Is it better to invest in Bitcoin or Bitcoin Miners?

Looking at risk and return from 2024.

On the one hand, bitcoin itself is the superior asset because it is the purest exposure to the Bitcoin network. On the other hand, Bitcoin miners are publicly traded corporations that raise capital, buy machines, and hire employees to convert fiat currency into bitcoin. Presumably, if these miners are successful in their business, they can do this efficiently and earn abnormal returns, at least compared to Bitcoin. And even though every miner may not beat Bitcoin, some surely can.

To examine this, let's consider the risk and return from a 2024 investment into Bitcoin against Bitcoin miners. I'm going to calculate the annual return over 2024, defined as a purchase on January 1, 2024, and a sale on December 31, 2024. So, the holding period is one full year, with no trading in between. For risk, I will use annual volatility, which is the standard deviation of log daily returns over a rolling one-year window.

Note that an alternative, possibly more conventional, approach to measuring risk and return is to use Sharpe ratios, which is a ratio of abnormal return over a risk-free rate divided by daily volatility. I prefer my method for two reasons. First, Sharpe ratios give you a single number, whereas I'm going to give you risk and return separately so you can see it in a graph. Second, the average daily return is the mean of the daily return over the year, but I'm more interested in holding the asset for the entire one-year horizon.

So here is the chart for the 2024 returns and volatility of Bitcoin against Bitcoin miners.