What exactly is “finance”? At a very high, abstract level, it can be defined in many ways, and one possible definition is defining value. This is obvious with the basic question of whether one should take a dollar today or two dollars at point x in the future, but it also applies in much more complex ways to other financial circumstances. In short, it is about determining values and where those values are coming from and going to.
We can take this even deeper if we pick apart the word “value”. You certainly have heard talk about having “good values” or “bad values” and seeing “values” as referring to some sort of moralistic code. In non-financial everyday situations, this is a pretty typical use of the word.
Finance, however, isn’t everyday life, and it really should be seen as a form of applied economics with a more consistent but also more simplistic mathematical backbone. As an offshoot of an offshoot of math, then, “value” in finance should be related to the mathematical concept. When we do this, a lot of ambiguity disappears.
Consider a hedge fund analyst who says that a company is worth $10 per share based on its free cash flow of $1 per share that is growing 10% per year. That analyst believes that the value of the future cashflows now has a value of $10, and she got there through a simple TVM calculation. Values, then, are statements of current solutions to equations. In this case, the question is “what is the value of share X when it has cash flow y growing at level Z.” This is simple algebra, and the value is the answer to the question.
Values in math are objective, having been built on axiomatic systems of statement, expression from statement, and logic to get from expression to expression. This is very different from political or personal values and should not be misunderstood!
They very often are, however, because humans are fallible and make mistakes. Confusion between a simple mathematical calculation and ethics is common, because many fail to consider that “value” and “value” are homophones meaning different things. A mathematical value cannot be good or bad—it can only be wrong or right.
Going back to the hedge fund analyst example, this is a conundrum. The analyst’s math can be completely correct, and she can conclude that there is a $10 per share value and be correct. However, the analyst’s premises can be completely wrong, resulting in a value that is correct according to the analyst’s axioms, but it is ultimately a wrong value in the market because the analyst’s axioms are different from the market’s.
This can work the other way—different axioms by the analyst can make the analyst more correct than the market. This is how investors can produce “alpha” and make many millions of dollars.
This should also give every analyst and aspiring rich person pause. You don’t get an edge in markets by having better math, not really—there are correct values and incorrect values, and as long as the calculations in your model are correct then the values are correct. according to the assumptions and beliefs of the model. It’s just that the assumptions and beliefs are wrong.
Consider the 10% growth rate in the above calculation. If the analyst is correct that there has been 10% growth in the past, the analyst is also assuming as axiomatic that that growth rate will continue at that rate.
What if it doesn’t? What if there is a pandemic, or a competitor produces a better product, or the company releases an even better product with larger or smaller margins? What then?
None of these change the mathematical principles of the model, so better math won’t make a better analysis. They do change the axioms of the model—the basic assumptions behind it—and if changing those assumptions produces a value that is closer to what the company actually produces in the future than other estimates, the analyst can make a lot of money.
This may sound trivial, but it has important implications. This means that analysts who focus their time on improving the models themselves will underperform—the analysts who focus on improving the assumptions of their models will do better. It also suggests that assets that have less volatility in their fundamentals—in other words, companies with stable revenue and earnings growth—are likely to have the least upside/downside potential for analysts without exogenous shocks disrupting the trend.
The important exception is when very new and unexpected news hits the market, which can cause sudden spikes or declines from otherwise stable companies. That new and unexpected news comes from the outside, is almost always not immediately recognizable as a financial or even mathematical question and is very hard to research. Consider Abercrombie & Fitch (ANF), a fashion stock that’s up over 100% in 2024 thanks to aggressive pivots in strategy and offerings by the firm that have also become trendier.
Can you predict that before it happens? Can you create a system that predicts them early? And if you could, would the uniqueness of that system be thanks to its use of complex financial math—or something else?