Liquidity and Fundamentals (Part 2)

I want to warn everyone - this is a highly speculative and mostly argumentative/descriptive post series. I have no idea yet if it is right, and it will likely change as I think about this more thoroughly, and create a series of testable predictions and a more formal mathematical notation to describe it. That said - enjoy.

If you follow the argumentation I describe in Part 1, in this framework of economic thought there exist two major sources of valuation:

1) Fundamental value—as I described a bit sarcastically on Twitter:

While there are specific definitions of fundamentals for various economic niches, it turns out it’s really difficult to come up with a comprehensive, quantitative, one-size-fits-all to describe what it is. Undeniably you run paradoxes and edge cases when dogmatically asserting a single metric of fundamental value. For example, a naïve approach to covering most marketable, non-consumable assets is the value of an asset is the highest price another individual would pay for it. This, however, not only fails to consider the ramifications of market composition (our liquidity value), but fails to account for the value of non-marketable assets entirely. It would be profoundly difficult to argue that value in the most generic sense does not cover the human condition. This author fails to see the irrationality of trading dollars for a nice vacation, even though it is a largely one-way transaction (once you book a vacation, you generally cannot resell it).

In a more abstract definition, one could define a fundamental value precisely by that metric—the value of something assuming there is no way to resell it. Unless I am redistributing it, when I purchase a toothbrush I am making a statement of what I think its fundamental value is, since I plan to use and eventually discard it.

Though that’s an extreme example, it shows continuation trivially with the traditional forms of fundamental value we all know and love. In the absence of a secondary market for an equity and no claim on liquidation, the fundamental value should be equal to the net present value of all future dividends I will receive from owning the equity. A fundamental value in all but the simplest of cases is more accurately described as a probability distribution, representing all potential future paths. Despite this neat-and-easy definition, the fundamental value of an asset tends to be largely a latent variable—even for a single individual there is a significant amount of uncertainty in all but the simplest cases.

2) Liquidity value - this can appear as a directly observable premium (the liquidity premium), can be tautologically described as “the rest of the market price component when fundamental value is subtracted”, or more rigidly defined as the ability from time of transaction to buy or sell an asset without incurring market impact associated loss (e.g. a firesale, in the case of liquidation value) at any given time point in the future (until I no longer hold a position in the asset). This can be described more properly in two components/premia:

1) Premium of immediate liquidity - In a markedly illiquid market (for instance, art sales), there is a high cost associated with demanding immediate liquidity for an asset (e.g. the Picasso). Conversely, in an asset like $AAPL, the market is fairly liquid and without large size, there usually is fairly low cost to demand immediate liquidity.

2) Premium of market uncertainty - Even in the absence of immediate liquidity demand, there should be an existing premium associated with future implied liquidity (buyers/sellers), given the uncertainty attached to the market composition.

In the absence of any future buyers/sellers of an asset, we expect that the maximum utility I will derive from holding an asset is the fundamental value (minus any costs associated like cost of carry). This value may or may not decrease over time.

However, let’s look at it from the other angle. Let’s say you buy a share of Altria for some price, with the expressed rule again that it can never be sold. In the previous example, the principle of regret minimization need not apply, given your max loss is $0 (you were gifted it for free, and have no recourse to sell it). In this case, if I buy the share for $50, I must believe the sum of all future discounted cash flows is equivalent to $50 today. However, this is also the price I agree to pay under regret minimization—that is, I am stating my belief when the transaction occurs that the expectation of all future potential discounted cash flows (the entire distribution of outcomes, including ones where Altria goes out of business) is worth $50 of regret to me.

This is a much more interesting statement, for a few reasons. First off - the unit of regret is not dollars. In fact, in future posts I will talk a bit about the impact of macroeconomic and personal factors on regret, including most notably credit relaxation. That said, this veers uncomfortably close to behavioral economics and Kahneman’s prospect theory, which has limitations and controversies. It’s undeniable that regret and utility are primary drivers of rational decision-making, but measuring those factors directly is complex (and potentially impossible).

Secondly—the implication here is that regret minimization changes the calculus in a much more liquid market. Why is that?

Let us go back to transactions as an expression of belief. When I do an action, I am expressing my view of the state of the world. When I purchase Altria at $50 a share, I am implicitly stating that my concept of its value (in this framework, the addition of its liquidity and fundamental values) is $50 (or more precisely, whatever $50 to me is worth in regret-units). This of course really only holds true in two cases:

1) Lack of future liquidity - If the day after I purchased the share Altria was to go out of business, I would not have received any dividends nor would have been able to sell (in the above example regardless I could not sell the share). Therefore the Regret Principle tells us that if I agree to make the transaction with no ability to sell in the future, rationally the $50 (in whatever the conversion is to regret-units) should be the expected value of all future cash flows to me. This again is an expected value - there are certain histories of course where Altria will take over the planet, and others where it goes out of business the next day.

2) Belief is fixed — If I was a True Believer in Altria, I may discount future information which could impact my original transactional belief (e.g. Altria hits $5 the next day due to some scandal). In this case, regardless of future liquidity, I would decide to hold the asset, making the outcome isomorphic to #1.

Neither tend to be reality in practice. As rational actors, we tend to follow a modified Bayesian version of reasoning, where our beliefs are expressions of the now, but may change as we gather new information over time. Similarly, very few assets are completely illiquid (unless you get truly unfortunate at time of purchase, or buy options on niche stocks).

In a more practical reality, we do not and should not regret minimize over the entire value of an asset. Assuming we are not True Believers (there are a few aspects of memetics, like religion, where true belief likely holds uncomfortably well), the existence of a continuous (over the entire price range, from $0 to infinity) market of buyers and sellers gives us opportunities to minimize regret. If I purchase Altria at $50, given Altria is a liquid market and I am not a fanatic, in reality perhaps I have $5 at true risk (this is captured in marketable assets in a Value-at-Risk framework). This is a more practical interpretation of regret minimization—when I purchase an asset, I minimize my expected regret in the outcomes where my original belief is invalidated. For an asset like an equity, this usually falls under the purview of market price (if I buy Altria expecting it to go up in value and it instead falls, the point where my belief is invalidated is the point at which I decide to sell it).

Intuitively, this is directly proportionate to the asset’s overall liquidity — in an infinitely liquid market I can always minimize my regret by selling at the point where my original belief was invalidated. This is similar to argumentation of illiquidity premium via transaction cost - in a market of zero liquidity, my transaction cost in essence will be the entire purchase price of the asset. In a liquid market, whatever price point (or more generally, any piece of new information) invalidates my original belief, I should be able to relatively quickly sell the asset and cap my expected losses (and hence minimize my regret).

Let’s imagine an asset trading at precisely its fundamental value. For a marketable asset, this could be - to keep it simple and uncertainty low - an investment grade bond issue (or even less risky - a new issue Treasury). If I am an individual who has no need for immediate liquidity, under risk-neutral decision making I should have no preference for cash versus holding an asset at its fundamental value. Therefore, if the price of an asset were to drift below its fundamental value, I would never rationally sell it either (I might buy more). However, if I had a need for liquidity — all bets are off.

Looking at the market in aggregate, we would anticipate that this should, with the exception of liquidity shocks, present an asymptotic resistance for the spot price of an asset. In our Treasuries example, the fundamental value is well defined, so it presents a pretty static barrier on what the price should never dip below. This maps quite well to empirical observation — a new issue Treasury (“on the run”) trades at a slight premium to off-the-run (old issue) Treasuries, largely due to the increased liquidity.

What’s interesting, however, is this also implies the converse about returns — if I am willing to pay more now for increased liquidity (the off-the-run vs on-the-run issues), I should similarly expect decreased returns, at least compared to an illiquid asset. Thankfully, this isn’t terribly speculative either; while it doesn’t happen in equities much anymore (thanks a lot, efficient markets), illiquidity is a well known excess returns factor, being documented by Amihud, Damoradan, and others by the early 2000s (if not earlier).

In my next post, I’m finally going tie a lot of these fancy concepts together into a neat framework and discuss how we can use these techniques to better understand potential valuations of meme stocks, cryptocurrencies, and our beloved non-fungible tokens.


  • Lily