Meaning of market capitalisation

finance econ

The following is a response to this blog post. Below I discuss:

Block-quoted text is from the original post while all other text is mine.

What are we to make of the recent near-total wipeout of the stablecoin Terra and its companion coin Luna, in which around $50 billion of value vaporized in less than a week? [https://elmwealth.com/hassan-and-ali-on-terra-luna-crash/] One perspective that might be useful comes from a parable beloved by Vic’s dad:[https://elmwealth.com/hassan-and-ali-on-terra-luna-crash/]

Hassan and Ali are antique dealers in the bazaar. Hassan notices a beautiful antique bowl in Ali’s shop, which Ali was given by an itinerant dervish in return for a cup of rice. Hassan asks Ali for a price to buy it, but Ali doesn’t want to part with it completely, so offers to sell Hassan a 3/4 share for 75 Rials. The next day, Ali drops by for tea and expresses regret at having sold a majority interest in the bowl. Ali proposes buying back half his previous sale, but Hassan is reluctant. Now Ali has to offer 75 Rials for a 3/8 share to get the deal done. The next day, Hassan is having some FOMO,[https://elmwealth.com/hassan-and-ali-on-terra-luna-crash/] so he wants to buy back a 3/16 interest in the bowl – and again, it takes 75 Rials to get Ali to the table.

After thirty days of this very sociable pattern of trading, Ali and Hassan congratulate each other on discovering such a valuable business. Based on their last trade, in which Ali bought back a roughly 1.5 billionth interest in the bowl for 75 Rials, they valued the bowl at about 50 Billion Rials, with ownership split almost exactly 50/50, and their bank accounts exactly as they were before the very first trade.[https://elmwealth.com/hassan-and-ali-on-terra-luna-crash/]

I think what fundamentally differentiates this from most uses of “market capitalisation” is the lack of demonstrated preference:

When the market cap of a company such as Google is calculated, it is done so by multiplying the last trading price of a share by the quantity of shares in existence.
The difference between this and the above bowl scenario is that there is no liquidity at the bowl’s last price, whereas for companies like google, there always is.

As a result, for most companies the last price is economically meaningful, as shareholders have the option to sell at said price.

The existence of this (“bid orderbook”) liquidity at the last price proves that all shareholders value every one of their shares more highly than the last price (or more specifically, than the price of the highest bid). Were they to value any of the shares less than this last price, they would have sold them into the available bid liquidity.

This situation can be contrasted with that of the bowl in the above scenario, where there is no liquidity at the last trading price: no bids committing to buy from the current owners of the bowl, were they to decide to sell.

As a result, the continued possession of the bowl by Hassan and Ali proves very little about how much they value their shares of the bowl. Unlike in the case of google, their continued possession of the bowl does not prove that they value every fraction of it more than the last price they traded it for, as there is no one who is offering to buy it from them at said price.

As a result, they may in fact be willing to sell their entire stake for $100 at the present moment, but no one would know. They aren’t being presented with this opportunity, and as a consequence aren’t able to refuse it.

The above tells us that in the context of most companies, the market capitalisation is meaningful in the sense that it represents the maximum value someone could offer to all shareholders in exchange for their shares, yet still not succeed in acquiring a single share from them.

Whereas in the context of the bowl, we have no such guarantee. The “last price” is economically meaningless, as neither Hassan nor Ali are able to sell their shares at said price were they to want to do so. There is no liquidity.

They spend the evening drinking to their success, hatching plans to sell a small interest in the bowl to passing tourists, or posting the bowl as collateral for a large loan that will give them a chance to enjoy their new-found riches.[https://elmwealth.com/hassan-and-ali-on-terra-luna-crash/] But that very night, the bowl is stolen. Down on his luck, the thief exchanges it for a bowl of rice in the bazaar of a distant city.

What Was the Bowl Worth?
Were Hassan and Ali the victims of a colossal theft which robbed them of 99.99% of their wealth? Looking at the price at which they last traded a minuscule fraction of the bowl, the answer would seem to be “yes”, in line with the modern market convention of computing value by taking the last marginal trade price and multiplying by the number of shares.
But we suggest a more sensible way to think about the wealth generated by an asset is as the present value of the future consumption it can support.

As I demonstrated above, there is no need to appeal to notions of future consumption to understand why the bowl’s valuation was deceptive.

Rather, all that is necessary to appreciate this is to realise that what differentiates the bowl’s market capitalisation from most other assets is simply that there was no liquidity at the last price.

Hassan and Ali may have been able to sell a few fractional shares to unsuspecting tourists, or hoodwink a hapless loan officer into giving them a small loan against the bowl, but it’s clear there’s no way this bowl could support 50 billion Rials of future consumption or anywhere close to it. The true wealth stolen from them was a lot closer to one cup of rice.

Given that value is ultimately subjective, any assessment of how much the bowl is “really” worth must be made in reference to certain individual’s preferences.
As far as Hassan and Ali are concerned, I’d agree that the bowl was probably worth to them something closer to a cup of rice, purely due to lack of evidence to the contrary (as a result of liquidity lacking at the prices at which they were trading it amongst themselves).

Attempting to ascertain the “true value” of the bowl from how much consumption it can support is ultimately futile. The amount of consumption that the bowl can support depends on how people value what the bowl provides over the course of its consumption.

It is very possible for example that someone would value being able to use the bowl for its serviceable lifespan as much as they value being able to eat a cup of rice. It is also however possible that the bowl is actually a “priceless” antique, in which case someone may value possessing and displaying it (“consumption”) significantly more than they value a cup of rice.

The above demonstrates that how much consumption the bowl supports is not something that can be objectively ascertained. This is because the consumption of the bowl can only be compared to the consumption of a cup of rice by assessing what subjective value people assign to each type of consumption.

However different people will value each type of consumption differently. Antique collectors may value the bowl far more than a cup of rice, whereas someone looking for a quick meal may prefer the cup of rice to the bowl.

The price system exists to address this by allowing for those who value something most to acquire it by way of being willing to pay more for it than others are. The result is that prices emerge for goods, reflecting the minimum amount one must forgo to acquire a certain good, in order to outbid all other prospective buyers.

As a result, the “future consumption” theory of value suggested by the author either results in the value of the bowl and a cup of rice being impossible to compare, due to each person valuing them differently, or simply results in using prices to assess the relative (marginal) values placed on each good.

Let’s contrast this to an asset like the common stock of General Motors, currently worth about $50 billion. If every holder of GM decided to sell simultaneously, they might receive less than $50 billion

The answer to this question is much divorced from what market capitalisation is supposed to measure. Market capitalisation measures the value placed upon the shares by their current owners. It is derived from the fact that at any moment in time, all share holders are willing to hold their shares despite having the option to sell them for near the last price.

From this observation, the market cap measurement effectively calculates a minimum aggregate value placed on all shares by their owners. It is not supposed to reflect how much all shareholders would receive were they to simultaneously sell their shares. To answer that, one would need to know how much the marginal share is valued by everyone other than those who currently hold shares.

Given that those who value shares the most will be those who already hold them, the clearing price will almost certainly be lower if those who currently hold shares are excluded from holding them (in the hypothetical where they all sell).

or they might receive more (controlling stakes often trade at a premium) – but the ownership of an interest in GM is sufficiently deep and broad-based that $50 billion is a reasonable estimate for the wealth that would be lost by stockholders in aggregate if the GM stock price suddenly went to zero.

I think that this mostly mischaracterises what fundamentally differentiates the bowl hypothetical from what determines the value of GM shares. By far the most important difference is that there is no liquidity at the last price in the bowl hypothetical, whereas there is large liquidity at the last price for GM shares.

Despite this being the most important difference, I also do agree that a secondarily important difference is the broad-based nature of the GM share holder base relative to the very centralised (consisting of only Hassan and Ali) ownership of the bowl.
Centralised ownership can result in less accurate pricing, as few owners may more easily collude to withhold supply (not sell their shares), which is much more difficult to coordinate amongst millions of shareholders in the context of GM.

There’s a continuum between assets like GM’s common stock and Hassan and Ali’s bowl. Your evaluation of how much wealth was created and destroyed by the rise and fall of Terra and Luna will depend on where along this continuum these assets lie.

Based on the two above factors I have identified as being necessary for meaningful pricing of an asset, being:

The Terra stablecoin satisfies both, as it was both held by millions of people and had very liquid markets at its former $1 “peg”. As a result, the crash of Terra represented a loss of value at least equal to its nominal $20 billion dollar market cap, for the holders of Terra tokens.

  1. This not is not an offer or solicitation to invest, nor should this be construed in any way as tax advice. Past returns are not indicative of future performance. Thanks to John Karubian, Vildana Hajric and Anna Wroblewska for their helpful comments.
  2. Terra and Luna were “worth” about $20 billion and $40 billion when they were changing hands at their highest prices, in early April 2022. See Matt Levine’s excellent post from May 11th, 2022 for more on specifics: Terra Flops.
  3. We talked about this parable before, in a slightly different form in 2017: A Brainteaser Double-Feature for the Holidays
  4. FOMO = Fear of Missing Out.
  5. The final share of the bowl traded was 3/(231), and the cup’s exact “value” using the last trade price was =75/[3/(231)]=53,687,091,200 Rials.
  6. Or selling some of the bowl to yield-seekers by offering to pay a 20% rate of interest on their bowl investment – in kind, of course.

If you found this interesting, have feedback or are working on something related, let’s chat: twitter (@0xdist) or schedule a 20 min call

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Distbit

Interested in econ, cryptoecon, agents, finance, epistemology, liberty.