# Alpha Coefficient

## Definition

The investing term alpha coefficient refers to a measure of an asset's risk-adjusted performance.  Alpha is a measure of "excess" returns and is frequently used along with beta values to judge the performance of an individual stock or mutual fund manager.

### Calculation

Alpha = Return of Asset - (Risk Free Rate + (Benchmark Return - Risk Free Rate) x Beta)

Where:

• Return of Asset = total return of an asset such as an individual stock or portfolio of stocks
• Risk Free Rate = total return of an investment which is thought to be risk free.  The return on Treasury Bills is often used as a proxy for the risk-free rate.
• Benchmark Return = in the case of common stocks this is the return provided by the entire market. The S&P 500 Index is often used as a proxy for the benchmark return.
• Beta = also known as beta coefficient, this is a measure of the relative volatility of the asset.

An online alpha spreadsheet is available to perform these calculations.

### Explanation

Alpha is a measure of an investment's return relative to its risk.  The calculation compares the investment's return to that of a risk-free security such as Treasury Bills, and relative to a benchmark such as the S&P 500 Index.

Interpreting alpha is fairly straightforward, and requires the knowledge of only three rules:

• Alpha < 0:  the investment has provided a return that is low relative to its risk; in the case of a mutual fund, the manager has destroyed value.
• Alpha = 0:  the investment has provided a return that is aligned with its risk; in the case of a mutual fund, the manager has neither created nor destroyed value.
• Alpha > 0:  the investment has provided a return that is high relative to its risk; in the case of a mutual fund, the manager has created value.

Like the beta coefficient, alpha is a key metric used in the capital asset pricing model.  The calculation of alpha had its beginnings when academics challenged the notion that mutual fund managers could consistently outperform what was thought to be an efficient market in terms of information.  To this day, it's often used to evaluate the performance of mutual fund managers.

### Example

The performance of Mutual Fund A's manager over the last three years was measured against the S&P 500 Index.  The spreadsheet referenced earlier indicates Company A's alpha was 0.10.  The interpretation of this value is as follows:

Since the alpha is greater than 0, Mutual Fund A's return is higher than predicted based on its risk.  In fact, with an alpha of 0.10, the mutual fund provided excess returns of 10%.  If the CAPM predicted a return of 5%, Mutual Fund A's returns were 15%.