You will often come across the terms alpha and beta when talking about investments. These are two different measures that are part of the same equation stemmed from a linear regression. Don’t fear if that sounds too complex, we’ll explain it all in this article.

The article explores Alpha and Beta in depth, how alpha and beta are calculated and CAPM alpha formula.

Table of Contents

## What is Alpha in Finance?

The term “alpha” refers to the measure of the highest return possible from a minimum amount of investment risk. In other words, alpha is the evaluation tool to measure the ability of a portfolio manager to produce a higher return on a risk-adjusted basis. The formula for alpha can be derived by subtracting the expected return of the portfolio from its actual return.

Even Though the Alpha figure is often shown as a single number (like 3 or -5), it actually explains a percentage that measuring how a stock of mutual fund performed compared to a standard index. The numbers stated would mean the investment respectively performed 3% better and 5% worse than the broader market. Hence, an alpha of 1.0 means the investment outperformed its standard index by 1%, while on the other hand, an alpha of -1.0 means the investment underperformed its standard index by 1%.

For example, if you invest in a stock, and it returns 20% while the S&P 500 earned 5%, the alpha is 15. An alpha of -15 would imply that the investment underperformed by 20%.

Alpha is also a measure of risk. In the above example, the -15 suggests the investment

was far too unsafe given the return. An alpha of zero suggests that investment has earned a return equal to the risk. Alpha of greater than zero means an investment outperformed.

Remember, alpha is a historical number. It’s beneficial in tracking a stock’s alpha over time to see how it performed, but it can’t inform you how it will do tomorrow.

For individual investors, alpha facilitates in indicating how a stock or fund might perform in relation to its contemporaries or to the market as a whole.

Professional portfolio managers calculate alpha as the rate of return that surpasses the model’s prediction or comes short of it. They use a capital asset pricing model (CAPM) to forecast the potential returns of an investment portfolio.

If the CAPM analysis suggests that the portfolio should have earned 5%, based on risk, economic situations, and other factors, but instead the portfolio earned just 3%, the alpha of the portfolio would be a disappointing -2%.

Portfolio managers pursue to generate a higher alpha by expanding their portfolios to balance risk.

### CAPM Alpha Formula

The CAPM is used to calculate the amount of return that investors need to be aware of 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 anticipates as compensation for the risk. The CAPM alpha formula is expressed as follows:

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

Therefore,

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

Where:

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

For instance, assume 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 demonstrates that the investment in this example outperformed the standard index by 8.8%.

### How to Calculate Alpha in Excel?

To calculate alpha in excel lets assume a portfolio with a Beta of 1.5 that produced an Actual Return of 6% during last year. If the current Market Return is 4% and the Risk-Free Rate is 2%, then calculate the Alpha of the Portfolio.

Solution:

Market Risk Premium is calculated using the formula given below

Market Risk Premium = Market Return – Risk-Free Rate

- Market Risk Premium = 4% – 2%
- Market Risk Premium = 2%

The Expected Rate of Return is calculated using the formula given below

Expected Rate of Return = Risk-Free Rate + β * Market Risk Premium

- Expected Rate of Return = 2% + 1.5 * 2%
- Expected Rate of Return = 5%

Alpha is calculated using the formula given below

Alpha = Actual Rate of Return – Expected Rate of Return

- Alpha = 6% – 5%
- Alpha = 1%

Therefore, the Alpha of the Portfolio is 1%.

Now let us take another example of a Portfolio of three securities yielding Actual Returns of 5%, 8%, and 7% during last year. The beta of the Respective Securities are 1.2, 1.5, and 1.0 and their Weight in the Portfolio is 0.30, 0.45, and 0.25. S&P 500 is the suitable standard index for the Portfolio and it Realized a Return of 4.74% during the last one year. The 10-year treasury bill currently offers a Return of 2.07%. Based on the given information, determine whether the Portfolio Manager could generate any Alpha.

Solution:

Actual Rate of Return is calculated as:

- Actual Rate of Return = (0.30 * 5%) + (0.45 * 8%) + (0.25 * 7%)
- Actual Rate of Return = 6.85%

Portfolio Beta is calculated using the formula given below

- Portfolio Beta = (0.30 * 1.2) + (0.45 * 1.5) + (0.25 * 1.0)
- Portfolio Beta = 1.29

Market Risk Premium is calculated using the formula given below

Market Risk Premium = Market Return – Risk-Free Rate

- Market Risk Premium = 4.74% – 2.07%
- Market Risk Premium = 2.67%

The Expected Rate of Return is calculated using the formula given below

Expected Rate of Return = Risk-Free Rate + β * Market Risk Premium

- Expected Rate of Return = 2.07% + 1.29 * 2.67%
- Expected Rate of Return = 5.50%

Alpha is calculated using the formula given below

Alpha = Actual Rate of Return – Expected Rate of Return

- Alpha = 6.85% – 5.50%
- Alpha = 1.35%

### Advantages of Alpha in Finance

Alpha can provide fund managers a general idea of how their portfolios are doing compared to the rest of the market. In trading and investing, alpha can be a useful tool for determining market entry and exit points.

### Disadvantages of Alpha in Finance

Using alpha as a method to calculate returns has its drawbacks – it cannot be used to compare different investment portfolios or asset types, as it is limited to stock market investments.

There is a lot of discussion about the accuracy of alpha as a measurement. According to the efficient market hypothesis (EMH), all securities are always correctly priced, so it would be impractical to identify and take advantage of mispricing. If EMH is true, there would be no way to ‘beat’ the market, and alpha would not be present.

## What Is Beta in Finance?

Beta is a measure of the volatility—or systematic risk—of a security or portfolio compared to the market as a whole. Beta is used in the capital asset pricing model (CAPM), which illustrates the relationship between systematic risk and expected return for assets (usually stocks). CAPM is commonly used as a method for pricing risky securities and for producing estimates of the expected returns of assets, taking into account both the risk of those assets and the cost of capital.

### How Beta is Calculated?

A beta coefficient can assess the volatility of an individual stock compared to the systematic risk of the entire market. In numerical terms, beta signifies the slope of the line through a regression of data points. In finance, each of these data points represents an individual stock’s returns against those of the market as a whole.

Beta successfully describes the activity of a security’s returns as it reacts to fluctuations in the market. A security’s beta is calculated by dividing the product of the covariance of the security’s returns and the market’s returns by the variance of the market’s returns over a specified period.

Beta is calculated using the following formula:

Beta coefficient(β) =

where:

Re = the return on an individual stock

Rm = the return on the overall market

Covariance = how changes in a stock’s returns are related to changes in the market’s returns

Variance = how far the market’s data points spread out from their average value.

The beta calculation is used to assist investors to comprehend whether a stock moves in the same direction as the rest of the market. It also gives insights about how volatile–or how risky–a stock is comparative to the rest of the market. For beta to offer any useful insight, the market that is used as a benchmark should be associated with the stock. For example, calculating a bond ETF’s beta using the S&P 500 as the standard would not provide much useful insight for an investor because bonds and stocks are too different.

Eventually, an investor is using beta to try to determine how much risk a stock is adding

to a portfolio. While a stock that differs very little from the market doesn’t add a lot of risk to a portfolio, it also doesn’t increase the possibility for greater returns.

In order to make sure that a specific stock is being compared to the right benchmark, it should have a high R-squared value in relation to the benchmark. R-squared is a statistical measure that shows the percentage of a security’s historical price movements that can be described by movements in the benchmark index. When using beta to ascertain the degree of systematic risk, a security with a high R-squared value, in relation to its benchmark, could imply a more relevant benchmark.

One way for a stock investor to think about risk is to divide it into two categories. The first category is called systematic risk, which is the risk of the entire market declining. The financial crisis in 2008 is an example of a systematic-risk event; no amount of diversification could have stopped investors from losing value in their stock portfolios. Systematic risk is also known as un-diversifiable risk.

Unsystematic risk, also known as diversifiable risk, is the ambiguity associated with an individual stock or industry. This risk is specific to a company. Unsystematic risk can be partially alleviated through diversification.

### Types of Beta Values

Beta Value Equal to 1.0

If a stock has a beta of 1.0, it implies that its price activity is strongly correlated with the market. A stock with a beta of 1.0 has systematic risk. But, the beta calculation can’t detect any unsystematic risk. Adding a stock to a portfolio with a beta of 1.0 doesn’t add any risk to the portfolio, but it also doesn’t increase the possibility that the portfolio will provide an excess return.

Beta Value Less Than One

A beta value that is less than 1.0 indicates that the security is theoretically less volatile than the market. Including this stock in a portfolio makes it less risky than the same portfolio without the stock. For example, utility stocks often have low betas because they are likely to move more slowly than market averages.

Beta Value Greater Than One

A beta that is greater than 1.0 suggests that the security’s price is theoretically more volatile than the market. For example, if a stock’s beta is 1.2, it is assumed to be 20% more volatile than the market. Technology stocks and small-cap stocks are likely to have higher betas than the market standards. This shows that adding the stock to a portfolio will increase the portfolio’s risk, but may also increase its expected return.

Negative Beta Value

Some stocks have negative betas. A beta of -1.0 will indicate that the stock is inversely correlated to the market standard. This stock could be thought of as an opposite, mirror image of the benchmark’s trends. Put options and inverse ETFs are created to have negative betas. There are also a few industry groups, like gold miners, where a negative beta is also common.

## Calculation of Beta in Finance

### Variance-Covariance Method

The beta of a security is calculated as the covariance between the return of the market and the return on security divided by the variance of the market.

Beta = Covariance of the Market and the Security/ Variance of the Security

Let’s suppose a portfolio manager wants to calculate beta for Apple incorporation and wants to include it in its portfolio. He decides to calculate it against its benchmark, the S&P 500. Based on the past years’ data, Apple incorporation and S&P has a covariance of 0.032, and the variance of S&P is 0.015. Calculate Beta for Apple.

Beta of Apple = 0.032/0.015 = 2.13

### Standard Deviation and Correlation Method

Beta can also be calculated by dividing –Standard Deviation of the return of the securities divided by the standard deviation of the returns of the benchmark.

This value is then multiplied by the correlation of the market and securities returns.

An investor is looking to invest in Amazon but was concerned about the volatility of the stock. He, therefore, decided to calculate Beta for Amazon in comparison to the S&P 500. Based on the past data, he found out that the correlation between the S&P 500 and Amazon is 0.83. Amazon has a standard deviation of returns of 23.42% while S&P 500 has a standard deviation of 32.21%. Calculate Beta for Amazon.

Beta = 0.83 x (23.42% divided by 32.21%)= 0.60

The beta for the market is 1, while for Amazon is 0.60. It shows that the beta for Amazon is lower than the market, and it means that the stock has experienced 40% less volatility than the market.

### Advantages of Beta in Finance

The most common use of a beta is to calculate the cost of equity while performing valuations. The CAPM uses beta to calculate the systematic risk of the market. In general, this can be used to value a lot of companies with a variety of capital structures.

Beta is the only measure that facilitates the investors to understand stock volatility compared to the market. It helps the portfolio managers in evaluating the decisions concerning the addition, deletion of the security from the portfolio.

Beta is a measure of systematic risk. Most of the portfolios contain unsystematic risk removed from the portfolio. Beta only considers systematic risk and thus provides the true picture of the portfolio.

### Disadvantages of Beta in Finance

Beta can assist to evaluate systematic risk. Though, it does not promise future returns. Beta can be calculated at a variety of frequencies, including two months, six months, five years, etc. Results using past data can’t be applied to the future. It makes it hard to forecast the stock’s future movements.

Beta is calculated based on the stock prices in comparison to the market prices. Therefore for startups or private companies, it is tough to calculate beta. There are methods like unleveraged beta and leveraged betas, but that also involves a lot of assumptions to be made.

Another downside is that beta cannot reveal the difference between an upswing and a downswing. It does not inform us when the stock was more volatile.

## Difference between Alpha and Beta

Alpha and beta are both normally used to measure performance. Alpha is a measurement of the excess return or active return of an investment or a portfolio. Beta in finance measures the volatility of a portfolio or security as compared to the market.

Both alpha and beta assess the past performance of a stock or a portfolio. However, this cannot ensure that the stock or portfolio will perform the same in the future.