Alpha

Alpha is the part of a fund manager's or a single security's performance that cannot be attributed to the movement of the market. First the risk-free rate is subtracted from the actual return, then the premium the portfolio was bound to earn simply because of its sensitivity to the index. Whatever is left is counted as alpha: the contribution of decisions rather than the contribution of market exposure.

What remains once the market is stripped out

The whole mechanism rests on a preliminary step: estimating beta. Beta tells you how much of the market's movement the portfolio takes on, and therefore what return it earns "for free", without any skill at all. If beta is measured inaccurately, the error migrates into alpha: understating beta in a rising market turns ordinary market gains into an illusory outperformance. Hence the dependence on the benchmark: the index chosen for comparison determines both the market return and beta itself, and it is easy to change. The second source of sensitivity is the calculation window: the same trading history, sliced into months or into weeks, produces a different beta and a different residual.

The persistence of alpha is judged not by its size but by its ratio to the dispersion of the residuals, which is what the information ratio measures. Where the Sharpe ratio compares performance with the portfolio's total volatility, alpha compares it with one specific cause: the market.

What it looks like in the data

Take Sberbank ordinary shares and a one-year window:

The chart provides the first term: the stock's return over the period. Beyond that you need exactly the same dates for the index, the stock's beta against it and the risk-free rate. Alpha appears only after the rate, and beta multiplied by the index's excess return, have been subtracted from the stock's return. A rise on the chart is not in itself alpha: for a high-beta stock it may be explained entirely by the market.

Where alpha gets substituted

The most common substitution is calling the simple difference between the portfolio's return and the index's return alpha. Without a beta adjustment this is not alpha but the result of heightened market exposure: leverage produces the same effect without any stock selection whatsoever. The second source of confusion is costs: alpha calculated before commissions, taxes and slippage describes a model, not an investor's account. Finally, in the logic of the efficient market hypothesis, positive alpha is not a property of the portfolio but a statement that the chosen risk model is incomplete: adding one more factor often eliminates the residual altogether.