The forward-start put
Illiquidity
Assets that can easily be sold or redeemed for cash are "liquid"; those that cannot are "illiquid". "Easy" generally encompasses both a component of time (how quickly the sale can be made) as well as price (how close the price was to the asset's value) since it is generally expected that an asset of any liquidity can be sold more quickly at a lower price.
Because of this time-price tradeoff, it is mostly the case that things which are more liquid are also more valuable. That notional amount more that someone is willing to pay for a liquid version of an asset relative to an illiquid one is the "liquidity premium"[1]. The important exceptions to this, those cases which draw an illiquidity premium, are private equity/private credit funds, where reducing an asset's liquidity also implies or permits a reduced frequency of revaluation[2]; and startups. Obviously, at heart, these are really the same exception.
Startups
A common way for startups to incentivize their employees is with equity plans, which issue stock in the company in some form or another, subject to a variety of conditions on sale, voting rights, option exercise, tax benefits, etc. The pitch is generally that this is a straightforward way to bet on the success of the company and thus (implicitly, though somewhat falsely) on yourself. The equity plans and conditions are correspondingly easy to understand, which should mostly be seen as window dressing for the fact that they are extremely difficult to rationally value either in totality or on a condition-by-condition basis.
At BND, the handful of us that joined prior to the seed round were issued options with single-trigger vesting, right of first refusal, and early exercise. During the closing of the seed round, our counsel requested that we add a transfer restriction to the shares issued under that plan: while RoFR grants the company the option to substitute itself as counterparty to any good-faith offer to buy, a transfer restriction would imply that the company could simply refuse to allow the sale. The rationale was a perfect recitation of the "illiquidity premium" discussion from the previous section — without some limitation on when shares could transfer and at what value, the company might risk a valuation that it didn't want.
One way to look at a transfer restriction is that being allowed to sell something only at the discretion of a third party is equivalent to being able to sell it and at the option of a third party being required to (atomically) repurchase it at the same price. That option of the third party is a put option, so we now have a financial equivalent: accepting a transfer restriction on equity you own is equivalent to selling a put option now with a strike price set in the future, which is a "forward-start" option[3], at the money, with a very long expiry. So the price of giving up the transfer right should be the price of a forward-start put. As with conventional at-the-money options, the price of the forward depends on an estimate of the volatility during the "active" period of the option.
While estimating the forward volatility of illiquid startup equity is even sillier than estimating the future price, the exercise does show how the impairment has nonzero economic value in both directions: it is genuinely valuable to the company to exercise that put, and so it is completely reasonable for the company to pay for that right. The difficulty of actually calculating its price in dollars is why real VCs trade transfer rights in kind, with tag-along, drag-along, and other terms, none of which you'll ever see in an employee equity plan.
| [1] | Understanding of course that this a continuous relationship more than a binary. There doesn't seem to be a Greek for "derivative of value with respect to liquidity", but this paper uses Λ (lambda) for a similar purpose, though it's a derivative with respect to liquidity of more than one asset. |
| [2] | e.g. if you hold an asset that never trades with a public price and against which you don't take out any callable loans, it may be favorable to simply never mark it down — and you'd pay a premium for the right to maintain that ignorance. |
| [3] | Musiela, pp 195. Not that this is a particularly rigorous argument, but this "conventional" pricing of a forward-start option should be seen as a lower bound, since the option can be exercised arbitrarily many times vs a canonical option which is exercised at most once before expiry. |