An introduction to Beta, a foundational concept in finance that measures exposure to general market risk (systematic risk)
A precursor to truly understanding the concept of Beta is an understanding of the difference between systematic (unverifiable) and unsystematic (diversifiable) risk. These terms sound complicated, but they really aren't.
Here's a very brief review of the difference between these two types of risk:
Keeping in mind the above definitions, it would be useful to know how much systematic risk you are being exposed to with a given security (eg. a stock) relative to the market as a whole. Stated another way (and hopefully more simply), if you're going to hold a stock, it's useful to know how risky that stock is relative to the market - this knowledge will allow you to understand how the stock will fit into an already diversified portfolio and it will also allow you to use the important Capital Asset Pricing Model (CAPM) down the line. Stated yet another way for the purposes of clarifying a possibly confusing topic, the beta of a stock will allow you to know the market risk of the stock (the risk arising from general market factors) - it is not, however, a measure of the idiosyncratic risk fo the stock.
Boats, Water, and Rain: An Example to Help Clarify the Meaning of Stock's Beta and Why We Care About It
A question that arose for me in studying finance was in this effect:
If we are only looking at systematic (eg. market risk), why would any stock have a different exposure to market risk? If finance theory says that there is a certain risk called diversifiable market risk that you're still exposed to even if you have a diversified portfolio, why would betas be different? Shouldn't all betas be the same?
Stated another way, this question might sound like:
Why does beta tell you about systematic (market) risk and not unsystematic (idiosyncratic) risk - and why does that even really matter?
This question evinced a deep lack of understanding of finance and further study clarified things for me enough so that the question itself seemed foolish. I will attempt to provide context here so that such foolish questions don't arise.
Let's leave finance altogether and travel to a port. In that port, there are wooden boats of all shapes, sizes, and designs on the shore. The port is open and you can take any one of them and go out into the water. The port has constant clouds overhead and there is constant rain. This is a unique port b/c the rain is different in different places - if you're standing on the beach and you walk just 10 feet to another direction, the amount and strength of the rain will change.
Now, imagine you take a boat out into the water. You'll feel the rocking and the swaying of the water. No matter where you are in the port area, you're going to feel the water. If a heavy wind storm comes in, all boats will be affected. If it's calm today, all boats will be calm. The way your boat feels, however, is going to be based on the design of your boat - a large heavy boat will sway less than a small boat and a swiftly designed boat that can cut through the water will react differently than a rugged boat. Before you go onto the water, in anticipation of the chaotic rain in this unusual port, you can easily construct a quasi-roof over your boat to totally protect you from the rain. You can choose to go out with no roof at all and be totally exposed to the rain. You can choose to go out with a poorly made roof and just have limited protection against the rain. You can also choose to go out with a fully-built roof and be totally protected from the rain.
You go out into the water now and some wind comes in. No matter what you do, your boat will be affected by the water moving. This is like systematic risk - all boats are affected by it. This risk is not diversifiable - no matter what you do, if you're in the water (eg. if you're in the market), you are exposed to this general risk of moving waters (eg. general market risk). So, if a systematic risk is moving water, a unysystematic risk is the rain - you can choose to diversify that risk away by simply putting up the roof we discussed earlier. You don't have to be exposed to it and many people on the water probably aren't because they've put up roofs - this risk is idiosyncratic to each boat and is diversifiable.
In choosing a boat, therefore, you might want to think about a few things. For one, you might want to decide if you want a roof up. Another important thing to think about is the shape of the boat. Since you know the water will move and you will always be exposed to that movement, you'll want to know how your boat will move relative tot he movement of the overall water. You'll want to look at each boat and think about whether or not it will move calmly or forcefully whenever the water moves. Forceful movement isn't necessarily bad, but you'll still want to know what kind of a journey you're about to have.
This looking at the boat and seeing how it will react to movements of the water is exactly what the beta is about - knowing a stock's beta will allow you to know how the price of that stock will move relative to moves in the market overall. Clearly, the beta then will not tell you about idiosyncratic risks (just like the shape of the boat will not tell you whether or not you'll be exposed to the rain - that's something for you to decide based on your diversification). It's not up to you to control as stock's beta just like it's not up to you to control how the boat will move - the boats are there laid out for you and built already, you can simply choose a pre-built one.
Going further, we now can see that just because the water moves a certain way (eg. just because the market goes a certain way), it does not at all imply that each stock will move the same way. It is obvious when we think of our port - no one would ever question that boats designed differently would move differently in the water. By the same token, it should be easy to see that firms (which are comprised of different people, processes, assets, liabilities, products, knowledge, etc.) will move differently when the overall market shifts and changes.
Why do firms move differently with the market?
Going a bit further, we can ask what the underlying causes are for different betas (for different movements relative to market risk). We know why the boats move different (because they are designed differently), but understanding why firms move differently is a far more complicated matter.
Firms are different in many ways. Some of these ways include:
These things, and much more, clearly influenced the way a firm's cash flows and stock price (which is dependent on both cash flows and overall market sentiment int the short run) will change based on changes in the market. A firm located in a single US state in Middle America that sells basic goods to people of that state exclusively is clearly exposed to less market risk (eg. less geopolitical risk, less market risk, exchange rate risk, economic downturns, etc) than a multinational firm that produces services that businesses generally purchase in prosperous times but can do without in difficult times. Clearly, one firm's beta would be less than the other if the beta is a measure of a firm's relative exposure to market risk.
Quick Note on the Beta of the Market
The beta of the market (eg. the beta of the S&P 500) is said to be 1. This will make sense further down the line because we will see that the beta is calculated by seeing how a stock's prices more relative to the S&P 500. A beta greater than 1 indicates a stock more volatile than the S&P 500 and vice versa - clearly, then the S&P 500 will have a beta of 1 because it moves with perfect correlation to itself.
Another Quick Note on What Diversification Means
Now that we've gone through the basics, we must define diversification. True diversification when discussing beta and when saying that an investment is diversified involves holding the entire market - meaning all stocks, all bonds, all real estate, etc. (or a portion of a basket of them). Holding just a diverse portfolio of stocks still exposes the holder to idiosyncratic risk - they are exposed to shocks that only or primarily affect the stock market.
Now, it is difficult and cumbersome to use as total market basket - one doesn't really exist because it's hard to value things that don't have regular market prices like stocks. Therefore, most finance texts use a proxy for the market - that proxy is the S&P 500 most of the time. We'll note that this is a weak proxy because it only focuses on 500 major US stocks - ignoring all of the other stocks and asset classes that one could invest in. Keeping that in mind, we can proceed with using the S&P 500 due to the fact that it is commonly used and that it will still produce reliable results and metrics for our use and understanding.
And Finally...How to Actually Calculate the Beta
We've spent a lot of words and sentences discussing what the beta is, but without an actual walkthrough of the calculation, the entire concept is likely to still be obscure to those who have not studied finance before. Let's dive right into the calculation.
Another way to take the beta is the correlation of price movements of a stock to price movements of the S&P 500 (eg. the market). We talked about risk before this, but in order to actually quantify these concepts, we must move from a world of words to a world of numbers. We can do that by talking about prices - risk can be represented by volatility (by price movements). We can look at the price movements of a stock and the price movements of the S&P 500 side by side and see how the move - they might move in tandem, the stock might move more aggressively than the S&P 500 (more volatile - higher beta), or it might move more calmly than the S&P 500 (lower volatility - lower beta).
In order to get the numbers (both the stock you're looking at and the S&P 500), you can simply use the internet to obtain historical prices - it's a relatively simple exercise. You'll want daily prices and you'll want to make sure that the data lines up in terms of day and the exclusion of weekends - you'll want a day-to-day match up. Additionally, if any stock splits occurred over the period you're looking at, you'll want to take the post-split stock price for the entire time period - this will avoid adding a lot of error because if you don't adjust the price it will seem like the price dropped significantly on the day of the split. It's pretty easy to use a post-split number for the entire period (post and pre-split) because most online repositories of historical stock data will do this for you automatically.
Next, you'll have to calculate daily returns - this is simply done with the follwoing formula and should intuitively makes sense:
return = (today's price - yesterday's price)/(yesterday's price)
This is a simple percentage change over a single day and this should be done for both your stock and for the S&P 500. You'll now have a list of daily price changes for both the stock and the S&P 500. The reason we look at price changes is because we want to see how the movements of the stock related to movements of the s&P 500 - in effect, we don't really care about the absolute prices of either the stock or the S&P 500 but are only concerned with their movements over time.
One important thing to note is that you'll want to capture enough time within your analysis - you'll likely want a full year's worth of data.
Finally, you'll compare the price movements of the stock to the S&P 500 using the most commonly used formula for calculating the beta of a stock:
beta = cov(x,y)/var(x)
where x is the stock and y is the S&P 500 and where var(x) does not equal 0.
This formula might seem complicated, but it really isn't - it can be easily explained and easily performed din a program such as MS Excel using the functions COVAR() and VAR() over a list of price changes.
Covariance (which is represented by cov in the above formual) is simply a measure of the joint variability of two random variables - it's a measure of the degree two random variables (here the random variables are the price changes) move in tandem with each other. Variance (which is represented by var in the above formula) is simply a measure of how much a random variable (here the random variable in question is S&P 500 price changes) moves about its mean.
Once you have the covariance of the stock and the S&P 500 and the variance of the S&P 500, you simply divide the two numbers per the above formula to obtain the stock's beta - you now have a very powerful piece of information telling you how a stock moves relative to the S&P 500 (which is a proxy for the market). You now know how risk the stock is relative to the market and how much risk the stock would add to a diversified portfolio - you now know the systematic (undiversifiable) risk of the stock.
The 5 types of beta
We touched on this above, but let's formally review the possible betas:
There are No "Bad" Betas
Remember, in no place did we say that any beta measures are bad. A beta of less than 1 is not bad. A beta of greater than 1 is not bad. Beta simply tells you how much the price of a stock varies relative to the market, it does not imply anything beyond that. A beta of less than one might be desirable for a conservative investor while a high beta might be desirable for a more aggressive investor who is looking for more return. A stock's beta tells us a bit about the expected turn of the stock with higher betas indicating higher expected returns - this makes sense because more risk should entail more reward. However, this discussion about translating beta measures into an understanding of a stock's expected return is beyond of the scope of this present discussion.
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