The alpha is calculated by going back to the past performance of the shares, expressed in excess returns, and its calculation is derived from the formula:
To exemplify, assume a stock has a return of 25 percent. From this return 5 percent represents the short-term interest rate, which leaves an excess return of 20 percent (Ri). The market return is 9 percent (Rm), and the beta (b) of the stock is 2 (making it twice as risky as/more volatile than the market). This means that the risk associated with the stock is 18 percent. Since the actual return of the stock is 20 percent, and alpha is the risk adjusted indicator, this leaves the stock’s alpha at 2 percent.
Simply put, alpha is a value that the stock manager adds to or subtracts from the stock’s returns.
So the formula to calculate alpha is:
In the example, the alpha is positive, of 2 percent. This means that the stock outperformed the market by 2 percent, meaning that it produces excess returns compared to those expected. An alpha coefficient of 0 would have indicated adequate returns, while a negative alpha would indicate the stock underperformed compared to the market and that the returns are too low compared to the risks.