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Last Updated on 10 February, 2024 by Trading System

As an investor or trader, and most especially if you have been following our posts, you must have known about alpha and beta, two of the common ratios for measuring investment risks and risk-adjusted returns. While you may already be aware or even using both metrics, you may want to know the difference between alpha and beta in trading.

**Alpha is a metric for measuring the risk-adjusted performance of an investment relative to a market index, while beta is a historical measure of the systemic risk or volatility of an asset or portfolio compared to the volatility of the market as a whole. While beta measures risks, alpha measures risk-adjusted returns.**

To help you understand both metrics and how they differ, we will discuss the topic under the following subheadings:

- What are alpha and beta?
- Understanding alpha and beta in trading
- What is the difference between alpha and beta in trading?
- How to combine alpha and beta in evaluating an investment?
- The merits and demerits of alpha and beta in trading

**What are alpha and beta? **

Alpha and beta are among the five popular risk ratios in financial investments; others are standard deviation, R-squared, and the Sharpe ratio. They are generally used to determine an investment portfolio’s returns.

By definition, alpha is a measure of the excess return on an investment compared to the expected return based on the capital asset pricing model (CAPM). You can use it to know if an investment has consistently performed better or worse than CAPM predicts based on its beta coefficient. For a stock portfolio, alpha tells you how the investment has performed compared to the broad stock market index, such as the S&P 500 Index, considering its risk level (beta).

To put it differently, alpha measures the degree to which you have managed to ‘beat’ or underperform the market over a given period. The metric can be zero, positive, or negative, depending on whether your portfolio made the same return as the market, beat the market, or underperformed the market considering its beta value and the expected returns.

Beta, on the other hand, measures the systemic risk, or volatility, of an investment compared to a relevant market index. Beta can be described as the responsiveness of an asset’s returns to swings in the market. A security that has a higher beta has more risk, and based on the CAPM, it is expected to offer more returns.

**Understanding alpha and beta in trading**

The main use of alpha is to know whether an investor is being compensated for the extra risk taken since it measures the performance of an investment on a risk-adjusted basis. When we say risk-adjusted basis, we mean that the return of the investment should compensate for volatility — beta.

For example, if a financial asset is twice as volatile as the benchmark, an investor should receive at least twice the return of the benchmark for assuming the additional risk. Alpha, in fact, measures how much more or less returns the investor receives compared to this expected return for the assumed risk. If the investor receives more than the expected, he has “beaten” the market; if he receives just the expected, he has performed the same as the market; and if he receives less than the expected (even if it’s more than that of the benchmark), he has underperformed the market.

To put it differently, alpha is presented as numeric values: an alpha of zero shows that the investment has exactly earned a return that matches the volatility assumed; an alpha value that is above zero reveals that the asset has outperformed its benchmark index by earning a return that is more than the volatility risk taken; and lastly, an alpha of less than zero means the investment has earned a return that has not compensated for the volatility risk assumed.

The beta of an investment, on the other hand, tells an investor how much volatility an asset has compared to the market benchmark and, therefore, the level of risk he is taking by investing in the asset. Just like the alpha, beta is represented with numerical values. A beta value of 1.0 implies that the volatility in the asset is the same as the overall market. A beta of less than 1 means that the asset is less volatile than the market, while a beta greater than 1 indicates that the asset is more volatile than the market. Since the baseline value of beta is 1.0, then a stock, for example, with a beta value of 1.4 is considered to be 40% more volatile than the overall market.

**How to calculate alpha and beta**

Investors use both the alpha and beta ratios to calculate and compare risk and the expected returns. These calculations are made with respect to the risk in a benchmark index, such as the S&P 500. To calculate alpha and beta, you need to use the alpha and beta formula. Since you would need the beta to calculate alpha, we would discuss beta first.

**Beta Calculation:**

Beta is calculated by dividing the covariance of the return of an asset with the return of the benchmark by the variance of the benchmark’s return over a certain period.

Mathematically, the beta formula is given as follows:

*Beta = Covariance*

Variance

**where:**

*Covariance* = measure of a stock’s return relative to that of the market

*Variance* = measure of how the market moves relative to its mean

**Alpha Calculation:**

Mathematically, the alpha formula is given as follows:

*α = Rp – [Rf + β(Rm – Rf)]*

**Where:**

α = alpha

Rp = Portfolio’s Realized Return

Rf = Risk-Free Rate

β = Beta of the Portfolio

Rm = Expected Market Return

Rf = Risk-Free Rate

Note that the portfolio’s minimum expected return could be written as:

E(R) = Rf + β(Rm – Rf)

Hence,

α = Rp – E(R)

To put it in words, the formula goes like this:

*Alpha = Portfolio’s Realized Return – [Risk-Free Rate + Beta of the Portfolio X (Expected Market Return – Risk-Free Rate)]*

Or

*Alpha = Portfolio’s Realized Return – Expected Return*

**Where: **

Expected return = Risk-Free Rate + Beta of the Portfolio X (Expected Market Return – Risk-Free Rate)

**What is alpha in trading?**

In trading, alpha is the excess returns of an asset compared to the expected return based on the capital asset pricing model (CAPM). It is a metric for measuring the risk-adjusted performance of an investment relative to a market index.

It is essential to understand that alpha does not tell you if an investment was profitable — an investment can grow but still have a negative alpha and vice versa. An alpha measures how well an investment performed compared with putting that same amount of money in an index fund. For example, say that Stock C has an alpha of 5 when compared to the S&P 500 over 16 months. This means that if you had put your money in Stock C 16 months ago, you have made 5 points more than if you put that same amount of money in an S&P 500 index fund. If the index lost money, the stock would have a positive alpha value if it had lost less money than the index. So, a positive alpha value does not necessarily imply a profitable investment.

**Is alpha or beta better?**

It would not be easy to exactly tell which is better between alpha and beta as both are not substitutes but complementary tools. Alpha and beta are risk ratios that investors use to compare risks and returns. They are generally essential metrics investors use to choose the right asset to invest in.

Since beta is a necessary part of the calculation for an alpha, you can’t just choose one and leave the order. You need the beta to calculate the extra risk in an investment, while you need the alpha to find the expected returns for that risk and know whether the investment is outperforming the expected returns or underperforming it.

**What is a good beta for a stock?**

Stocks are ranked according to how much volatility they have compared to the market. A stock that fluctuates more than the market would have a beta value of 1.0, a stock that moves less than the market, would have a beta value of less than 1.0. High-beta stocks are considered riskier but provide higher return potential; low-beta stocks are believed to be less risky but offer lower returns.

When it comes to the right beta for a stock, different investors have different preferences. A lover of growth stocks may prefer high-beta stocks, while investors who seek steady returns and lower risk would avoid such stocks.

Generally, risk-averse investors, such as retirees who seek a steady income, are attracted to lower beta, while the risk-tolerant investors who seek bigger returns are often willing to invest in high-beta stocks.

**What is the difference between alpha and beta in trading?**

Apart from being complementary metrics for calculating investment returns, alpha and beta have some significant differences. Some of the differences are as follows:

· Alpha is the excess return or active return of an investment or a portfolio relative to that of the market index, while beta measures the volatility of a security or portfolio compared to the market.

- The baseline value of alpha is zero, while the baseline value of beta is 1.
- While a positive alpha is always more desirable than a negative alpha, beta is not as clear-cut; it simply depends on the investor’s risk tolerance.

**How to combine alpha and beta in evaluating an investment**

The basic model for evaluating the performance of a stock or an investment funds may be given as follows:

**y = a + bx + u**

Where:

- y is the performance of the stock or fund.
- a is alpha, which is the excess return of the stock or fund.
- b is beta, which is volatility relative to the benchmark.
- x is the performance of the benchmark, which is often the S&P 500 index.
- u is the residual, which is the unexplained random portion of performance in a given year.

For example, let’s say that a stock ETF made a return of 15% for the year. Suppose the beta value of the fund is +1.3 and the benchmark index during the period is 10%. Can we say that investing in this fund is a wise decision?

We can determine if the fund in the above example is a good investment by substituting the figures in the equation below:

**y = a + bx + u**

Given that: y = 15%, b = 1.3, x = 10%, and a = ? Let’s assume that the residual, u, is zero;

We can evaluate the value of alpha (a) from the equation as follows:

**y = a + bx + u**

15% = a + 1.3*10% + 0

a = 15% ₋ 1.3*10% + 0

a = 15% ₋ 13%

a = 2.

The alpha for this fund is 2%, which means the investment outperformed after adjusting for its beta (volatility). Therefore, it is a good investment.

**The merits and demerits of alpha and beta in trading**

While alpha and beta are important metrics in the financial markets, they also come with some limitations. Let us discuss some of the merits and demerits of these two risk ratios.

**Merits**

- Alpha and beta are two vital elements of the Capital Asset Pricing Model, which can help you decide if an investment is worth its risk.
- As risk ratios, alpha and beta can be used by investors to calculate and compare risks and returns.
- Alpha can be used to measure a portfolio manager’s aptitude.
- Beta can give a measure of the risk involved in an investment relative to the market index.
- Investors use beta to determine how much risk they are taking in an investment.

**Demerits **

- Evaluating beta is not as simple as other risk ratios, and it requires a good level of expertise to master.
- Alpha and beta make use of historical data, and since past performance is not indicative of future performance, they cannot be used to forecast future risks and returns.
- Beta is best suited for short-term investments only because, in long-term investments, a stock’s volatility can change significantly from year to year, depending upon the company’s growth stage and other factors.
- Alpha and beta work best in stock market investments.
- The performance of the benchmark index affects the alpha value.

## FAQ

**How are alpha and beta used in evaluating an investment?**

Alpha and beta are complementary tools in evaluating investments. Alpha assesses if an investment compensates for the assumed risk, while beta measures volatility compared to the market.

**What are the calculations for alpha and beta in trading?**

Beta is calculated by dividing the covariance of an asset’s return with the benchmark by the variance of the benchmark’s return. Alpha is calculated using the formula: α = Rp – [Rf + β(Rm – Rf)], where Rp is the portfolio’s realized return, Rf is the risk-free rate, β is the beta of the portfolio, and Rm is the expected market return.

**Is alpha or beta better for evaluating investments?**

Alpha and beta are not substitutes but complementary. Both are essential for evaluating investments. Beta calculates extra risk, while alpha determines if the investment outperforms or underperforms the expected returns for that risk.

**How do you combine alpha and beta to evaluate the performance of an investment?**

The model y = a + bx + u is used, where y is the performance of the stock or fund, a is alpha, b is beta, x is the performance of the benchmark, and u is the residual. The equation helps determine if an investment is a wise decision based on its alpha and beta values.

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