Choosing Between a Forward and a Call for a Bullish View
Summary
The discussion considers a bullish investor choosing how to gain exposure to a forward, with position size capped at a stated maximum. The response explains that an optimal position cannot be determined from the expected direction alone: it depends on the investor's objective or utility function. Buying the maximum forward volume creates a payoff tied to the difference between the terminal forward value and its market price at entry, leaving the outcome uncertain.
A forward generally has no upfront purchase premium, while a collateralized contract can require margin as prices move. A call requires an upfront premium and offers downside protection relative to a naked forward position. The choice therefore involves risk tolerance, capital, and the cost of protection. The answer offers no utility specification, probability distribution, or quantitative optimization, and its suggestion that a capital constraint could make the problem more interesting is not worked through.
Key ideas
- A bullish expectation alone does not specify an optimal position; the objective or utility function matters.
- A forward position has uncertain gains or losses based on the terminal value relative to the entry price.
- Collateralized forwards can require margin, while a call requires an upfront premium and limits downside exposure.
- The forward-versus-call choice trades downside protection against exposure to larger losses and potential returns.
Tags
Full text
# Finding optimal trading of option on a foward
# Finding optimal trading of option on a foward
Assume you have a option on a forward $F$ with a payoff: $\max(F_T - K, 0)$.
Assume also, that you have a bullish view on the forward in such a way that $E_{0}[F_T] > F_0 = E_{0}^{*}[F_T]$ (where the star indexes risk neutral expectation). You can buy (or short) the forward $F$ up to the volume $M$. What is your optimal investment strategy?
I am not sure how to proceed with this, does anyone have any suggestions?
My guess is that given that there is no assumption of risk aversion or transaction costs we would buy $M$ of $F$ from time $0 < t < T$. I do not really see what else we could do here.
## Answer by bhutes (score 3, accepted)
https://quant.stackexchange.com/a/45700
The optimal investment strategy depends on the investment goals, or equivalently your utility function (which the investment strategy is supposed to maximize).
The forward will trade at $\mathbf{E}^*_0(F_T)$ in the market when you invest at $t=0$.
If you buy your maximum volume $M$, then gain/loss at $T$ is given by $M(F_T-\mathbf{E}^*_0(F_T))$ (which is unknown at $t=0$).
If it is a forward contract, you do not have any upfront investment. If the contract is under CSA (Credit Support Annex) i.e. collateralized, you are exposed to margin calls. If you were to buy options (long call option), you won't have any margin calls but an upfront investment in the form of option premium is required.
If it is an uncollateralized forward contract, you are only exposed to the gain or loss at $T$.
It's all a question of whether your risk appetite requires you to buy the downside protection (which a call option offers), inspite of your bullish view.
Or, whether you are open to a large downside risk in exchange for a larger return offered by a naked forward position (when compared to a call option).
Btw.. I think the question becomes more interesting if the constraint of volume $M$ does not exist; rather you have a limited capital. In this case you would want to maximize the volume (given your bullish view) - by factoring in the margin / collateral calls you may need to provide in case of naked forwards or the maximum option premium you can afford given the capital constraint. Options provide leverage, so that you deal with a larger volume - and can enhance returns on a limited capital.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.