**What Is Alpha in Investing?**

Alpha is one of five popular technical risk ratios. It measures past performance in relation to an appropriate benchmark index. The others are beta, standard deviation, R-squared, and the Sharpe ratio. All five ratios are used in modern portfolio theory (MPT). Investors use these indicators to help decide the risk-return profile of an investment.

Alpha is positive or negative and is a historical measure. With an alpha of two, with a baseline of zero, an investment has exceeded the returns of the market average by 2%. A negative alpha indicates the investment is underperforming when compared against the market average.

**Key Takeaways**

- Alpha is a measure of performance in relation to an index. Positive alpha shows movement higher than an index, while negative numbers show performance under the index over a period of time.
- Beta is a measure of volatility in relation to an index. Positive beta shows movement higher than an index, while negative numbers show performance under the index over a period of time.
- The Capital Assets Pricing Model (CAPM) calculates the level of return investors need to compensate them for the level of risk.
- Knowing the differences between alpha and beta, as well as the limitations, will help investors. While alpha compares returns, beta follows relative volatility against the overall market.
- Alpha is best geared for comparing stocks against an index, but an appropriate index may be hard to find for some investments.

## The Alpha Beta Equation

Image via Flickr by free pictures of money

Alpha and beta are terms often used when discussing investments. The two measures are part of the same equation obtained from a linear regression.

The formula for the basic model is:

y = a + bx + u

Therefore:

- y = performance of the stock or fund.
- a = alpha or the stock or fund’s excess return.
- b = beta or the volatility in relation to the benchmark.
- x = performance of the benchmark index.
- u = the residual or unexplained portion of the investment performance over a year.

## Defining Alpha

Alpha is a historic measure that shows how well a mutual fund or similar investment performs against a relevant benchmark index, often the S&P 500. Alpha is typically a single number; this number represents a percentage by which an investment outperforms or underperforms the index.

Compare the alpha over more extended periods of time to see the value of the investment related to the index it is seeking to outperform. This number can also show how well a portfolio manager has performed in an actively managed mutual fund compared to passively managed index funds.

Alpha goes back to the first weighted index funds to reach the market. Such funds attempt to mimic the performance of the overall market. They equally weigh each aspect of investment. Weighted index funds then led to a new measure of investment performance. Investors required portfolio managers of actively managed funds to have returns that were higher than those of passively managed funds. Alpha is used as the measurement tool for comparing active investments with index investing.

- An alpha value of 1, with a baseline being zero, shows the investment outperformed its index by 1% during a specified time frame. A negative alpha number indicates how the investment underperformed its index.
- An alpha of zero is given to an investment that equaled the return of the chosen benchmark index.
- Portfolio alpha is a calculation that shows the return it brings and the performance of the benchmark index. High alpha appeals to investors seeking a high return on investment (ROI).

The alpha ratio’s common counterpart is the beta coefficient, which gives a number to the volatility factor in investments. The Capital Assets Pricing Model (CAPM) uses alpha and beta to examine a portfolio of investments. CAPM assesses theoretical performance.

## Defining Beta

Beta is a historical measure of volatility in relation to a benchmark or the overall market. It measures the market risk of a security or portfolio compared to an index that matches its sector. Growth stocks often have a beta value over 1, while low-risk investments like T-bills have a value approaching zero because prices don’t move much compared to the entire market.

Beta is a multiplicative factor. An exchange-traded fund (ETF) with a beta close to 2 moves twice as much as the index over a specified time frame. A negative beta shows movement on the opposite of the index. A beta of -2 shows an investment moved in the opposite direction times two. Most investments with negative beta values hold funds that typically are a haven when markets decline.

Beta shows that risk can’t be completely diversified. Mutual fund beta figures show how much market risk they have.

High or low beta often leads to outperforming the market. A fund with many growth stocks and high beta typically outperforms the market in years of positive market growth. Funds that are conservative and focus on bonds have a low beta and most commonly do better than the S&P 500 when the market performs poorly.

## Capital Assets Pricing Model (CAPM)

The CAPM quantifies the return investors require in order to make up for a certain amount of risk. It takes the risk-free rate off of the expected rate, weighing it with a beta value to find the risk premium. The risk premium is then added to the risk-free rate of return (RoR) to calculate the RoR investors should expect to compensate them for the risks involved.

CAPM formula:

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

Such that,

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

Where:

- R = the return on the portfolio being analyzed.
- R
_{f}= the risk-free RoR. - Beta = a portfolio’s systematic risk.
- R
_{m}= the return of the benchmark, or the market for the portfolio.

## Difference Between Alpha and Beta

Investors use both alpha and beta ratios to calculate, compare, and predict their returns. Both ratios are based on benchmark indexes and compare specific securities or portfolios against the benchmarks.

Alpha is the risk-adjusted measure that compares a security to the overall market’s average return. The loss or profit relative to the benchmark represents the alpha. Beta, also known as the beta coefficient, measures the relative volatility of a security compared to average volatility in the overall market.

Volatility is another element of the level of risk in an investment. Its baseline for beta is 1. A security with a beta of 1 is in line with the benchmark index. If the beta is less than 1, the security’s price is less volatile than the market average.

A beta value over 1 means the security is more volatile than the market in general. An investment with a beta value listed at 2 is likely twice as volatile as the S&P 500 index. A -2 beta value doesn’t mean less volatility. Instead, it indicates the security tends to move in the opposite direction of the market in general by a factor of 2.

## Limitations of Alpha

Consider alpha’s limitations when using this tool. Alpha has limited success in comparing different types of funds. Investors can come up with misleading numbers if they use alpha to compare different types of investments. The diversity between an index and the investment will affect metrics like alpha and produce inaccurate results.

Alpha works best when used only for stock market investments rather than investments of other asset classes. If used as a fund comparison tool, then it is best applied to evaluating similar funds. For example, use alpha to compare two large-cap value funds instead of comparing a mid-cap growth fund and a large-cap value fund.

While the S&P 500 is the most common benchmark index for alpha value calculation, other benchmark indexes may be more relevant for a portfolio. Some portfolios may require using different indices to have an accurate comparison. Where relevant benchmark indices don’t exist, analysts use mathematical models to simulate an index.

Alpha and beta are both risk ratios that investors use to compare historical data and predict returns. They are both significant numbers, but investors must carefully look at the underlying ways they are calculated. While alpha measures historical performance against a benchmark index, beta focuses on volatility in relation to an index. Both measures require an appropriate index to create an accurate picture of performance.