Crypto Assets: Rethinking Risk and Volatility in this Emerging Market

Unheard of only a decade ago, crypto assets* have suddenly turned into a phenomenon attracting front-page headlines and worldwide attention. The top-selling digital coins like Bitcoin and Ethereum have captured the imagination of the investing public like no other financial assets in history.

Despite their mystique, a hallmark characteristic of crypto assets involves their ostensible jaw-dropping price volatility—that is, how much their prices vary over time. That volatility translates into risks of price declines that discourage many investors.

Who could blame them? Recently the price of Bitcoin collapsed in late May 2021, falling to less than half of its all-time high of $63,000 only five weeks before, and crashing the entire digital coin market along with it. But as soon as the following August, Bitcoin’s price rebounded. The coin regained almost $20,000 of those losses, or about 60 percent. And at the time of this writing in late September, Bitcoin’s price continues to gain upside momentum.

“Price whiplash” is a frequent complaint of investors too afraid to buy even small amounts of crypto assets. However, many ardent crypto adherents aren’t phased by digital coin price swings because they don’t think about volatility in the ways that most of us do. And believe it or not, those crypto bulls justify their optimism by relying on several of the quantitative analysis methods and textbook finance tools that MBA programs have taught for decades.

*BSchools doesn’t use the term “cryptocurrency” because the research we cite from the Yale/Rochester team could not establish that crypto assets function as a unit of account, like typical money. In fact, their research could not find any similarities between the behaviors of crypto assets and five major currencies; they include the Euro, Canadian Dollar, British Pound, Australian Dollar, and Singaporean Dollar.

Crypto’s Decreasing Volatility Trends

Since their introduction in 2009, the price volatility of crypto assets has indeed seemed remarkable when compared to equities and other traditional investments. For example, during much of the period through 2017, daily price fluctuations as large as 50 percent were not unusual for Bitcoin, despite the coin’s track record as of the more stable crypto assets.

By contrast, except for financial crises like the recent pandemic-induced stock market crash during March 2020, only rarely have traditional investment vehicles like stocks or bonds changed by such large percentages in any 24-hour period.

The charts on the Bitcoin Volatility Index present visual representations of these price trends. However, instead of absolute percentage changes, economists and investors prefer to evaluate volatility by using statistical measures of the variance in these daily price changes. That’s why the BVI’s charts plot trends in the standard deviations of daily price changes for the preceding 30 and 60 day periods instead of absolute fluctuations.

Nevertheless, irrespective of how one measures variance, an interesting trend appears in charts like these: the magnitude of the price oscillations has significantly decreased over time. These assets appear to be gradually losing their volatility.

In fact, two business school professors recently cited this trend in a high-profile 2020 paper evaluating the feasibility of crypto assets as investments, published by Oxford University’s Review of Financial Studies. This landmark study comprises the first comprehensive economic analysis of crypto assets and their underlying blockchain technology. Also, the paper likely provides the theoretical framework driving decisions late in the summer of 2021 by Goldman Sachs, Morgan Stanley, and JPMorgan Chase to offer crypto assets to their wealth management clients.

Dr. Aleh Tsyvinski, the Arthur M. Okun Professor of Economics at the Yale School of Management, and Dr. Yukun Liu of the Simon School of Business at the University of Rochester modeled eight years of the crypto coin market’s performance. Specifically, they built a value-weighted model encompassing returns from all 1,707 crypto coins in circulation from 2011 to 2018 with capitalizations exceeding a million dollars per coin.

They write:

We find that the standard deviation of coin market returns decreased significantly from the first half to the second half of the sample period. The figure in the Internet Appendix shows a significant decrease in the volatility of the coin market returns over time.

The research by Dr. Tsyvinski and Dr. Liu validates what the crypto bulls at ARK Investment Management and the newly public crypto exchange Coinbase Global have claimed for nearly five years.

Moreover, the analysts at ARK and Coinbase believe that the diminished volatility stems from a confluence of improving market characteristics, including “more stable and liquid spot exchanges, greater regulatory clarity, broader ownership, and increasingly reliable price discovery data.” If they’re correct, volatility should continue to diminish along with such continued market evolution and advances.

Crypto’s Astonishing Returns

Software entrepreneur and crypto industry superstar Michael Saylor loves to talk in his CNBC interviews about his 2020 “crypto epiphany.” Stuck at his home near Washington, DC during one of the first lockdowns during 2020, he learned a remarkable fact from a “deep dive” into internet resources later collected on his new website, Bitcoin is Hope.

Saylor found out that since 2009, Bitcoin yielded an average CAGR—a compound annual growth rate—of 200 percent. That’s when Saylor decided to sink every last penny belonging to his company, MicroStrategy Incorporated, into Bitcoin.

As this video montage illustrates, journalists and audiences certainly welcome Saylor’s crowd-pleasing flair for dramatic storytelling. But returns like these sound way too good to be true. Is his repeated assertion about Bitcoin’s 200 percent gains really accurate?

Actually, not all experts agree on that 200 percent figure. In half an hour of Google searching, one can find authoritative estimates all over the spectrum, some even higher than Saylor’s and a few even approaching as much as 250 percent. But what’s astonishing is that in an era of interest rates approaching negative levels, these crypto growth rate estimates seem phenomenal by any standards. In fact, BSchools’ research never uncovered any Bitcoin CAGR estimate lower than 75 percent. And what’s more, Saylor’s 200 percent estimate indeed stood confirmed by other authorities.

One way to find data with higher accuracy standards is to examine government filings. That’s because companies in the United States—and especially startups—need to be exceedingly careful never to knowingly and willfully make a materially false, fictitious, or fraudulent statement on any documents that they file with the federal government, and especially with the Securities and Exchange Commission. Doing that won’t just derail an entrepreneur’s chances of taking their startup public. Under the virtually limitless reach of Title 18, §1001 of the United States Code, intentionally lying to the SEC amounts to a felony punishable by prison sentences.

To enable Coinbase’s initial public offering, under the Securities Act of 1933, the exchange had to file a Form S-1 Registration Statement with the SEC. In that lengthy document, Coinbase precisely disclosed the average compound annual growth rate for the crypto industry. Here’s the exact quote:

The overall market capitalization of crypto assets grew from less than $500 million to $782 billion between December 31, 2012 and December 31, 2020, representing a compound annual growth rate, or CAGR, of over 150 percent.

By authorizing Coinbase’s IPO, the SEC essentially validated the S-1’s assertion as a fact on April 14, 2021, the day that the company went public on the Nasdaq stock exchange. That stunning 150 percent growth rate makes crypto assets the highest-earning investments in the history of economics. Whether we’re talking about stocks, bonds, mutual funds, precious metals like gold and silver, commodities, real estate, objets d’art, or any other investment, no other asset class even remotely approaches the historic long-term performance of crypto assets. And as this article points out, even the growth rate of Elon Musk’s stock in Tesla—with a 60 percent CAGR—still doesn’t even come close.

Crypto’s Risk-Adjusted Returns

Volatility along with returns are both necessary indicators to consider when evaluating any potential investment, including crypto assets. However, they are not sufficient characteristics. Today’s modern portfolio theory, as taught in MBA programs and practiced by successful investment managers, requires adjusting the returns to compensate for their volatility. That way, one can calculate a third indicator: the investment’s risk-adjusted return.

The Sharpe Ratio

Of these three indices, this third one is arguably the most interesting, in part because a Nobel laureate’s ingenious theory led to its derivation. This tool embodies a relatively new kind of financial ratio analysis, a decision-support approach that all MBAs learn during their courses in financial and managerial accounting, financial management, corporate finance, and investment principles.

Called the Sharpe ratio, this indicator was created by William F. Sharpe, the famous finance professor at the Stanford Graduate School of Business. Dr. Sharpe won the 1990 Nobel Prize in Economic Sciences for his pioneering work during the 1960s when he formulated the theory of financial asset price formation, the Capital Asset Pricing Model (CAPM).

The Sharpe Ratio’s Formula

Before we talk about what Sharpe’s ratio implies for crypto assets, let’s look more carefully at the ratio’s expression:

Sharpe Ratio = Rp – Rfσp


p The particular portfolio of financial assets
Rp The return expected from the portfolio
Rf The risk-free rate of return, such as the government bond rate
σp The portfolio’s risk, with the variance (sigma) expressed as the returns’ standard deviation

Interpreting Sharpe Ratios

Generally, Sharpe ratios above 1.0 are considered acceptable, with a portfolio’s values above 2.0 considered very good. Ratios above 3.0 are amazing—and extraordinarily unusual.

On the downside, any value under 1.0 is suboptimal. A negative value—corresponding with a negative return on investment—indicates that the portfolio manager would earn more revenue by liquidating the portfolio and instead investing in U.S. Treasury bonds.

Now, what do these values tell us? Briefly, the Sharpe ratio measures the return that exceeds the risk-free interest rate—such as the interest rate on government bonds—per unit of volatility measured through statistical variance. The ratio helps investors ascertain if higher returns accrue from smart investment decisions, or from assuming excessive risk. Two portfolios may offer comparable returns, but the Sharpe ratio identifies which portfolio requires more risk. Of course, higher returns with lower risk are always better, and comparing Sharpe ratios helps investors optimize that blend.

In other words, now investors have a common, normalized benchmark that they can use to help compare different financial assets despite profound differences in their volatility or returns. Using Sharpe ratios, investment managers can compare assets effectively because now they can standardize each dollar earned per unit of risk.

Other things equal, when comparing tradeoffs between two potential investments, investors will find themselves best compensated for their risks by the investment with the largest Sharpe ratio.

What Sharpe Ratios Reveal About Crypto’s Risk-Adjusted Returns

But what do Sharpe ratios have to do with decisions to invest in crypto assets? What’s surprising is that the Sharpe ratios clearly show that, per unit of variance, crypto assets like Bitcoin do not seem nearly as risky as the headlines claim. In fact, with Bitcoin, the exact opposite conclusion seems to instead hold true.

Extending back through June 2013, this interactive chart programmed by financial forecaster/analyst Willy Woo compares the risk-adjusted returns of Bitcoin with the risk-adjusted returns of five other major asset classes. These assets include stocks and real estate in the United States, bonds, gold, and emerging currencies. The chart also displays a second crypto coin, Ethereum, starting in the fourth quarter of 2019. In other words, the chart plots the Sharpe ratios of all these assets against each other on the same axis.

What can we conclude from Woo’s chart? In short, both Bitcoin and Ethereum have trounced all other asset classes, consistently producing superior risk-adjusted returns compared with all other competitors.

Moreover, remember what we said about interpreting the Sharpe ratios? Bitcoin and Ethereum have always returned Sharpe ratios above a very good 2.0. Furthermore, careful analysis reveals that Bitcoin equaled or exceeded an amazing 3.0 level during five of these years, most recently exceeding that level during 2019 and the second quarter of 2021.

How did some of the other asset classes perform? Stocks in the United States amount to the next-best class. The Sharpe ratio for stocks hovers around a 2.0 until early 2018, then dives and never again clears that level except for a single brief instance early in 2020.

Furthermore, Bitcoin is often referenced by Saylor and others as “digital gold,” but in terms of risk-adjusted returns, that’s a misleading comparison. Woo found that the Sharpe ratios of the digital coins are typically double to triple those of gold. Indeed, gold never clears a 1.0 until late in 2019 just before the pandemic hit, and even after a rally in prices, gold rarely does better than a Sharpe ratio of about 1.3. Meanwhile, down in the asset cellar, bonds are one of the worst performers; they are negative from mid-2019 onward.

In their paper, Dr. Tsyvinski and Dr. Liu concur:

We observe that the mean and standard deviation of the coin market returns are an order of magnitude higher than those of the stock returns during the same period. The Sharpe ratios at the daily and weekly levels are about 60 percent and 90 percent higher, and the Sharpe ratio at the monthly level is comparable to those of stocks.

What does this language mean? Dr. Tsyvinski explains:

We documented a high return but with a lot of volatility. Does the high return compensate for the high volatility? This is called the Sharpe ratio, which measures the performance of an asset by adjusting for risk.

Surprisingly, we found that cryptocurrency’s Sharpe ratio shows that the return is higher than the risk implied by its volatility. It’s higher than the Sharpe ratio for stocks and bonds, but not drastically so. There have been asset classes and trading strategies with Sharpe ratios that are either the same or similar to cryptocurrencies. So if you just look at return versus volatility, cryptocurrency looks more or less normal.

In other words, Dr. Tsyvinski’s analysis is that these higher Sharpe ratios indicate that investments in crypto assets are worthwhile because their superior returns more than compensate for these assets’ added volatility. But his explanation still doesn’t answer the big asset allocation question on the minds of most investors: “How much crypto should a typical investor hold?”

The conclusion of an earlier version of this paper published by the National Bureau of Economic Research thoroughly addresses that question. Dr. Tsyvinski summarized that analysis for YaleNews:

If you as an investor believe that Bitcoin will perform as well as it has historically, then you should hold 6 percent of your portfolio in Bitcoin. If you believe that it will do half as well, you should hold 4 percent. In all other circumstances, if you think it will do much worse, then you should still hold 1 percent.

Of course, one has to remember that, as with any other assets, past performance is not a guarantee of future returns. Maybe cryptocurrency will completely change its behavior, but currently, the market does not think it will.

Disclaimer: BSchools does not intend this article as a basis for our audience’s decisions about any potential or current investments, nor a recommendation to buy or sell any investments, including securities and crypto assets. In no event can BSchools be held responsible for the investment-related actions of our readers. As all MBA students and graduates should know, crypto asset transactions involve substantial risk and can swiftly result in the unexpected loss of invested capital. Ensure that you thoroughly understand the full extent of all risks involved and consider your level of trading experience before executing any transactions. Even prospective and current MBA students with trading work experience before business school find that advice from objective investment professionals with even more experience provides valuable learning experiences. We encourage you to consult with such advisors routinely before executing any significant investment transactions.

Douglas Mark
Douglas Mark

While a partner in a San Francisco marketing and design firm, for over 20 years Douglas Mark wrote online and print content for the world’s biggest brands, including United Airlines, Union Bank, Ziff Davis, Sebastiani, and AT&T. Since his first magazine article appeared in MacUser in 1995, he’s also written on finance and graduate business education in addition to mobile online devices, apps, and technology. Doug graduated in the top 1 percent of his class with a business administration degree from the University of Illinois and studied computer science at Stanford University.

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