How long do you need to hold Bitcoin to beat the market, regardless of when you bought or sold?

Michael Saylor once claimed that you should never hold Bitcoin for less than four years because you are guaranteed to not lose money. The idea is that if you are holding a highly appreciating asset like Bitcoin, what really matters is the holding period rather than the specifics of when you bought or sold. If the asset appreciates enough, that appreciation will swamp the details of what specific price you bought or sold and, therefore, erase some of the stress from the volatility.

Let's evaluate this claim against Bitcoin price data. First, I'm going to generalize the conjecture to be: "If you hold Bitcoin for time x, you will be guaranteed to earn a return above y." Saylor took x = four years, and y = zero, but we can actually find what horizon gives the worst return on Bitcoin, and compare that to other investments, like the S&P500.

I'm going to use a trick from computer science called worst-case analysis. This is a method for evaluating algorithms when you don't necessarily have good information on uncertainty, and instead just want to ask how the algorithm would perform in a worst case. In this case, our "algorithm" is the return to holding Bitcoin, so we want to come up with a measure for the worst return from holding Bitcoin over different horizons. That is the lower bound on your return, since it will represent buying at the highest possible price and selling at the lowest possible price. This is your worst case.

Here's my method. I use daily Bitcoin price data from January 2011 to January 2024. For a fixed holding period, I calculate the return over all possible buys and sells. For example, consider a two year holding period , and compute the 2 year return from buying on 1/1/2011 and selling 2 years later, buying on 1/2/2011 and selling 2 years later, buying on 1/3/2011 and selling 2 years later, etc. That will generate a different return for each possible 2 year holding period. Find the lowest of those returns -- - that's the worst possible 2 year return. (If you're curious, the worst 2 year return was -46% per year, with a buy on 12/4/2013 and sale at 12/4/2015). Now repeat this calculation for all possible holding periods (2 years, 2.1 years, 2.2 years, etc). With this in hand, you can now plot the worst return as a function of the horizon:

Here are a few observations that are apparent. First, Bitcoin's volatility for short holding periods can lead to big losses, north of 75% of invested capital. That is the volatility that captures almost all attention in the financial press. What they don't realize is that volatility has both downside and upside. The upside appears on the right half of the graph, where Bitcoin's returns steadily increase, peaking at 150% per year if held for the full 13-year horizon, from January 1, 2011 to January 1, 2024.

Second, the graph is not monotonic. It does not steadily increase but has peaks and valleys. For example, Bitcoin's worst return crosses 0% first at 3.25 years, again at four and a half years, and finally at over five years. So after 5.09 years, no one would have lost money by investing in Bitcoin, since the worst return is a lower bound on their payoff. After 5.86 years, Bitcoin would return at least the stock market's historical return of 8%. After 6.08 years, Bitcoin would return at least Warren Buffett's historical return of around 22%. And after a little more than 10 years, Bitcoin will have returned more than 50% annually, greater than nearly all other investments.

Now let's compare Bitcoin against other assets:

While the worst return from holding the S&P 500 is positive after around three years, it never really takes off. You can see the greater volatility of Bitcoin, but also the higher returns. SPY looks very safe in comparison, but that safety comes at a price.

This graph shows the volatility of Bitcoin in a new light. The worst returns from other assets like gold, real estate, and bonds are (a) similar to each other, and (b) nearly flat compared to Bitcoin. It's true that other assets may not lead to large initial losses, but they also do not lead to longer-term gains. By way of comparison, the worst return from the S&P 500 exceeds 0% after 3.61 years, and 8% after 9.85 years. Similarly, it takes gold 12.38 years to escape breakeven in its worst case. This graph also gives the best indication that Bitcoin really is a new kind of investment. Notice how stocks, bonds, and real estate cluster together, while Bitcoin is markedly different.

What about a basket of tech stocks? Here are the worst returns of Bitcoin against those of Tesla, Apple, and Nvidia from January 1, 2011, to January 1, 2024:

Compared to the previous chart, the top tech stocks look more like Bitcoin, with larger losses for small holding periods and bigger gains for longer holding periods. It takes 4.23 years for Apple to guarantee a return of 0% and 6.83 years to exceed a return of 8%. It takes Tesla 5.71 years exceed break even, and it takes 6.21 years for Tesla to beat the historical stock market return of 8%.

Finally, here is Bitcoin against 9 large companies

Even if you had bought Bitcoin at the highest possible price and sold it at the lowest possible price, you would have eclipsed the worst return from all other stocks after year 10.

The graphs illustrate the value of scarcity. A bare economic logic governs the price of Bitcoin: the supply is fixed and predictable, while demand has increased. There is no other way for price to respond but to go up.

You may think, however, that all of this rests on social consensus: people want Bitcoin because they believe it to be valuable. That is true, but there is an important feedback loop here. The fixed supply is what makes it valuable, which in turn drives price up, which then attracts new buyers, which in turn increases demand, which then causes price to increase again, and so on. The fixed supply is existential for this feedback loop to occur. And that fixed supply is what is missing from all other investments, such as fiat currencies, gold, and real estate. So we may not have exactly returns of this same magnitude in the future, I cannot believe that the underlying forces at play will simply vanish altogether.

The analysis here is a snippet of a longer research paper on worst-case analysis that I'm writing for an academic audience. Bitcoin motivated this problem, but a worst-case metric can apply to any investment. All the data in the analysis above comes from publicly available resources, such as SPY for the S&P 500 and ETFs like GLD for tracking the return from gold. This is part of a longer project for worst-case returns. Subscribe to the paid version of this newsletter to see the full analysis, including the code for the computations.