Financial markets are collections of billions of decisions being made by different people, and all of those decisions culminate into prices, cash flows, valuations, yields, and more.
Many of these decisions are trivial, and I mean that word literally. Remember that in mathematics, a trivial statement is one that is self-evident, like 2=2. Extended to finance, we could say that a trivial statement is one where the answer is objectively derived from numbers within the system and given the contextual framework of the question.
A simple example may be illustrative. The NPV of three years of $100 cash flow at a 5% discount rate is $272.32, not because of any opinions from different analysts or different methodologies of analyzing data. That’s simply a fact because the NPV calculation is NPV = Rt / (1+i)^t, so the answer will be the same for everyone at all times.
Digging deeper, we quickly discover that this method of analysis is objective, but the assumptions in the analysis are not. The $100 cash flows are in the future and not realized—how do we know they will actually be $100? In the real world, there are many assumptions here on the amount and timing of the cash flow that the initial calculation does not incorporate. These are qualitative factors influencing one input of the model, which is really just the output of another model. The NPV is a model of how much those cash flows are worth today; another model has told us that we will have those cash flows, when we will have them, and how much they will be.
There are more assumptions in our analysis—why a 5% discount rate? What, after all, is a discount rate? Technically, it is supposed to reflect the cost of capital (i.e. how much does it cost to acquire the capital to buy the future cash flows? How much could our cash return elsewhere?), but the buyer of capital does not set their cost—the cost depends on borrowing rates, the borrower’s creditworthiness, liquidity availability in the market, and many other elements that are a mix of quantities and qualitative assessments.
Similarly, if we look at our future cash flows from the perspective of a credit rater, we can say the same things about our future cash flow. It depends on the legitimacy of the business (assuming it’s a business), its ability to operate and expand, and so on.
The point here is that the future is uncertain and all financial formulas and models attempt to quantify the certain and uncertain aspects of cash flows—and this is the core of the art of finance, and something often misunderstood.
Let’s extend our example further and say we’ve been offered an opportunity to buy a product line from a company, and we know that this company’s product is well established and popular—but it is old and its popularity is waning, and if a competitor releases a really good competing product, the product we’re investing in will see its cash flow decline at a faster rate than the current rate we’re seeing.
We would then need to apply a rate of decay to our cash flows. If one analysis says we’ll see a 50% drop in year 3 after two flat years, we’ve got $250 in cash flows (100 + 100 + 50 after the 50% drop), with a $229.13 NPV. If, however, we see the cash flow declining by 20% in year 1 and 12.5% in year 2, we get $250 in cash flows (100 + 80 + 70) but a $228.27 NPV. We now have two different prices for our cash flow asset although the cash flows end up being equal.
That’s a small valuation difference, to be sure, but the differences will only grow as the cash flows get more complex and we incorporate more and more qualitative modifiers to our analysis. One also sees how the more features we put in our model, the more it disagrees with other models.
To do this properly and comprehensively, you need to vectorize the qualitative. That simply means you take all of your qualitative factors—like the popularity of a competing product that may be produced in the future—and turn them into quantities that you then incorporate into your model. These factors become little nudges that move the price point of your model over time, and ideally they will nudge your model’s price point closer to the cash flow’s real NPV incorporating all factors into the cash flow analysis.
In math, you’re often taught to focus on the objective and reject subjective assessments. In finance, you’re often encouraged to turn subjective assessments into objective values. This is hard, it is always imprecise, and most analysts get frustrated with the task. However, those who are really good at it end up becoming extremely valued, especially in the world of asset allocation.