Salience and valuation.

One of my good friends recently mentioned Gamestop to me. Many of you probably remember my efforts in January and February to document the ongoing saga, which earned some notoriety both in the Twitter metaverse and in the larger financial sphere (my first citation in Bloomberg!).

But, like most of us, I haven’t really been paying attention to GME since March. I noted early on in January the parallels I observed to cultural and religious mythos, and it could not have been more true; there’s still dedicated online communities which unfortunately demonstrate the cognitive dissonance about GME akin to a doomsday cult.

That said, it’s not like salience and the narrative was defined by GME. The salience trade, or as Shiller calls it, “narrative economics”, has existed as long as the market has, and will live and die with humanity. It’s an integral part of human nature to wish to be part of something bigger, to invest with the heart and perhaps not the mind.

I think though a lot of people stop there, and discount the madness of meme stocks and the salience trade as a zone of investment to avoid. Externally, it does look truly mad; ignoring punditry or post-facto reasoning, no one could have predicted GME would rally to $400+ with a straight face. There was no contextual crutch (fundamentals, technicals, whatever tea leaves you prefer) which would’ve supported that target, and this makes many squeamish. How do you know the unknowable?

One of the most interesting ways I’ve stumbled on for understanding meme stock valuations comes from the idea of credit risk—essentially, what is the valuation of a business which may or may not default?

In a healthy, functional business and market, the valuation of the shareholder’s equity is largely driven by the several fundamental factors (market beta, sectoral trends, discounted cash flow, etc.). Businesses tend to have two major ways they finance operations (outside of normal cash flow)—Equity (like stocks) and debt. Equity of course entitles the owner to a percentage of the business (or cash flows, or the like), and debt is a promissory to repay the money in the future. In general, it is substantially easier for businesses to raise debt (and presents tax advantages) than equity. However, there tends to be a substantial differential in the counter-party interest for equity and debt obligations:

  • If I loan you money (debt), I am solely focused on getting my principal (plus interest, of course) repaid, not on the business’s future operations.

  • If I instead purchase equity, I am invested in the business’s health rather than short term obligations.

If we think about it intuitively, very few investors are worried (at least in current year) about a behemoth like Apple or Microsoft defaulting on debt issued. Unsurprisingly, this is the foundation of the relationship between bond yields and bond prices — companies more likely to default on debt will have cheaper bonds (with higher yields), while companies unlikely to default (or governments, for example) will have substantially lower yields (and higher bond prices). In most cases, when a company defaults, debt has seniority over equity—except in catastrophic cases, some portion of the debt will be paid back (pursuant to the company’s liquidation), but the equity tends to become worthless.

That said, most companies tend to have (in a normal year) a pretty low probability of defaulting on debt (or else we call it another financial crisis, or something). This allows the stock market to have some sort of ersatz stability—however, the implication of this is that the pricing of equity must always reflect the probability of default, no matter how remote.

This can be succinctly described by assuming, given rational pricing, that the pricing of equity on the open market is equal to its expected value (this is probably a safe assumption).

EV(Equity) = Value of equity * (1-P(default)) + Value of equity in default * P(default)

In the vast majority of stocks we trade (high liquidity, high market cap, for example), the EV(Equity) term will be roughly equal to the *true* value of the equity, since the probability of default is so remote. It gets far more interesting, however, when you consider degenerate cases—companies where the probability of default is extremely high.

What happens during a default? As we mentioned prior, the onus of the debt holder is not to worry about the firm - it’s to be repaid. This, in the case where a firm cannot renegotiate or continue servicing its debt, leads the debt holders to take control and liquidate the firm. If the firm’s book value is greater than the debt’s value, it doesn’t make sense to liquidate it (since the full debt can be repaid… eventually).

In the case of companies with substantial chance of default (“distressed assets”), this substantially weighs on the equity price (and of course causes bond yields to skyrocket), and leads to massive asymmetry in future outcomes (potential for high return if the company does not default, $0 equity value otherwise).

A very smart guy you might know from Black-Scholes-Merton fame, Robert Merton, thought about this from the perspective of the nascent school of options valuation—how do you value a company’s equity properly considering its probability of defaulting on debt?

Thinking about this, he developed what we now call the Merton credit risk model, which takes the form of the below equation:

Clever readers with some cursory understanding of options may recognize the above formula as basically plagiarism of:

Which is of course, our handy Black-Scholes formula!

I’m going to simply link a fantastic primer on why this is the correct way to value even an on-paper insolvent company courtesy of @DirtyTexasHedge on Twitter:

Essentially, despite the rules we’re taught from Monopoly, a business that is technically insolvent doesn’t instantly liquidate. Debt, like an option, pays back par at a fixed date (unless renegotiated), and between the now (where the company is technically insolvent) and the then (when the debt is actually due), a lot may change about the company’s fortunes (*cough* AMC). Because of this, there is some probability that by that date, the equity (which cannot, by definition, be worth less than $0) will have some positive value. This is identical in logic to the extrinsic value of an option - at the option’s expiry, the option will either be worth some amount of money (if it expires in the money) or will be worthless (but never below $0 for being long the option).

So what does this have to do with the salience trade?

Utility vs. Value

In traditional understanding of the markets, the valuation of some asset (the amount you are willing to pay for it, you being the market) should be identical to the expected utility gained by acquiring it. This essentially underpins the idea of rational pricing—a buyer will not pay for an asset more than the utility they will get by having it, and if they do, this will eventually be arbitraged away (since another buyer will not buy it at that price, etc.).

What we’ve seen however this year, perhaps due to bubble economics, is a pretty dramatic detachment of utility and value, driven largely by speculation and the pursuit of higher and higher yields (I can write a whole separate post about this and leverage). While Gamestop was perhaps one of the most dramatic examples, in the time since we’ve seen a rotation to even more divorced and hyper-normalized cases where there is a real, notional value but zero or unclear utility (e.g. $DOGE). How does this not contradict the idea of rational pricing?

Simply put—the you mentioned in the first paragraph isn’t one person. The value of an asset in a fair market isn’t the utility you derive from it, but the utility others derive from it. This idea is the Keynesian beauty contest—the pricing of assets is related to our best assumptions of how others weigh the asset’s utility.

In a speculative asset, which is what all meme stocks tend to become (this also holds true for crypto), once you detach from the traditional metrics of valuation, you see dramatic divergence in the utility estimations of an asset between various market participants. For most of us, we looked at the rise of Gamestop with a mix of disgust and envy—after all, no sane person thought Gamestop was actually worth $400? Or, to frame it more correctly here, it’s hard to imagine that the $400 per share valuation of Gamestop at the peak matched its true utility.

Veering a bit away from the philosophical implications of what utility means (is it financial? spiritual? emotional?), we can put on our Merton cap and understand what the future expected utility spread actually means in dollars and cents. When there is a large spread of future expected utility, this tends to imply higher volatility in the price discovery process—price changes largely (in the absence of new information) due to the change of market participants, and the larger our spread on what the true utility is, the more volatile we expect the spot price. Conversely, when the dynamics of the asset are well-defined (e.g. a stock like $AMZN), the expected utility spread is fairly narrow, and we see price as substantially less volatile (note: this assumes a fair and relatively evenly distributed market, and would break down in the case of massive ownership positions).

In the most extreme case, we can imagine a scenario where we have a dead (or mostly dead) company with negligible true equity value. It may be underwater (as in unable to service debts in the near future), or may not be. However, let’s imagine it gets a large internet following, simply because its CEO Beelon Tusk got popular for posting memes and skipping leg day. A small but increasing vocal online community starts to fixate on the stock, encouraging members to buy with fanciful due diligence. To an outside observer, you can now see two scenarios for our nascent meme:

1) There is some defined probability p that from the current spot price of the company’s equity that, in technical terms, “we moon”.

2) There is some other probability 1-p that “we dive”—the equity price hits 0 (or some other small number).

This plays out very well in practice on meme stocks, for a few reasons:

1) In general, the book value (or fundamental, or whatnot) of the equity is much less than the market value, especially during the boom cycle.

2) There is a massive implied spread of future expected utility from holding the stock—this leads to similarly massive volatility.

3) Most equity holders tend to be speculators/fair-weather — because the utility of holding has detached substantially from market value, very few equity holders have a vested stake in the business’s continued future (akin to the debt holder).

This allows us to intuitively relate our understanding of meme stock valuations to Merton’s risk model and the Black-Scholes. In general, we can understand that the fair way to value a meme stock is to treat its equity akin to a call option struck at some nominal price (either the book value, or perhaps the pre-meme price). This also lends itself well to a few observations, following the options valuation train of thought.

1) The Merton model gives us a pretty intuitive explanation for the relationship between price volatility and spot price. Much like prior posts explaining the basics of optionality (the Greeks), a call option on a more volatile asset is substantially more valuable than a less volatile one. This leads to a “fair” understanding of why a stock like Gamestop is worth more simply due to its speculative activity (both current and historical)—it has higher optionality and chance of being worth more in the future.

2) Stocks, unlike bonds or the traditional call option, do not have an expiration date (unless of course the firm liquidates). This can be simply modeled as holding a perpetual option, which, of course (to make our lives harder) has no standard pricing solution. In general I just model it as a very long lived LEAP, and call it a day (it should work well enough if you choose a suitably sharp discount factor).

3) In practice, it is likely positive expected value to buy a newly “dead” meme, as we saw multiple times in the past year. The caveat here is — during its descent from the first boom cycle, did it break the prior low in price? If it didn’t, this implies the market believes the optionality on it has increased, giving it a higher chance of “mooning” again in the future.

4) Salience has some sort of sharp decay function, gradually smoothing over time. When a boom-bust cycle occurs, usually a new bottom is reached, and owing to the long life of the option, it may stabilize for a while. However, as time passes and activity diminishes, we necessarily expect much like an option a decay in price (this is sharp initially and smooths out over time, and may be offset by fundamental factors).

Well, this was a long post. I hope you enjoyed it!

Cheers,

Lily