June 29

# What Is Alpha In Trading? How Do You Calculate It?

Last Updated on 29 June, 2022 by Samuelsson

Admitted! Financial investments are full of risks. But at least, we can look for those ones that offer us the best returns for the risks we have taken so that we get adequately compensated for taking risks. Fortunately, there different ways to assess the risk-adjusted returns of an investment, and alpha is one of them. But what is alpha in trading?

In financial trading, alpha is a measure of a portfolio’s excess returns compared to a particular market benchmark. In the case of a stock portfolio, the benchmark would be the broad stock market index, such as the S&P 500 Index. To put it differently, alpha measures the degree to which a trader has managed to ‘beat’ or underperform the market over a given period. The metric can be zero, positive, or negative, depending on whether the portfolio had the same return as the market, beat the market, or underperformed the market, considering its beta value and the expected returns based on CAPM.

Alpha is one of five popular technical investment risk metrics — alpha, beta, standard deviation, R-squared, and the Sharpe ratio — that help investors determine the risk-return profile of an investment, and you would certainly want to know more about it. In this article, we will be discussing the concept of alpha in detail. Here are the things we would cover:

• What is an alpha in trading?
• Importance of alpha
• How to use alpha in financial analysis?
• Limitations of alpha
• How is alpha different from the beta?

## What is an alpha in trading?

Alpha, often dubbed the active return, is a metric used to measure the performance of an investment against a market index or benchmark that represents the market’s general movement. It is one of modern portfolio theory’s (MPT) statistical measures used to quantify the returns made from an investment against that of a benchmark market index. In other words, the excess return of an investment relative to the return of a benchmark index is the investment’s alpha.

We can use the concept of alpha to know when a strategy, trader, or portfolio manager has managed to beat the market over the period under review. Alpha is represented by a single value, which can either be positive or negative depending on whether the investment is outperforming or underperforming the relevant market benchmark. If, for instance, the alpha of an investment is +1, it shows that the investment’s returns over a given period were 1% better than the return on the benchmark market index (the S&P 500 Index for example) during that same period. In contrast, an alpha value of -3 infers that the investment’s returns over the period under review were 3% worse than the return on the benchmark market index during that same period.

### What does alpha mean in stocks?

The main objective in stock trading — just like in most financial markets — is to make the maximum returns while taking the least amount of risk. To achieve this objective, traders have to use some risk-adjustment metrics to evaluate the past performance of their stocks portfolios, and alpha has proven to be a reliable metric for this.

Therefore, if you trade stocks, you can use alpha to assess how well you have performed by comparing your profits over a certain period with how much the S&P 500 Index has returned over the same period. If you have made more profits than the S&P 500 Index’s returns over that period, your alpha would be positive, but if your profits weren’t as much as the gains made by the index, your alpha would be negative. Taking it further, if you just made as much profit as the S&P 500 Index’s returns over that period, your alpha would be zero.

The general idea of alpha in trading is to help investors determine the risk-return profile of an investment. To correctly apply investment alpha with your portfolio, you need to understand what is alpha is all about.

But first, let’s introduce a new concept: the modern portfolio theory (MPT). The MPT was developed in the 1950s to stress the need for investors to diversify into various non-correlated assets to earn the maximum expected return for a given amount of portfolio risk. With the help of MPT, an investor will find a combination of investments that has the best possible expected level of return for an appropriate level of risk. This is also referred to as the efficient frontier or finding the most “efficient” level of expected return for the lowest possible risk.

You may ask the question: how does the knowledge of MPT help me to understand alpha in trading? Well, alpha is a concept within MPT. Five MPT risk ratios help investors determine the risk-reward profile of an investment; they include alpha, beta, standard deviation, R-squared, and Sharpe ratio.

With the help of modern portfolio theory (MPT) and the risk statistics within MPT, such as alpha, investors can assess whether the potential return for specific investments is worth the assumed amount of risk. Alpha as a risk ratio helps investors measure an investment’s performance on a risk-adjusted basis.

Every investor is curious to know if they are being compensated for the risk taken in their investment, and alpha helps assess whether or not an investment is worth investing in. Since we mentioned earlier that alpha shows the performance of a portfolio relative to a benchmark index, it can be inferred that alpha represents the value that a portfolio manager adds to or subtracts from a fund’s return. This means that alpha is not primarily the return on investment but the excess return attributed to a general movement in the more significant market.

For example, an alpha value of zero does not mean that there is zero return on the investment; instead, it shows that the fund manager has not added or lost any additional value compared to the broad market index — the investment earned the same risk-adjusted return as the benchmark.

Overall, the alpha coefficient indicates how an investment has performed after accounting for the risk (beta) involved. The following statements represent how to interpret alpha coefficients:

αi < 0: the investment has earned too little for the risk taken (or, was too risky for the return)

αi = 0: the investment has earned a return adequate for the risk taken

αi > 0: the investment has a return above the risk taken

### Origin of alpha

Alpha was formulated in 1968 by a renowned economist Michael Jensen; little wonder, the concept is also known as Jensen Index after its creator. It is one of the risk ratios used in finance. It 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.

However, the idea of alpha became more popular with the advent of smart beta index funds tied to indexes like the S&P 500 index and the “Wilshire 5000 Total Market Index”. It was eventually developed as an investing strategy, making investors require portfolio managers of actively traded funds to produce returns that exceeded what could be expected to make by investing in a passive index fund. Hence, alpha became the metric for comparing active investments with index investing.

### How is alpha calculated?

To calculate alpha, you have to calculate beta first. Alpha and beta are close cousins — they are both risk ratios that investors use to estimate risk-adjusted returns. But how do you calculate alpha and beta?

#### Beta Calculation:

Beta is a measure of an investment’s price volatility in comparison to the volatility of the broad market index. This means that if the value of beta is 1, it has the same volatility as that of the broad market index. But a beta value that is higher than 1 shows that the asset’s returns have more volatility than the general market and vice versa. So the beta of an investment tells you how much risk you are taking.

The Covariance method is the most common way to measure the value of beta. To calculate beta, you need to first get the covariance between the return of the security and the return of the market, as well as the variance of the market returns.

Covariance is a measure of how two stocks move together: A positive covariance reveals that the stocks tend to move together when their prices go up or down. Conversely, a negative covariance means that the stocks move opposite of each other. On the other hand, variance is a term that represents how far an investment moves relative to its mean.

Beta is calculated by dividing the covariance between the return of the security and the return of the benchmark by the variance of the benchmark’s return over a certain period.

The formula is mathematically 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:

As you can deduce from our discussion so far, Jensen’s alpha, also known as the Jensen’s Performance Index, is a measure of the excess returns earned by the portfolio compared to returns suggested by the CAPM. So mathematically, alpha can be calculated from the CAPM formula.

The formula for Jensen’s alpha can be presented 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)

Since alpha is a measure of the performance of an investment relative to its benchmark, whatever value we get from the alpha calculation shows how much better or worse — as the case may be — an investment performed relative to its benchmark. Thus, it allows the investor to statistically test whether the portfolio produced an abnormal return relative to the overall capital market It gives the excess risk-adjusted return achieved over the benchmark’s returns.

#### How to calculate monthly alpha

The monthly alpha is calculated by subtracting the product of the average monthly excess return of the benchmark index and the portfolio’s beta from the average monthly excess return of the portfolio.

Mathematically, Monthly alpha is given by the formula below:

alpha(M) =  – Beta * ()

Where:

= average monthly excess return of the portfolio

= average monthly excess return of the benchmark index

Beta = the portfolio’s beta

We can also deduce the annualized alpha by multiplying the monthly alpha by 12.

Thus:

alpha = 12(alphaM)

#### How to calculate alpha in mutual funds

The formula for calculating the alpha in mutual funds is given as:

Alpha of the mutual fund = Actual rate of return – Expected rate of return

For example:

A mutual fund realized a return of 22% during the last year. If the appropriate benchmark index for the fund has a book annual return of 15%, and the beta of the mutual fund relative to its benchmark index is 1.5 while the risk-free rate of return is 6%. What is the alpha of the mutual fund?

Given the following parameters:

Risk-free rate of return = 6%

Beta (β) = 1.5

Benchmark return = 15%

Actual rate of return = 22%

Expected rate of return = ?

Since the formula for calculating the alpha in mutual funds is given as:

Alpha of the mutual fund = Actual rate of return – Expected rate of return

We have to get the value of the expected rate of return

Thus:

Expected rate of return = Risk-free rate of return + β * (Benchmark return – Risk-free rate of return)

= 6% + 1.5 * (15% – 6%)

Expected rate of return = 19.5%

Therefore, the calculation of alpha of the mutual fund will be as follows –

Alpha of the mutual fund = Actual rate of return – Expected rate of return

Alpha = 22% – 19.5%

Alpha = 2.5%. Therefore, the alpha of the mutual fund is 2.5%.

### Is alpha a technical analysis tool?

Technical analysis tools are those indicators and tools that aid investors in making educated and effective decisions before entering or exiting a trading position or making an investment. Following the above description, we could safely describe alpha as a technical analysis tool.

Since alpha shows the performance of an asset or a fund, it could help traders decide what funds (ETFs and mutual funds) to invest in. Consistent underperformance may be an indicator of limited growth potential or inefficient business practices. A positive alpha indicates the security is outperforming the market, while a negative alpha indicates the security fails to generate returns at the same rate as the broad market index. Hence, for a mutual fund manager or an overall strategy, alpha can indicate the overall effectiveness of the fund or the strategy.

## Importance of alpha

Alpha offers a lot of benefits to investors and other market participants. They include

• Investors and fund managers can use the alpha to measure the performance of their portfolio against the rest of the market.
• It helps investors gauge the highest possible return from an investment with the least amount of risk — the portfolio’s risk-adjusted performance.
• The alpha value can reveal how much worse or better a managed portfolio has performed relative to passive funds that track the broad market index, such as the SPY and IVV that track the S&P 500 Index.
• Investors can use alpha to compare the performance of two or more different funds to choose the best one to invest in.

## How to use alpha in financial analysis?

For an individual trader who is testing out different strategies to know the best one to use in his trading, alpha could be a useful metric for assessing the risk-adjusted returns of those strategies. Since the values can be graded, you would be able to choose the strategy that offers the best risk-adjusted returns — the one with the highest positive alpha.

Alpha can also be used to measure the performance of a fund manager. It can tell whether the fund manager has made superior returns given the amount of risk taken. It does this by measuring a fund’s return with its expected returns: a fund that consistently generates a higher return relative to its expected return (positive alpha) can be said to beat the market. In comparison, a fund that generates a lower return vis-à-vis its expected return (negative return) is an underperformer.

Interestingly, the performance of an asset — as calculated by the alpha — can continue the trend in the middle and long term. For example, an asset that generates excess returns is more likely to outperform in the medium term and the long term. The inference to be drawn is that we can use the alpha value to know the right fund to invest in.

Let us calculate the alpha values for the three funds in the table below to determine the most efficient fund to invest in:

 PORTFOLIO METRICS FUND A FUND B FUND C Realized Return 16% 20% 17% Risk Free Rate Of Return 4% 7% 5% Beta Of Portfolio 1.3 1.8 1.2 Expected Market Return/Benchmark Return 11% 13% 15%

Recall that the basic formula for calculating alpha is given as

Alpha = Portfolio’s Realized Return – Expected Return

But the Expected Return is not given in the table above. So, the first step would be to evaluate the value of the expected return on each of the funds from the given metrics.

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

Therefore:

Expected Return (Fund A) = 4% + 1.3 * (11% – 4%)

= 4% + 1.3 * (7%)

= 13.1%.

Expected Return (Fund B) = 7% + 1.8 * (13% – 7%)

= 7% + 1.8 * (8%)

= 21.4%.

Expected Return (Fund C) = 5% + 1.2 * (15% – 5%)

= 5% + 1.2 * (10%)

= 17%.

Now, let us evaluate the alpha values for the three funds.

Alpha = Portfolio’s Realized Return – Expected Return

Alpha (Fund A) = 16% – 13.1 %

= 2.9%

Alpha (Fund B) = 20% – 21.4 %

= – 1.4%

Alpha (Fund C) = 17% – 17%

= 0%

The alpha values for Funds A, B, and C are 2.9%, –1.4%, and 0%, respectively. Therefore, the most effective fund to invest in is fund A because it has a positive alpha value, which indicates outperformance.

## Limitations of alpha

Alpha has some limitations in its application. It is that important for investors to consider these limitations when making investment decisions with alpha. Some of the limitations include:

• Alpha can give misleading results, especially when used to compare portfolios from different asset classes. This is because the diverse nature of the funds often affects the alpha value.
• Alpha works best for stock market investments and may not work as well in markets that don’t have a reliable benchmark index.
• The benchmark index affects the alpha value. So investors should select a relevant benchmark, such as the S&P 500 stock index for stock investments.

## How is alpha different from the beta?

While alpha and beta are two of the five measurements used to evaluate the performance of an investment portfolio, a subtle difference exists between the two metrics, such as the following:

• Alpha measures the amount that the investment has returned relative to a benchmark index. Beta, on the other hand, indicates the relative risk of an investment as it measures its volatility.
• While alpha gives a measure of risk-adjusted returns, beta measures only risk.

## Final words

Overall, alpha is considered an investment’s excess return and is used to understand how an investment is performing compared to the general market index. It is a very important risk-adjustment metric that can be used to compare the performance of different strategies and fund managers.

What Is Beta In Trading? How to Calculate It?

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