Overview – A High Level of Precision Is Always a Good Thing, Right?
Imagine you’re baking one of your favourite desserts – a chocolate cake. Like any other baked good, the recipe calls for all sorts of different ingredients, one of them being flour. You read that 4 cups of flour is needed, but you accidentally go a bit over and instead measure out 4.25 cups.
Will that make a huge difference? Probably not. Your cake may be ever so slightly bigger, but the difference will be so negligible that it doesn’t matter anyway.
Now, let’s say the balance you owe on your credit card for the previous billing cycle is $135.56. You pay your credit card bill manually, so you log on to your online banking account just like you normally would, but you make a mistake and enter $135.50 for the funds that need to be transferred – a mere $0.06 short. By the time you notice the mistake, the payment due date has already passed.
Even though you’re just a few cents off, that still counts as an unpaid balance in the eyes of the card issuer, resulting in points being deducted from your credit score. For some people with shaky credit scores, this could mean the difference between getting approved for a loan that they need or not.
As you can probably tell from your own life, different aspects of it assign varying degrees of importance to precision. In some cases, it might not matter if you’re slightly over or under, but in others, it could potentially make all the difference.
We know that investing depends very heavily on analysis, calculation, and logical thinking. We’ve even talked about the importance of investors having a sufficient level of mathematical skill in order to work with numerical data effectively. Sometimes, incorrect calculations, misinterpreted data, or imprecise data can have a significant impact on an investor’s work and subsequent decisions.
If that’s the case, then how precise do investors need to be to avoid ending up in a sticky situation?
Understanding the Basics: Precision vs. Accuracy
Before continuing our discussion, it’s important to first understand the difference between precision and accuracy. Though commonly used interchangeably, these terms talk about two very different things. The image below visually showcases those differences.
A high degree of accuracy means data is close to a desired measurement’s true or accepted value. Meanwhile, precision is how close measurements are to one another.
Let’s go over a simple example: imagine you’re asked to identify which municipalities are closest to the Canadian city of Edmonton.
If you answered Calgary, Red Deer, Lloydminster, and Medicine Hat, you’d be accurate because these cities are all in Alberta (the same province Edmonton is in), but imprecise because none of them are close to Edmonton.
Had you instead answered Toronto, Brampton, Mississauga, Markham, and Oshawa, your answer would be very precise because all of these municipalities are very close together (all are part of the Greater Toronto Area), but inaccurate because they’re in an entirely different province.
How Important Is Precision Out in the Real World?
Given investing’s quantitative and analytical nature, it’s natural for some people to think that it’s a very precise activity.
There is some truth to this belief – investors rely on correct, high-quality, and up-to-date information, but it’s important to remember that all investors operate in the real world. Because of this, not all the information that investors receive is ideal, and as a result, investors may not always get the desired level of precision they want in their work.
This may sound like a serious problem, but is it really? In the real world, achieving a high level of precision is sometimes necessary, but it comes at a cost. Depending on the circumstances, this cost may or may not be justifiable.
Imagine you’re a soil biologist that’s part of a multinational team responsible for analyzing soil samples from Mars. Soil samples are relatively easy to obtain, store, and transport, so because of this you’re used to working with very large sample sizes, and because of this, your work can achieve a high level of precision. This time, however, your sample of martian soil is less than you’re accustomed to.
You’re still able to perform your work properly, but you want more soil to achieve a higher level of precision in your measurements and calculations. Slight problem: Mars missions take months, if not years, of preparation. Lots of time, effort, energy, and money are poured into making sure these missions succeed. With this in mind, it’s very unlikely that another Mars mission will be prepared in the near future for the sake of attaining a slightly higher degree of precision in your soil analysis.
What if, instead of a soil biologist, you’re a cardiac surgeon? When performing an operation such as open-heart surgery, the last thing you’d want is to make an incision that’s slightly too big or cut the incorrect artery – even the slightest mistake can result in complications at best or death at worst.
In this case, you want to be precise as possible, but as was mentioned earlier, this comes at a cost. Given the severity of the consequences of an imprecise surgery, the extra cost is justifiable: spending more money on high-quality tools and taking hours on end to perform an operation to near perfection is worth minimizing the risk of experiencing the lawsuits and grief associated with killing or severely injuring a patient.
Every day, people all over the world decide if the benefits of being more precise outweigh the price that comes with it. For some people, the answer is very clear, whereas for others the answer must be determined on a case-by-case basis.
Investors are free to pursue a higher level of precision in their work if they feel it will ultimately benefit them, but they must seriously ask themselves how much they’re willing to pay in order to achieve that, and if the benefits of more precise work are worth the extra time, effort, energy, and money they must spend.
While there’s nothing wrong with trying to perform more precise investment work, in many cases a high degree of accuracy while only having a moderate level of precision is usually more than enough.
In Investing, It’s Better to Be Approximately Right Than to Be Precisely Wrong
In you’ve gone through the value investing article, then you know that the major tenets of this investment paradigm are intrinsic value and having a margin of safety.
We know that intrinsic value is, at best, an approximate estimate of what an investment’s true (i.e., intrinsic) value should be. Of course, this isn’t just some wild conjecture – this is something that’s calculated based on numerical data and other inputs. However, given the countless ways it can be calculated and all the different factors that can go into that calculation, it’s impossible to arrive at a “true” intrinsic value.
Graham and Dodd understood the imprecision that intrinsic value inherently had, so they attempted to overcome this weakness by introducing the concept of having a “margin of safety” as a sort of fudge factor.
An imprecise valuation tool, intrinsic value, coupled with a mechanism to compensate for that imprecision, margin of safety, went on to revolutionize investing. Intrinsic value and margin of safety are by no means perfect but are still effective ideas used by all kinds of investors to this day.
When going through financial statements, investors plug in all sorts of data into a variety of different ratios and equations. When crunching the numbers, different investors may opt to carry out their work with varying degrees of precision – one may opt to use up to 6 significant digits in their calculations, while another may be content with using only 3.
Despite the varying levels of precision between investors, chances are the final numbers won’t vary by a very wide margin, and the conclusions they form will more or less be the same. An investor who has a calculated P/E ratio of 5.3649 probably won’t stress when someone else’s value is 5.5523 since they’re roughly in the same ballpark.
When creating a valuation model such as a discounted cash flow analysis, some investors take certain mathematical liberties to make their calculations a bit easier. Sure, their final numbers may not be as precise as they originally hoped, but as long as they feel that their model will still produce results they feel are accurate based on their past experiences and expectations, then there shouldn’t really be a problem.
Whether it’s trying to ascertain the value of a certain investment or going through numerical data, investors usually place a greater emphasis on being accurate rather than being precise. This may seem odd for such a quantitative field, so let’s take a step back and understand why it may not be so.
Looking back at the image that showed the difference between accuracy and precision, an accurate but imprecise set of data is closer to the true/expected value than a precise yet inaccurate data set. It’s entirely possible for an investor’s work to be extremely precise and still be wildly off the mark (hence the saying “it’s better to be approximately right than to be precisely wrong”). Talk about a massive waste of time and effort.
This leads us back to another previous point: achieving a high degree of precision is possible but it comes at a cost. Based on how important you think a greater degree of precision is, the extra cost may or may not be worth it.
Some investors may find an increased level of precision to be worthwhile. Perhaps a certain decision they need to make has a very narrow margin for error, so they must ensure their numbers are correct down to a t. These sorts of investment decisions are few and far in-between, but they may pop up during some investors’ careers.
For most investors, however, a higher degree of precision in their work won’t dramatically alter their decision-making, so the extra time, effort, and energy needed to obtain that usually isn’t worth it.
Emphasizing Accuracy Over Precision Is No Excuse to Perform Subpar Work
Although being approximately right is usually more than enough for investors to make informed decisions, this doesn’t give them a free pass to start performing substandard work. After all, this makes it sound like investors are free to take some liberties with the quality of their work as long as it’s “good enough”, but that certainly isn’t what’s being advocated here. To understand why let’s go back to one of our previous discussions.
Earlier we discussed how intrinsic value is a classic example of an investment tool that focuses on being approximately right, and it certainly is, but that doesn’t mean calculating intrinsic value is something that can be done on a whim.
Regardless of how an investor goes about calculating it, they’re responsible for making sure they use the correct data, any assumptions they make are reasonable, and that the number crunching they perform is done correctly. The objective may be to calculate an approximation, but an investor is still responsible for making sure that all the in-between steps are carried out correctly and rigorously.
When performing ratio and other numerical analyses, it may not matter if an investor chooses to work with 3 significant digits instead of 6 when performing their calculations, but they’re still responsible for making sure their math is right and that they’re using the correct data in the right places.
Therefore, emphasizing accuracy over precision can be thought of as the overarching philosophy that guides an investor’s priorities when performing their work, not something that dictates the quality of it.
Investors may not need to go the extra mile in order to make their work more precise, but given that their decisions are influenced by the quality of the work they perform, it’s still important that they always put their best foot forward.
Wrapping Up
Investors rely on numerical data, analysis, and logical thinking to help form conclusions that will guide their decision-making. A misstep here can have some very serious consequences, so it’s in an investor’s best interest to ensure that their results are as high-quality as they can reasonably make it.
If that’s the case, then surely this means an investor must ensure their work is very precise, right?
While it certainly doesn’t hurt to have a high level of precision, achieving it comes at a cost. In real-world applications, sometimes this cost isn’t worth it, and other times it is – it all depends on the specific situation at hand.
With respect to investing, investors are usually better off focusing on achieving a high level of accuracy while making some concessions with precision. Of course, investors are free to pursue a high level of precision if they feel it’s worth it, but they must seriously ask themselves if the cost associated with doing so will be worth the results they’re seeking.
Emphasizing accuracy over precision may sound like investors can take some liberties with the quality of their work, but that isn’t the case at all. A final answer may be highly accurate and slightly imprecise, but they’re still responsible for making sure that all of the in-between steps that must be taken to get to that final result are performed correctly and rigorously.
