What is alpha?

Alpha is the part of an investment's return that cannot be explained by the market risk it took. It is the return a manager or strategy added through skill — or luck — rather than by simply being exposed to a rising market. A portfolio that beat the market by taking far more risk than the market has not necessarily produced any alpha at all.

The formula

In the capital asset pricing model (CAPM), the return an investment should earn for its market risk is:

E[R_p] = R_f + \beta_p \, (R_m - R_f)

where $R_f$ is the risk-free rate, $R_m$ the market's return and $\beta_p$ the portfolio's sensitivity to the market. Jensen's alpha is the difference between the actual return and that expected return:

\alpha = R_p - \left[ R_f + \beta_p \, (R_m - R_f) \right]

A positive alpha means the portfolio earned more than its market risk would explain; a negative one, less.

A simple illustration

Over a year, the risk-free rate is 2%, the market returns 10%, and a portfolio returns 13%. It beat the market by three points — but its beta is 1.4, so it is considerably more aggressive than the market:

E[R_p] = 2\% + 1.4 \times (10\% - 2\%) = 13.2\%

\alpha = 13\% - 13.2\% = -0.2\%

The portfolio earned about what its extra risk would have been expected to deliver, and slightly less. A defensive portfolio with a beta of 0.8 that returned 10%, merely matching the market, would have an alpha of +1.6%.

Beyond market risk

Many apparent sources of alpha turn out to be exposure to known factors: small companies, cheap value stocks, momentum or quality. In a multi-factor model, alpha is what remains after all of them:

R_p - R_f = \alpha + \beta_{\text{mkt}} (R_m - R_f) + \sum_k \beta_k F_k + \varepsilon

where $F_k$ are the factor returns and $\beta_k$ the portfolio's exposures to them. Measured this way, the alpha of most funds shrinks further.

How to read it

Alpha is relative to a model. It depends on the benchmark and the factors chosen; the same portfolio can show positive alpha against one model and none against another.
It needs a long record. Returns are noisy, and many years of data are needed before an alpha can be told apart from chance.
Costs come first. Before costs, all investors together earn the market's return; after costs, the average alpha is negative. That arithmetic is behind the success of low-cost index funds.

A worked example

Worked through on a sample portfolio. The figures below are that portfolio’s, not yours.

Am I outperforming because of skill or because of higher risk?

You have both higher returns and higher risk over the measured period. Here are the key figures from your portfolio so you can see how they sit together.

Metric	Value
Portfolio value (today) [€]	106.217,89 €
Total gain [€]	+23.302,52 €
Total return (%)	+40,46%
Time-weighted return (%)	+43,13%
Money-weighted return (%)	+11,31%
Annualized volatility (%)	16,00%
Daily volatility (%)	0,84%
Max drawdown (%)	-24,64%
Sharpe ratio	0,50
Sortino ratio	0,71

What this means (descriptive):

Your portfolio shows a strong positive return (+40,46%) alongside a relatively elevated annualized volatility (16,00%) and a material max drawdown (-24,64%).
The Sharpe (0,50) and Sortino (0,71) ratios summarise risk-adjusted performance: they reflect how much return you earned per unit of risk taken.
The difference between time-weighted (+43,13%) and money-weighted (+11,31%) returns shows performance as an investment manager (TWR) versus how your personal cash flows influenced results (IRR/MWR).

In short: your higher absolute returns come with measurable higher volatility and drawdowns, and your risk-adjusted metrics (Sharpe/Sortino) show the return per unit of risk rather than pure outperformance alone.

See these numbers for your own portfolio

Floreo works out every figure on this page from your own holdings — returns, risk, allocation, currencies — and the assistant explains them the way this page does. Import from your broker, or try it on the sample portfolio first.

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The demo opens straight away on a sample portfolio — no account needed.