Companies buy options to reduce the variability in future cash flows.
Institutional investors invest in portfolios to maximize return for a fixed amount of risk. If an investor owns stock in company A whose cash flows are negatively correlated with the price of commodity B, then he can reduce risk by investing in company A and buying call options in commodity B.
Example 1: Suppose my publicly traded company produces corn. Then my company will very likely buy corn futures to reduce the risk associated with the price of corn falling. My question asks: why don't investors investing in the corn company just buy the corn options themselves? Why are they better off buying the options through the corn company?
Correction for example 2: Apparently there isn't a futures market for lithium. You still get the idea, right?
Example 2: Suppose my publicly traded company produces batteries. Then my company will very likely buy lithium options to reduce the risk associated with the price of lithium rising. My question asks: why don't investors investing in the battery company just buy the lithium options themselves? Why are they better off buying the options through the battery company?
Question: Please prove that, under whatever reasonable assumptions of your choice, it is optimal for the company rather than the investor to trade the options. Under what conditions would it be optimal for the investors rather than the company to buy call options in commodities negatively correlated with the company's profits?
Note: The purpose of this question is to understand the assumptions under which it is optimal for companies (rather than investors) to buy options. That is why I ask for a proof.