In the last post we talked about the importance of understanding what explicit and implicit assumptions we were making as we attempt to make important investment decisions. I want to focus on one particular erroneous assumption that I see all the time in investing – false precision. Good scientists are always trained to understand precision well. Those who aren’t trained can pick this concept up quickly, though, once it is explained.
To give an easy to understand example of how this is important, let’s say you must know which of 2 mountains is tallest. Maybe because you want to build a communication tower on the tallest one. You measure how tall 2 mountains are using a laser or GPS let’s say, but your method is only accurate to 100 feet, and you measure one mountain as 9,999 feet tall, and the other mountain as 10,001 feet tall. Which mountain is taller? The answer is – you don’t actually know which mountain is taller. Your measured value and the true value may differ and reporting the height of the mountain to the nearest foot doesn’t change the fact that you only really know the height of each mountain to the nearest 100 feet. You have reported the height of these mountains with a false degree of precision (to the nearest foot, when to the nearest 100 feet is really all you should be reporting).
Now let’s look at this for an investing example using discounted cash flow analysis. You analyze a company and its market in depth and determine that its earnings will grow at 3.0% forever. You determine that the discount rate for these cash flows should be 5.0% based on a risk free rate of return on some US bond or based on a particular return hurdle that you require. You determine that the stock price should be $12 / share based on summing up all these future cash flows discounted to their present values. The actual stock price is $11. You are getting a discount, right? Wrong. You will be 100% guaranteed to be wrong in your assumptions here. The question is by how much, and whether you are wrong in a favorable or unfavorable direction. Let’s say that the actual growth rate (measured many years later) was 2.5% on average and that the earnings jumped around quite a bit. Further the company had a few bad years right after you bought, but later returned to a higher than expected level of performance. In addition, the Federal Reserve started raising interest rates soon after you bought the stock, so your actual discount rate should have been 7%. Based on this, the stock price that you would have determined if you had perfect information should have been $8 / share. You overpaid in part because you assumed a higher level of precision than you actually had. When you thought you were getting the stock at a 10% discount, you were actually overpaying by 27%.
So what is to be done about this? After all, you can’t really know what the exact numbers are supposed to be until they can be observed for many years after the fact. By then, it is too late and the market will have chosen a different price for the stock based on its new performance and new theories about its future. There are actually a couple of things you can do. The first is called sensitivity analysis. You can look at different growth assumptions for the company or different discount rates and understand the effect these have on the stock price. If you assume the discount rate is 5% and it really ends up being 7%, does that change your opinion of the stock or is it still a good deal? If you assume that growth is 3% and it really ends up being 2.5% what happens to the share price you calculate? What about if the sequence of returns changes (i.e., same average growth rate but more growth earlier, and less later or vice versa)? By running through several scenarios, you start to get an idea of most likely outcomes. This is more of a probabilistic analysis than arriving at a precise share price down to the nearest penny. The importance of learning how to do a discounted cash flow analysis is to understand how all the parts and pieces interact and move with each other, so you can understand what decisions to make based on changing information in the future.
The second thing you can do about this imprecision is to look for companies that are definitely underpriced – not just a little underpriced and balanced on a knife’s edge where if one little assumption goes wrong you end up losing money. To put it into easier terms, let’s use an analogy of Benjamin Graham‘s that I will term the Fat Man / Skinny Man Principle. It goes something like this. Imagine that you are looking at a man and he is very obese. You do not need to know his exact weight to know that he is very overweight. Similarly, if you look at a very skinny man, you do not need to know his weight to know that he is very underweight. Further, if you had to classify people by weight into only 2 categories (overweight and underweight) and you saw a very overweight or underweight man, it would be easy to place them in these categories. People in the middle might be quite difficult to classify, because who knows where the precise transition between overweight and underweight occurs.
To extend this analogy to stocks, you pick stocks where you can live with the imprecision. If you pick a company that, by every measure is undervalued, and you run several realistic scenarios and it is still undervalued, you probably have an undervalued company and can investigate further or invest. Lot’s of things can go wrong and you will still end up making money. While nothing is guaranteed, you have tilted the probable outcomes in your favor. If you have a company where you run several scenarios and in some it is undervalued, while in others it ends up being overvalued, you probably have a situation where you are stuck in the middle somewhere, where the outcome is more difficult to evaluate. In this case, you might analyze several different investments and pick the best one amongst those if there are no better alternatives to maximize your chances of success. What you don’t want to do is depend on being accurate to the penny, because you will always be incorrect about some measurement that you estimated, when it comes to stocks.
Remember also, that you never make a single decision only to purchase a stock. That decision is always paired with a decision to forego the purchase of anything else with that capital. So, it can be helpful to make this pairwise/multi-way decision-making process more explicit and use these cash flow analyses and other types of analyses to make decisions between multiple possible investments, choosing the best one. Also, keep in mind that there are other decisions that go into this selection than just valuation, such as the risk profile and diversification of the overall portfolio.
Many inexperienced investors purchase stocks without doing any kind of valuation analysis. A few more experienced ones will look as far as price to earnings of a stock. Far fewer do a discounted cash flow analysis which is a more detailed dive into the company’s valuation. And of all of these investors that do discounted cash flow analysis, fewer still understand that the discounted cash flow analysis contains a lot of false precision. Now, I would very much recommend that you learn to do discounted cash flow analysis, if you don’t already. Not because you will be calculating a stock’s value down to the penny, but because you will learn how different things affect the stock, and how all the parts work together. This will allow you to understand what assumptions you make that may have large effects on your future investment outcomes, and you can then make better decisions based on most probable outcomes. As you get pretty good at this, you will be able to look at a stock’s earnings and cash flows, and quickly understand in your head whether that company is a good deal without even going through the discounted cash flow analysis first. You will also understand how various assumptions can affect the stock quickly. This allows you to make good decisions more quickly when it comes to investing, or at least down-select potential investments rapidly before doing a deeper level of analysis. Finally, understanding how these models work can give you deeper insight into what is really important and how the variables affect your returns, such as the analysis we did with the Gordon growth model in a previous post.
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