Every so often I try to run CAPM on a crypto position and get stuck before the math even starts. The formula is easy. Expected return equals the risk-free rate plus beta times the market premium. The problem is that CAPM assumes two things exist that do not cleanly exist in crypto. A market portfolio, and a risk-free asset. In equities you shrug and use the S&P 500 and a T-bill and move on. Here you have to actually choose, and the choice quietly decides what your beta and alpha even mean.
So this is less about the equation and more about the two inputs everyone glosses over. Both are judgment calls. Both are defensible in more than one direction. And both move your results enough that a coin can look like it beats the market or lags it depending only on what you compared it to.
The market proxy problem
CAPM wants the return of the whole investable market. In practice you approximate that with an index. In equities the S&P 500 is a fine stand-in because it is broad, cap-weighted, and correlated with almost everything else you might hold. Crypto does not have that clean anchor, so you end up choosing between a few candidates, none of which is obviously right.
The most common choice is Bitcoin itself. It is liquid, it has the longest history, and most other assets are heavily correlated with it anyway. The catch is that using Bitcoin as the market means Bitcoin has a beta of exactly one by construction. You have declared it the market. That is fine if your mental model is that Bitcoin is the risk factor everything else trades against. It is a problem if you actually wanted to measure Bitcoin against something broader, because now you cannot.
The second choice is a total crypto index. Something cap-weighted across the top assets. This is closer to the spirit of CAPM, a real diversified market portfolio. But it is dominated by Bitcoin and Ether in weight, so it behaves a lot like a slightly diluted Bitcoin. It also inherits every mess in index construction, like how you handle stablecoins, whether wrapped tokens get double-counted, and what happens when a top-ten asset collapses and rebalances out. The index is more correct in theory and more fragile in practice.
A third option people reach for is an equal-weighted basket, which stops Bitcoin from swallowing the whole thing. That surfaces the behavior of smaller assets, but it also loads up on tiny illiquid names and turns your market portfolio into something you could never actually hold at size. It measures a market nobody trades.
Here is the part that matters. Your beta is the covariance of the asset with the proxy divided by the variance of the proxy. Change the proxy and both terms change. Measure a mid-cap altcoin against Bitcoin and you might get a beta above one, because it moves harder than Bitcoin in both directions. Measure the same coin against an equal-weighted basket of similar alts and the beta can drop toward one, because now the benchmark itself is volatile in the same way the coin is. Same asset, same window, different story. The beta is not describing the coin in isolation. It is describing the coin relative to whatever you called the market.
The risk-free rate problem
The risk-free rate is supposed to be the return you get for taking no risk. In crypto, take that phrase literally and nothing qualifies. So you approximate again, and there are two honest camps.
The first camp uses the T-bill yield, the same short-term government rate equities use. The logic is that this is the true opportunity cost of capital denominated in dollars, and your crypto returns are usually measured in dollars anyway. It keeps you consistent with how the rest of finance defines risk-free, and it does not pretend any crypto instrument is safe.
The second camp uses a stablecoin lending or staking yield, the rate you would earn parking dollars inside the crypto system rather than outside it. The argument is that this is the real alternative for a crypto allocator. If you are not in a given coin, you are probably earning yield on stablecoins, not buying T-bills. So that yield is your actual next-best option.
I lean toward the T-bill for the base case and treat the stablecoin yield as a scenario, not the anchor. A stablecoin yield is not risk-free. It carries smart-contract risk, counterparty risk, and depeg risk, and it tends to spike exactly when the market is stressed, which is the worst possible time for your risk-free input to jump. A risk-free rate that rises during a crash is telling you something, and what it is telling you is that it was never risk-free. Using it inflates the number you subtract before computing excess returns and quietly flatters your alpha.
The size of the effect depends on where the asset sits. For a high-volatility altcoin, the risk-free rate is a rounding error, because monthly moves dwarf any plausible annual yield. For Bitcoin over a calmer stretch, or for anything you are levering, the choice starts to bite. Over a long flat window the risk-free rate can be the difference between a small positive alpha and a small negative one, and that sign flip is often the entire conclusion someone is trying to draw.
A workflow that survives contact
What I actually do is refuse to report a single beta or alpha from a single set of choices. I run the same asset against more than one specification and look at whether the story holds. If it does not hold, the story was an artifact of the benchmark, not a property of the asset.
- Pick a primary proxy and state it out loud. Bitcoin if you think of it as the risk factor, a cap-weighted total index if you want a real diversified market. Write down which one and why.
- Run a second proxy as a cross-check. If Bitcoin was primary, rerun against the index. If the beta flips from above one to near one, you have learned that most of the signal was Bitcoin correlation, not independent behavior.
- Use the T-bill yield as the base risk-free rate. Rerun with a stablecoin yield only as a sensitivity, and expect your alpha to shrink when you do. If the alpha only exists under the generous risk-free choice, it is not real.
- Match the sampling frequency to the holding period and keep it consistent across every run. Daily returns give you more data but more noise, and they annualize differently. Do not compare a daily beta to a weekly one and call it a change.
- Fix the window and reuse it everywhere. Beta is unstable in crypto, so a beta from a bull run and a beta from a chop range are different numbers about the same coin. Vary one input at a time.
The failure mode I see most is quietly shopping for the combination that makes a position look good. Bitcoin as the market, a fat stablecoin yield as the risk-free rate, a window that happens to start after the drawdown. Each choice is defensible alone. Stacked together they manufacture an alpha that evaporates the moment you change one input. When I build scorecards for this at Blockcircle, the rule is to show the beta and alpha under a couple of specifications side by side, so nobody mistakes a benchmark artifact for skill.
None of this makes CAPM in crypto rigorous. It just makes it honest about how much of the answer was baked in before the regression ran. Report the choices, not only the outputs, and let whoever reads it see how much the conclusion leans on them. Usually more than they would like.