Consequences of Small Price Bias in Crypoasset Markets and their Implications for Token Issuers

Introduction: Asset prices matter

To a rational value investor, the prices immediately before and immediately after a 3:1 stock split are immaterial. The fact that the stock now trades at $20 instead of $60 does not change the market capitalization of the underlying business unit. It also does not alter the underlying’s ability to generate future cash flows or change the likelihood that it will succeed in a competitive market. Rationally, the post-split $20 stock is not “cheaper” than the pre-split $60 stock.

But humans are not rational agents. Many retail investors who would not have considered the stock at $60 would take another look at $20. And they would do so for the sole reason that 20 is less than 60.

Before the advent of fractional share trading, stock splits fulfilled their goal of expanding retail access by way of lower share prices. But brokerages have been offering fractional share trading for years. Beyond possible liquidity gains of a lower share price, there is little material benefit to a lower share price. It thus stands to reason that companies do stock splits mainly for marketability purposes. Boards and leadership teams have considered the relationship between the share price and the perceived expensiveness of their stock, and have sometimes determined that a stock split is the correct decision in the pursuit of maximizing shareholder value.

This is a curious state of affairs. Blue chip equities, which see the vast majority of their trading volumes from institutional investors, evidently make decisions in part based on the perceived marketability of their stock price.

Crypto Motivations

Let’s consider the cryptoasset market, in which retail activity is vastly more important than it is in TradFi. Without fundamentals, other traditionally used financial characteristics, or an institutional investment apparatus, perceived value is the primary barometer that reflects market decisions.

If asset price matters in TradFi, then it is certainly of consequence in crypto. If blue chip equities, which enjoy trading primarily from index funds, feel the need to manage the perceived availability of their stock, then token issuers, which operate in a much more retail-driven space without fundamentals, ought to as well.

One working approach to this behavior in crypto is as follows. If the psychological bias of small prices influences markets, we would expect lower-price coins to outperform higher-price coins, even after controlling for market capitalization. The result would be due to a portion of retail holding the belief that, all else equal, low-price tokens are “cheaper” than high-price ones.

Real-world examples

Let’s consider a few examples to materialize the above conceptual approach.

Some individuals engaged with cryptoassets erroneously categorize projects and hold several untrue assumptions. Consider ETH and ETC, around which I’ve heard the following on several occasions: “Why would I pay $3,500 for ETH when ETC is only $55? It’s all Ethereum; it says it right in the name!” And in the same vein, the focus is often on price rather than on market cap. “ETC will 40x just to catch up to ETH.”

Furthermore, and perhaps due to the Dogecoin mania, there’s a feverish and incongruous focus on the $1 price point. We’ve all likely seen the TikTok shills and YouTube pumps: “Shitcoin x is only a third of a penny. When it moons to a dollar, a $1,000 investment would be over $300,000.” A project with a token that already trades at $17 doesn’t quite hold the same grandeur.

Additionally, many find it pointless to own less than one of something. A fractional unit of an asset might not produce an investment experience. Retail investing has been turned upside down in the past year by what we can broadly refer to as the WallStreetBets movement. For many, investing is no longer only a financial decision, but a social one as well. Agents consider not only financial returns, but also experiential rewards, social capital, FOMO, when making decisions. In other words, what’s the point? “Why would I buy BTC when I can only afford 3% of a coin?”

The above logical fallacies are human nature and will not be going away anytime soon. After all, their apparent persistence in TradFi seem in part the reasoning behind the continued existence of stock splits.

Analysis plan

This analysis has two main components.

1. Assess market performance and volatility of low-price coins relative to high-price coins.

2. Discuss the consequences of the results for token issuers.

Before getting into the results, consider the following data from TradFi. Several studies associate stock splits with high resulting performance in asset value. David Ikenberry, Chairman of the Finance Department at the University of Illinois at Urbana-Champaign conducted a 2003 study on the effect of stock splits in the equities markets. Between 1990 and 1997, shares of split stocks (N = 1,275) outperformed the market by 8% in the one year period following the split and by 12% in the three year period following the split. His 1996 study, which looked at splits between 1975 and 1990, reported figures of 8% and 16%, respectively.

Results: Volatility

Before looking at asset performance, let’s collect some qualifying evidence for our theory. Another reasonable consequence of our assumptions is that, even after controlling for market cap, low-price coins should be more volatile than high-price coins. The psychological bias of small prices should render these coins more speculated on, and thus more volatile.

We run a multivariate linear regression model to quantitatively assess this notion.

Where yi is volatility over the period (annualized standard deviation of daily log returns), xi1 is log price at the beginning of the period and xi2 is log market cap at the beginning of the period.

Even after controlling for market cap, price is a statistically significant feature (p = 0.009155). The model estimates that a 10x increase in price – for the same market cap – decreases annualized volatility by about 6.8 percentage points.

Asset price, irrespective of market cap, is associated with volatility in the cryptoasset markets. It stands to reason that lower price assets are more speculated on.

Note: It’s important to say that while this result is interesting, causation is not strictly implied. For there are tracks of reasoning that traverse in both directions between token price and volatility. For example, token price at onset of a project is not a random variable; it is endogenously determined by founders/developers, who select the supply schedule and are acting out their own vision for the project based upon knowledge of market behavior. It’s unclear how much the increased volatility of low-price coins is due our explanation of retail trading behavior, or other unmeasured factors.

Results: Returns

Now that we’ve established that low-price tokens are more volatile than high-price tokens (even after controlling for project valuation), let’s look at cumulative returns over a time period.

It wouldn’t be surprising if coins with lower prices outperformed higher price coins during a bull market, since lower-priced coins are often smaller projects with more upside. So it’s important to control for market cap. We split cryptoassets into three market cap categories and four price categories.

Market cap dominance categories:

  • 0 < MKD ≤ 0.0002
  • 0.0002 < MKD ≤ 0.002
  • MKD > 0.002

Price categories ($):

  • 0.00 < price ≤ 0.05
  • 0.05 < price ≤ 1.00
  • 1.00 < price ≤ 10.00
  • Price > 10.00

Cumulative Returns

  1. During the period considered, low price tokens outperformed higher price tokens
  2. Lower price tokens outperformed higher price tokens in all market capitalization categories, but the effect appears larger for less valuable projects.

Not stratified by market capitalization

Stratified by market capitalization

Model

We run the multivariate linear regression model over the period to ascertain a numerical estimate for the effect of starting price on cumulative returns.

Where yi is the log return multiple (price on the last day of period / price on the first day of period), xi1 is the log price at the beginning of the period and xi2 is log market cap at the beginning of the period.

The visual evidence holds up statistically. The model associates a price decrease of 90%, which is the change associated with a 10 to 1 split, 13.58% increase in the yearly return multiple.

Consistency of Relationship

Another interesting observation is that the relationship between cumulative returns and price is not consistent over time.

The majority of performance differences among price groups were accumulated in short periods during bull markets (e.g. April 2021). This asymmetry is not surprising and is expected under the previously discussed understanding of the behavioral consequences of small price bias.

Remember what we’re showing here. Token price, after controlling for market cap, should not matter. To the extent that we can regard token price at the beginning of a period as exogenous, the measured effect of price on returns could be the product of retail acting out the logical fallacies of small price bias. Namely, there is a portion of retail that believes small price tokens are “cheap,” destined to catch-up in price to other assets (ETC and ETH), or imminently awaiting a breakout to the $1 price point.

Such irrational behavior will show itself more strongly in exceptionally euphoric times, like the month of April of this year. We can roughly refer to the additional gains accrued by low-price tokens as an “irrationality premium”. In accelerated bull markets, oftentimes when new and uninformed agents enter the space, the “irrationality premium” will be higher. It’s also not surprising that the effect was stronger for lower market cap projects. Irrational decision-makers can more easily sway prices for smaller projects.

It’s also possible to consider the “irrationality premium” as a market barometer, a froth-meter to assess when valuations are getting out of hand. Low price tokens massively outperforming higher ones is a strong indication of retail froth and euphoric speculation. There unfortunately haven’t been enough market cycles to test this idea.

Results Interpretation

Let’s quantify the effect during different time periods and report the increase in the yearly return multiple associated with an 10-1 token split.

  1. Bull market of December 1, 2020 to May 5, 2021: 33.103% (pval = 0)
  2. Flat market of April 15, 2020 to August 31, 2020: 5.386% (pval = 0.473789)

Highlight: The model associates price as a significant feature of returns development during bull markets. There is reason to believe that billions of dollars of value have been created in cryptoasset markets by the psychological fallacies associated with low prices.

Results Summary

Key results:

  1. Price is inversely associated with volatility, even after controlling for market capitalization.
  2. Price is inversely associated with cumulative returns, even after controlling for market capitalization. This relationship appears strongest during euphoric stages in bull markets and for smaller value projects.

There’s evidence to suggest that these results are due to small price bias and its consequences on retail behavior. During bull markets, and especially so in exceptionally accelerated times, low-price tokens enjoy an “irrationality premium.”

What will be interesting to see going forward is what fraction, if any, of the “irrationality premium” holds during a bear market. A look-back at 2017 data weakly indicates that the effects of low-price persist following a market crash. But markets are much different now than they were in 2017.

Logic indicates that these supposed mis-pricings will readjust as the market matures. But on the other hand, the continued existence of stock splits in TradFi suggests that traditional financial markets have retained some irrationality.

Implications for token issuers

Token issuers take note: the perceived affordability of your token matters. A lot. In fact, it seems to be a large driver of volatility and price discovery during bull markets.

For current projects: Consider how token price, especially if very high or low, might impact retail activity around the project in different market conditions For future launches: A low price seems to attract increased speculation during bull markets. This quality might be desirable or undesirable.

If the effects of small price bias are important for a project, it’s not unreasonable to propose a token re-denomination (stock-split).

The reasoning on price and perceived affordability can also be generalized. In crypto, perception matters. A lot. This notion has very general consequences, but one thing is clear. The set of decisions affecting perception and the perceived availability of the token should be taken with care and attention.

Conclusion

There’s evidence to suggest that small price bias is a driver of price discovery, especially so in bull markets, when low-price tokens enjoy a large “irrationality premium.” It will be interesting to see how the relationship between token price and project valuation evolves as the cryptoasset market matures and an institutional investment apparatus develops.

But one thing is certain. The fallacies of human reasoning are not going away anytime soon. There is reason to believe that billions of dollars of value have been created in cryptoasset markets by the psychological fallacies associated with low prices. As a result, token issuers must confront this evidence and consider the impact of the token price on retail activity and the perceived affordability of the token.