Alpha versus Beta: Unbundling concepts and its importance for investors
Improving one’s portfolio by knowing how Alpha and Beta relate to investment risk
Are you familiar with the terms Alpha and Beta in investing and what they mean? More importantly, do you know how they can help you become a smarter investor?
We often hear the terms Alpha and Beta when talking about investments. Both of these indicators measure related, but different, things. Whether you invest in funds or stocks, understanding investment terms like Alpha and Beta can help you take more informed investment risks.
Whether you invest in funds or stocks, understanding investment terms like Alpha and Beta can help you take more informed investment risks.
Alpha (the Greek letter α) is used in investing to describe a strategy's ability to beat the market, or it's edge over the market. Alpha is thus also often referred to as ‘excess return’.
Alpha is often used in conjunction with Beta (the Greek letter β), which measures the broad market's overall volatility or risk, known as ‘systematic market risk’.
Alpha and Beta are historical correlations, in absolute terms. But this is where the application of probability kicks in. In all-time series data analysis, the relevance of data becomes useful when how one can interpret it in the context of probability. Knowingly or unknowingly, we all use probability in all decision making.
Let’s go each of these in depth below, along with how to calculate them for your respective portfolio.
Beta, a measure of volatility
Beta measures an asset’s historic volatility relative to an underlying benchmark index. In other words, the higher the Beta, the higher the volatility and risk.
The higher the Beta, the higher the volatility and risk.
Price volatility is a crucial measurement for the risk a stock contains.
The more you understand the risk you take, the safer your investment will be, as it tells you the eventual outcomes of your investment. This way, you can check to see if a stock will be a good fit for your portfolio.
The Beta coefficient is a tool that tells you how correlated a stock is to a benchmark index and gives you hints about the relative strength of each respective security.
It looks at the price performance of a stock and tries to tell you why that company performs the way it does. It does that by showing how correlated the stock is to a benchmark index.
Different Beta values and their respective implications
- • If Beta value is ‘0’: Zero correlation with the underlying benchmark index
- • If Beta value is between ‘0’ and ‘1’: The asset moves in tandem with the market but at a lower volatility
- • If Beta value is ‘1’: The asset is perfectly correlated with the market. For example, an Exchange Traded Fund that tracks the S&P 500 should have a Beta of 1
- • If Beta value is higher than ‘1’ : The asset moves in tandem with the market but at a higher volatility
- • If Beta value is negative: The asset moves in the opposite direction of the market.
Knowing Beta values allows you to better understand the assets in your investment portfolio. So if your portfolio consists purely of stocks with Beta values higher than 1, it is on the riskier side.
For example, if a stock has a Beta of 1.2, this means that a 1 per cent change in the market index will bring about a 1.2 per cent change in the stock’s price. Stocks with high Beta are considered to be more risky compared to the ones with low Beta.
Knowing Beta values allows you to better understand the assets in your investment portfolio.
How to calculate Beta of individual stock?
The Beta for individual stocks is readily available on the websites of most online discount brokerages or reliable publishers of investment research. But it’s beneficial to know how one can calculate the metric.
Beta for stocks is readily available, but it’s beneficial to know how one can calculate the metric.
First, get the closing share price for your stock on each day of the date range you need the data for (week/month/year). Then do the same thing for the index you are comparing against.
For each date, determine the change in price and the change on a percentage basis. (Using a spreadsheet eases calculation.) - Next, we need to calculate the daily price change for both the stock and index as a percentage.
To do that, subtract the higher current price from the previous day's, then divide by the previous day's price. Multiply by 100 to show the result as a percentage.
Lastly, we'll compare how the stock and the index move relative to each other with a covariance formula and then divide that result by the variance of the index alone.
In non-math terms, we're going to compare how the stock and index move together relative to how the index moves by itself. The result is the Beta.
The formula to calculate Beta is:
Beta (β) = Covariance (Stock's Daily % Change x Index's Daily % Change) ÷ Index's Daily % Change (Variance)
Whether you're calculating a Beta over a one month or one decade time frame, or if you're using the S&P 500 or the Shanghai Stock Exchange Composite index, the process is exactly the same.
There are other, more academic methods for calculating a company's Beta, but this technique is statistically sound and much simpler for the typical investor.
Armed with this tool, you can now calculate your own Betas, custom tailored to fit your stocks, your investment horizon, and with the perfect index to match.
The Beta shows you that there is a strong correlation between the XYZ stock and the S&P 500, which is (hypothetically) doing well, too.
This means that based on the overall market conditions, the price increase of XYZ stock is normal and it is not caused by an exclusive event.
(We generally consider correlations above 0.4 to be relatively strong; correlations between 0.2 and 0.4 are moderate, and those below 0.2 are considered weak.
When the value is closer to +1 or -1, it indicates that there is a stronger linear relationship or correlation between the two variables.)
Armed with this tool, you can now calculate your own Betas, custom tailored to fit your stocks, investment horizon, with an apt index to match
However, there are two key risk factors one should keep in mind when it comes to calculating Beta:
Beta is historical: Beta values are calculated based on the historical performance of an asset. There is no guarantee its Beta will not change in the future.
Beta only measures general market risk: Beta values measure the level of historical correlation with the overall market, so they only capture systematic or market-wide risk.
There is no guarantee that Beta values will not change in the future.
They do not account for other types of risks such as credit or liquidity risk of the asset, or any risk associated with a specific segment or industry.
Alpha, a measure of return
Alpha measures the return of an asset compared to the underlying benchmark index. Hence, while Beta is a measure of systematic risk and volatility, Alpha is a measure of excess return.
While Beta is a measure of systematic risk and volatility, Alpha is a measure of excess return.
Let’s say over the last year, the Straits Times Index returned 4 per cent and the stock returned 10 per cent, or 6 per cent over the benchmark index; this would give the stock an Alpha value of 6.
If the stock had instead lost 2 per cent in value, it would then have an Alpha value of -6.
In its most basic sense, the Alpha of the portfolio = 16 per cent – 15 per cent = 1 per cent.
Alpha values are typically used to rank the performance of actively-managed mutual funds and their investment managers.
A higher Alpha shows that a particular fund often outperforms the market. You can also use Alpha values to check the performance of a particular security against the benchmark index.
A higher Alpha shows that a particular fund often outperforms the market.
What does a stock’s Alpha coefficient tell us?
The Alpha figure for a stock is represented as a single number, like 3 or -5. However, the number actually indicates the percentage above or below a benchmark index that the stock or fund price achieved.
In this case, the stock or fund did 3 per cent better and 5 per cent worse, respectively, than the index.
A negative Alpha of -1 means the investment under-performed its benchmark index by 1 per cent.
If the Alpha is zero, its return matched the benchmark.
But an important point to keep in mind is that like Beta, Alpha is a historical number.
It's useful to track a stock's Alpha over time to see how it did, but it can't tell you how it will do tomorrow.
The formula to calculate Alpha is:
Alpha (α) = Actual rate of return – Expected rate of return
As one might have guessed, calculating the actual rate of return is by tabulating historical returns for the period that you are looking at for the respective stock or bond you are looking at.
So, next let’s look at how one can calculate the expected rate of return.
The purpose of calculating the expected return on an investment is to provide an investor with an idea of probable profit vs risk.
Let’s understand this with the help of an example.
Let us take an investment A, which has a 20 per cent probability of giving a 15 per cent return on investment, a 50 per cent probability of generating a 10 per cent return, and a 30 per cent probability of resulting in a 5 per cent loss.
The probabilities of each potential return outcome are derived from studying historical data on previous returns of the investment asset being evaluated
The probabilities stated, in the above example, might be derived from studying the performance of the asset over the previous 10 years.
Assume that it generated a 15 per cent return on investment during two of those 10 years, a 10 per cent return for five of the 10 years, and suffered a 5 per cent loss for three of the 10 years.
Expected return of A = Aggregate sum of (probability times return) in each of the time periods
So in this case, expected return of A = 0.2(15%) + 0.5(10%) + 0.3(-5%)
(That is, a 20%, or 0.2, probability times a 15%, or 0.15, return; plus a 50%, or 0.5, probability times a 10%, or 0.1, return; plus a 30%, or 0.3, probability of a return of negative 5%, or -0.5)
So as a result, expected return of A = 3% + 5% – 1.5%, which totals to 6.5%. Therefore, the probable long-term average return for Investment A is 6.5 per cent.
With the expected rate of return, one can then subtract it from the actual rate of return to get the Alpha.
Again, there are two key risk factors one should keep in mind when it comes to calculating Alpha:
Alpha is historical: Similar to Beta, past Alpha value does not imply future Alpha value.
Check the benchmark: Inappropriate benchmarks can often inflate Alpha values.
Similar to Beta, past Alpha value does not imply future Alpha value.
For instance, if a fund invested mostly in riskier technology stocks but benchmarked against a large cap market index like the S&P 500, then the Alpha value (assuming a profitable year) might seem very high.
However, a more aligned index such as the NASDAQ, which focuses more on the technology segment, would have shown a lower Alpha value.
For stock investors, Beta values can help you better gauge risk levels and structure your investment portfolio appropriately.
Investors can use both Alpha and Beta to judge a manager's—or individual stock's— performance. Investors would most likely prefer a high Alpha and a low Beta.
But other investors might like the higher Beta, trying to cash in on the stock or fund's volatility in price and shares sold.
However, if a fund manager or stock has had a high Alpha, but also a high Beta, conservative investors might not be so happy.
That's because the Beta might make them withdraw their money when the investment is doing poorly—due to the increased volatility and possible risk of losses indicated by the high Beta.
How to calculate Alpha and Beta for your entire stock portfolio?
Individual investors can determine the volatility of their portfolios by examining the Beta of each holding and performing a relatively simple calculation.
The calculation is simply a matter of adding up the Beta for each security, and adjusting according to how much of each you own. This is called a weighted average. The same applies to calculating Alpha for an entire portfolio.
The calculation is simply a matter of adding up the Beta for each security, and adjusting according to how much of each you own.
To determine the Beta or Alpha of an entire portfolio of stocks, you can follow these four steps:
While our example below discusses Beta in the context of stocks, Beta can be calculated for bonds, mutual funds, exchange-traded funds, and other investments.
Based on these values, determine how much you have of each stock as a percentage of the overall portfolio. (For example, if Amazon stock makes up off 25 per cent of your portfolio then Amazon has 0.25 share of your portfolio.)
Next, multiply those percentage figures by the appropriate Beta or Alpha for each stock. (Thus, if Amazon comprises 25 per cent of your portfolio and has a Beta of 1.43, it has a weighted Beta of 0.3575.)
And the finally, add up the weighted Beta or Alpha figures.
Importance of considering fees in conjunction with performance returns and Alpha!
Moreover, because most “traditional” financial advisors charge a fee, when one manages a portfolio and nets an Alpha of zero, it actually represents a slight net loss for the investor.
While Tim has indeed helped the performance of Bob’s portfolio, the fee that Tim charges is in excess of the Alpha he has generated, so Bob’s portfolio has experienced a net loss.
For investors, this example highlights the importance of considering fees in conjunction with performance returns and Alpha.