Overview – Investing Is, at Its Core, a Numbers Game
It doesn’t take long for new investors, or even investors-to-be, to realize just how quantitative of an activity investing truly is.
Every day, all sorts of numerical data is produced, recorded, and reported all across the investing world. Whether it’s something as relatively simple as a company recording its revenue over the past quarter, or something as complex as an investment bank trying to create a valuation for a company about to go public, numerical data is the lifeblood of investing.
Investors make use of numerical data all the time to help shape their decisions, and while they largely have access to the same numbers, not all of them can manipulate those numbers in the same way or identify the same insights. Put another way, not all investors have the same level of mathematical skill.
Because investors have varying degrees of skill in math, some are able to extract deeper insights from numerical data that others may have overlooked or simply didn’t recognize. The effects of this disparity can quickly accumulate, and can directly affect the quality of an investor’s decisions and even dictate their long-term investing success.
If that’s the case, then how much math do investors need to know, and how skilled do they need to be in those different areas?
Math in the Context of Investing
Many people think of math as nothing more than just working with numbers by performing the basic operations on them (add/subtract/multiply/divide) and by plugging them into some equations to get a final answer, but it’s much, much more than just that.
Mathematics, according to the online encyclopedia Britannica, is “the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation.”
Math can best be thought of as a tree made up of countless disciplines, each of which represents various topics such as calculus, linear algebra, and combinatorics, to name a few. Given the depth and breadth of these disciplines, they can be applied in all sorts of ways based on the context they’re being used in.
Computer scientists rely on discrete mathematics, boolean algebra, and combinatorics to solve all sorts of computer science problems. Insurance actuaries rely on statistical and probability models to help determine appropriate premiums for different types of people. Engineers rely on calculus, algebra, and statistics to ensure the systems and processes they design are safe and work effectively.
Different fields rely on math in different ways based on the quantitative data they’re working with and the type of logical conclusions they want to arrive at.
When it comes to investing, quantitative data is presented to investors in a seemingly endless stream and in all sorts of ways. Financial statements, charts, graphs, and tables are some of the common methods. The challenge investors face is to understand how all this data relates to one another, and by understanding that relationship, extract insights they feel are important.
If that’s the case then what sort of mathematical skills should investors have in order to extract the insights they need and form the correct conclusions?
The Math Investors Need to Know
Although investing is very quantitative in nature, for the most part, the math skills that most investors will need aren’t overly complex. Now, this isn’t to say that advanced math skills are useless (more on this later), but rather the point here is that investors don’t need to have advanced math skills in order to do their work effectively.
When talking about specific disciplines of math, by far the one that investors will use the most is algebra. Investors use a variety of ratios and equations when performing analysis, so understanding how to manipulate all sorts of equations in order to solve for a certain variable and being comfortable in doing so is certainly an invaluable skill to have.
Statistics is also another discipline of math that has the potential to serve investors very well. Although statistics can become very complicated very fast, investors don’t need to be subject matter experts in order for it to be helpful to them. Understanding statistical terms such as the mean, median, and outliers is a solid start. Investors who want to go a bit deeper may also want to look at understanding how confidence intervals work.
In the preceding section, it was mentioned how quantitative data is presented in all sorts of ways, and one of the most common is through visual tools such as tables, charts, and graphs. These tools certainly add to the aesthetic appeal of an otherwise long, boring document such as an annual report, and can be used to convey important information in an easy-to-understand manner.
Visual tools certainly look nice, but they’re also an easy way to hide certain unwanted blemishes in the data. Therefore, investors need to know how to dissect, analyze, and extract insights from all sorts of visual tools they come across. Math is more than just number crunching – being able to understand quantitative data despite being presented in different forms is another aspect of it too.
So, investors need some level of mathematical competency, but they certainly don’t need to be experts. However, what if you do have advanced knowledge and skills in math owing to your formal education/training or because of personal study? Does this give you an advantage over investors who don’t have the same level of skill or is it something that’s simply nice to have?
Is Advanced Knowledge and Skill in Math Useful to Investors?
Because investors come from all sorts of backgrounds, investing can be as mathematically simple or intensive as they want it to be.
On one end we have investors whose math education is limited to what they learned in school (not including any sort of post-secondary education), and on the other hand, we have those who hold advanced degrees in math or some other subject area that is very math-heavy (e.g., physics, quantitative finance, engineering, etc.)
Regardless of what background an investor comes from, the fact of the matter is that working with numbers is unavoidable in investing, so some degree of math skill will always be required. The skills that were discussed in the previous section represent the minimum that investors should have, and for many, this is usually more than enough to do their work effectively.
However, investing can become very mathematically intensive, very fast. The Black-Scholes model, Risk-Adjusted Return on Capital, Value-at-Risk, and a whole plethora of other models and equations are used on a regular basis by institutional investors, investment banks, and all sorts of financial institutions to guide capital allocation strategies and other major decisions.
Investors who have the required math skills needed to understand how these advanced tools work can apply them to their own analysis and decision-making processes, putting them at an advantage over investors who don’t have the same level of math savviness.
This advanced skill also grants investors the ability to look beyond traditional investment instruments such as stocks and bonds. Options, mortgage-backed securities, and a slew of other financial derivatives are traded on a daily basis but are mostly owned by institutional investors who have the capital and mathematical know-how needed to properly evaluate and trade them.
Investors who have the advanced math skills needed to properly understand and analyze these exotic investments can potentially add them to their portfolios without much issue.
Of course, an advanced understanding of math isn’t necessary, but if an investor wishes to take a more technical investment approach and/or wants to include exotic investment instruments in their portfolio, then a greater level of mathematical prowess will certainly be helpful.
Strong Math Skills Are Helpful for Any Investor, but It Doesn’t Guarantee Any Success
Given the quantitative nature of investing and the importance of being able to extract insights from a deluge of data, it’s clear that having sufficient math skills is important to perform investment-related work effectively. One of the worst things that can happen to an investor when performing their work is being unable to extract the insights that they want because they lack the skill needed to do so.
If an investor’s ability to perform high-quality work is so dependent on their ability to work with numbers, then this means that an investor should develop their math skills as much as possible and that their potential success is directly proportional to their mathematical competence, right?
While strong math skills are important and can certainly take investors a very long way, it doesn’t guarantee any sort of investment success. That’s because an investor’s temperament and ability to stay rational are equally as important as their ability to crunch numbers and understand data.
It’s no secret that there are many people involved in investing who possess superb math skills, yet despite their prowess, they’re still prone to making bad investment decisions and suffering steep losses. A classic example of prodigious amounts of brainpower ultimately amounting to failure is the now-defunct Long Term Capital Management.
Whenever some bad news starts to make headlines or recessionary fears are on the horizon, many investors are quick to panic sell, including the aforementioned math whizzes. What good are your number crunching, data analysis, and logical reasoning if the first thing you do upon running into signs of trouble is to let your emotions take over?
Knowing how to effectively and comfortably work with numerical data is a skill all investors should possess, but what truly makes them a force of nature is pairing those superb quantitative skills with an equally strong ability to keep their emotions on a tight leash and the ability to stay rational even in the most emotionally taxing circumstances.
Wrapping Up
Investors are bombarded with all sorts of numerical data that they need to interpret, analyze, and dissect in order to help form their decisions. Therefore, it comes as little surprise that investors need some degree of math competency in order to perform their work effectively. The question is, how mathematically skilled do investors need to be?
Fortunately, investors don’t need to be math experts in order to perform their work effectively. Knowing how to re-arrange equations, interpret data when presented in different forms, and some introductory knowledge in statistics is usually more than enough.
Those who possess a greater degree of mathematical prowess can make use of more advanced equations and models as well as explore more exotic investment options, but by no means do investors need to possess advanced math skills if they don’t already have them.
While all investors require some degree of mathematical competency, success isn’t guaranteed simply because an investor is more mathematically skilled than others – it’s not unheard of for math whizzes to make bad investment decisions or suffer from steep losses. Strong math skills coupled with equally strong emotional control are what set great investors apart from good ones.
