> Taking a salary implies you're forgoing a salary

You lost me there. How does taking a salary imply that you’re foregoing a salary? That sentence doesn’t make sense.

You seem to be conflating the expected value of equity with the general financial outcome of having a job, or you might not know precisely what expected value means. (That’s okay! I’m not judging.) You can’t say that equity is positive EV just because you didn’t lose money and ended up with some salary. To calculate EV, you must compare it to what happens when you don’t take equity. That is the definition of Expected Value: the probability of an event multiplied by the outcome gain/loss. Since accepting lower salary has a probability of 100%, and the probability of the value of shares being greater than $0 has a probability less than 100%, it is obvious and tautological that the EV of some equity can be negative.

If I take a half salary, and a bunch of equity to compensate for the low salary, and the company never goes public, then it’s a negative outcome, I lose 50% of the money compared to taking a full salary with no equity. (Even if I collected, say, $1M in salary in the mean time.) This is what actually happens all the time, equity ends up worth less than the value that it was traded for. Given that most startups fail and never go public, that means that the average EV of equity over all startups probably is negative.

Shower thoughts, I thought today about what you said, and realized that you might be thinking of the term “expected value” to mean the same thing as “what do I expect the future value of this equity to be?”. In that sense, you’re right, equity’s value cannot go negative. There are dumb little corner cases where you buy stock and get taxed and it tanks before you sell, or things like that. But speaking generally, the monetary value of equity is mostly zero or positive, and cannot go very far negative nor is very likely to go negative.

That would be logical and a reasonable assumption, but that’s not what the term “expected value” actually means. The term has a specific mathematical meaning in statistics that is very different from the calculation of what your options are worth. EV specifically means that you take the outcome of all possibilities, and you weight them by the probability of each possibility. This is why I was insisting that you need to account for the case where you take a larger salary and no equity, because that is the other major possibility, and it’s what you trade away when you take equity as part of a startup compensation package. This is what the term “opportunity cost” is referring to, it’s referring to the path you didn’t take.

So, I (perhaps) see what you were trying to say, and I agree with you insofar as equity won’t cost you actual cash once you have it. But it can and does cost you money that you could have had, if you took a different path. It’s important to understand what “expected value” and “opportunity cost” mean before you choose to take the equity. Once you have the equity, it’s too late and you’ve already paid the opportunity cost, now you have to hope the equity becomes valuable enough to exceed all the salary you traded it for.