Somebody shows me a strategy that returned some big number over a couple of years and asks if it is good. My first question is always the same. Compared to what. Because a strategy that leaned into a rising market and used a bit of leverage will look great on the surface, and most of that number is just beta doing its job. Jensen's alpha is the tool that tries to strip the beta out and tell you whether there was any real skill left over.
The idea is old and it is not complicated once you see the regression written down. Alpha is the piece of a strategy's return that its exposure to the market cannot explain. If the market went up and your thing has a beta of 1.2, you were supposed to make roughly 1.2 times the market's excess return. Anything you made above that predicted amount, on average, is your alpha. Anything below it is negative alpha, which is more common than people want to admit.
The regression, written out
Jensen's alpha comes straight out of the CAPM. You run a linear regression of your strategy's excess returns against the market's excess returns, and alpha is the intercept. The equation looks like this:
R_p minus R_f equals alpha plus beta times (R_m minus R_f) plus error.
R_p is your portfolio or strategy return over a period. R_f is the risk-free rate over that same period. R_m is the market return. You subtract the risk-free rate from both sides so you are regressing excess return on excess return. Beta is the slope, the sensitivity to the market. Alpha is the intercept, the average return you earned that the market did not hand to you.
The whole point of the intercept is that it captures the part of your return that is unrelated to how much market exposure you were carrying. If alpha is positive and holds up under scrutiny, you beat what your beta alone predicted. If it is zero, you are getting exactly paid for the risk you took, no more. That is the honest baseline, and most strategies sit there or below once you measure them properly.
Why the excess returns matter so much
The single most common mistake I see is people running the regression on raw returns instead of excess returns. They regress the strategy's return directly on the market's return, skip the risk-free rate entirely, and read the intercept as alpha. That number is wrong, and it is wrong in a direction that flatters you.
Here is the intuition. The risk-free rate is what you earn for taking no market risk at all. CAPM says your expected return is the risk-free rate plus a beta-scaled premium for the market risk you chose to take. If you leave R_f out of the regression, the intercept has to absorb it, and it gets folded into what you are calling alpha. So a chunk of your "skill" is actually just the return on cash that anyone could have earned by doing nothing.
The size of the distortion depends on the rate environment. When the risk-free rate is near zero, the error is small and easy to ignore. When rates are meaningfully positive, the error is large, and a strategy with low beta can show a fat positive alpha that is almost entirely the missing risk-free rate. If you are comparing two strategies with very different betas, this gets worse, because the low-beta one gets flattered more than the high-beta one. Always subtract the risk-free rate from both sides before you run anything.
Two practical notes on the risk-free rate. Use a rate that matches your return frequency. If your returns are monthly, convert the annual risk-free rate to a monthly figure, do not just paste the annual number in against monthly returns. And use the rate that applied during each period, not a single average, if rates moved a lot over your sample.
The mistakes that inflate alpha
Getting the excess returns right is necessary but not sufficient. A few other things quietly turn a real alpha estimate into a number you cannot trust.
- Survivorship in the sample. If your strategy universe only includes names that are still around, you have deleted the failures. The regression fits on the survivors, and alpha looks great because the dead weight is gone. This is the single biggest source of fake alpha in backtests.
- The wrong benchmark. Alpha is only meaningful relative to the R_m you regress against. If you run a crypto strategy against an equity index, or a small-cap strategy against a large-cap index, the beta is mismeasured and the leftover intercept is garbage. Pick a market that actually represents the opportunity set your strategy fished in.
- Too short a sample. Alpha is an average with a standard error, and over a short window that standard error is huge. A strategy can show a big positive intercept over one year that is statistically indistinguishable from zero. Look at the t-statistic on the intercept, not just its point value. A rule of thumb I use is that if the t-stat on alpha is below roughly 2, I treat the alpha as noise until proven otherwise.
- Ignored costs. Alpha computed on gross returns, before fees, slippage, and financing, is a fantasy for anything you actually trade. Compute it on net returns. A lot of "alpha" is really just the transaction costs you forgot to subtract, sitting there pretending to be skill.
- Non-linear exposure treated as linear. If your strategy sells options or has any convexity, its payoff is not a straight line against the market, and a single beta will not capture it. The regression will fit a line through a curve and dump the mismatch into alpha. Positive alpha from a short-volatility book is usually just premium you will give back in the next drawdown.
A quick workflow that keeps me honest. Pull the strategy's periodic returns and the matching market returns at the same frequency. Subtract the period risk-free rate from both. Regress strategy excess return on market excess return. Read the intercept as your alpha and the slope as your beta, and immediately look at the intercept's t-statistic and the regression's R-squared. If R-squared is very low, the market you chose barely explains your strategy and the alpha figure is not telling you much. If the t-stat is weak, you do not have enough evidence to claim skill. This is roughly the discipline we bake into the market scorecards on Blockcircle, because a raw return number on its own hides all of this.
None of this makes alpha a magic verdict. It is one lens, it assumes CAPM is a fair description of the world, and CAPM misses plenty. But computed carefully, on net excess returns, against the right benchmark, over a long enough sample, it answers a narrow and useful question. Did this thing earn more than its market exposure alone would have earned. Most of the time, once you clean it up, the answer is smaller than the person who sent you the strategy was hoping.