## What is Alpha?

Alpha is a measure of the performance of an investment as compared to a suitable benchmark index, such as the S&P 500. An alpha of one (the baseline value is zero) shows that the return on the investment during a specified time frame outperformed the overall market average by 1%. A negative alpha number reflects an investment that is underperforming as compared to the market average.

Alpha is one of five standard performance ratios that are commonly used to evaluate individual stocks or an investment portfolio, with the other four being beta, standard deviation, R-squared, and the Sharpe ratio. Alpha is usually a single number (e.g., 1 or 4) representing a percentage that reflects how an investment performed relative to a benchmark index.

A positive alpha of 5 (+5) means that the portfolio’s return exceeded the benchmark index’s performance by 5%. An alpha of negative 5 (-5) indicates that the portfolio underperformed the benchmark index by 5%. An alpha of zero means that the investment earned a return that matched the overall market return as reflected by the selected benchmark index.

The alpha of a portfolio is the excess return it produces compared to a benchmark index. Investors in mutual funds or ETFs often look for a fund with a high alpha in hopes of getting a superior return on investment (ROI).

The alpha ratio is often used along with the beta coefficient, which is a measure of the volatility of an investment. The two ratios are both used in the Capital Assets Pricing Model (CAPM) to analyze a portfolio of investments and assess its theoretical performance.

### Origin of Alpha

The concept of alpha originated from the introduction of weighted index funds, which attempt to replicate the performance of the entire market and assign an equivalent weight to each area of investment. This development as an investing strategy created a new standard of performance.

Basically, investors began to require portfolio managers of actively traded funds to produce returns that exceeded what investors could expect to make by investing in a passive index fund. Alpha was created as a metric to compare active investments with index investing.

### Capital Assets Pricing Model (CAPM)

The CAPM is used to calculate the amount of return that investors need to realize to compensate for a particular level of risk. It subtracts the risk-free rate from the expected rate and weighs it with a factor – beta – to get the risk premium. It then adds the risk premium to the risk-free rate of return to get the rate of return an investor expects as compensation for the risk. The CAPM formula is expressed as follows:

**r = R**_{f} + beta (R_{m} – **R**_{f}) + Alpha

_{f}+ beta (R

_{m}

_{f}) + Alpha

Therefore,

**Alpha= R ****– ****R**_{f} – beta (R_{m}-R_{f})

_{f}– beta (R

_{m}-R

_{f})

Where:

**R**represents the portfolio return**R**represents the risk-free rate of return_{f}**Beta**represents the systematic risk of a portfolio**R**represents the market return, per a benchmark_{m}

For example, assuming that the actual return of the fund is 30, the risk-free rate is 8%, beta is 1.1, and the benchmark index return is 20%, alpha is calculated as:

Alpha = (0.30-0.08) – 1.1 (0.20-0.08)

**= 0.088 **or **8.8%**

The result shows that the investment in this example outperformed the benchmark index by 8.8%.

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### Limitations of Alpha

Alpha comes with a few limitations that investors should consider when using it. One of these limitations relates to various types of funds. Some investors use the ratio to compare different types of portfolios, such as portfolios that invest in different asset classes, and this can result in misleading numbers. The diverse nature of the different funds will affect metrics such as alpha.

Alpha works best, first of all, when applied to strictly stock market investments (rather than to investments in other asset classes), and secondly, if used as a fund comparison tool, then it is best applied to evaluating similar funds – for example, two mid-cap growth mutual funds, rather than, say, comparing a mid-cap growth fund with a large-cap value fund.

Another consideration for investors is choosing a benchmark index. The alpha value is calculated and compared to a benchmark that is deemed appropriate for the portfolio. Investors should select a relevant benchmark. The most frequently used benchmark index is the S&P 500 stock index.

However, some portfolios, such as sector funds, may require using a different index in order to have an accurate comparison. For example, to evaluate a portfolio of stocks invested in the transportation sector, a more appropriate index benchmark would probably be the Dow transportation index. Where there are no pre-existing, appropriate benchmark indices, analysts may use algorithms and other models to simulate an index for comparative purposes.

### Difference between Alpha and Beta

Investors use both the alpha and beta ratios to calculate, compare, and predict investment returns. Both ratios use benchmark indexes such as the S&P 500 to compare against specific securities or portfolios.

Alpha is the risk-adjusted measure of how a security performs in comparison to the overall market average return. The loss or profit achieved relative to the benchmark represents the alpha. Beta, also referred to as the beta coefficient, measures the relative volatility of a security in comparison to the average volatility of the total market.

Volatility is another component of the level of risk associated with a given investment. The baseline number for beta is one. A security with a beta of one exhibits roughly the same level of volatility as the benchmark index. If the beta is less than one, that means that the security’s price is less volatile than the market average.

A beta value greater than one means that the security’s price is more volatile than the market average. For example, a security with a beta value of two can be expected to exhibit twice as much volatility as the S&P 500 index. If the beta value is negative, that does not mean less volatility – it means that the security tends to move inversely to the direction of the overall market, by a factor of two.

### Related Readings

CFI aims to provide you with a world-class education as a financial analyst. To learn more about evaluating investments, the following resources will be helpful: