative intuition.
• The argument is exploratory and omits formal market-clearing and trading-friction assumptions.

Tags

# Can arbitrage arguments be rearranged to avoid selling? (Hull, Chapter 5)


# Can arbitrage arguments be rearranged to avoid selling? (Hull, Chapter 5)












Suppose forward contracts are traded on a consumption asset, so there aren't necessarily people ready and willing to sell the asset to jump on an arbitrage opportunity. Suppose the asset has no yield, incurs no storage costs, and that the current price is $S_0$.

In the book Options, Futures, and Other Derivatives, Hull notes that the argument he uses to determine the correct forward price require being able to sell the asset, so should only be applied to investment assets.

However, can we not rearrange the arguments in these case? (I think he does this himself, with arguments about options):

Portfolio 1: Long 1 forward contract with a forward price of $F_0$, expiring at time T

Portfolio 2: Borrow $S_0$ to buy the asset now

Assume investors borrow and lend at a rate of r compounded continuously.

If $F_0 < S_0 e^{rT}$, more investors wishing to have the asset at time T will choose Portfolio 1 as the way to acquire that asset. Entering this position will drive up the foward contract price.

If $F_0 > S_0 e^{rT}$, investors will avoid Portfolio 1 in favor of the simpler Portfolio 2, which also lets them sell the asset early if they want. Since people won't be going long Portfolio 1, the forward price will fall.

It seems to me a lot of arbitrage arguments can be rearranged like this -- instead of creating offsetting positions, some short and some long in the same asset, creating a portfolio with known future cashflows, you can create two different positions that just require going long in assets with the same payoff. Then being able to short-sell is not an issue.

Is this reasonable, or am I missing something?

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.