Any individual decisions can be badly thought through, and yet be successful, or exceedingly well thought through, but be unsuccessful, because the recognized possibility of failure in fact occurs. But over time, more thoughtful decision-making will lead to better overall results, and more thoughtful decision-making can be encouraged by evaluating decisions on how well they were made rather than on outcome.
- Robert Rubin
The above wonderful quote by Robert Rubin offers great implications with regards to the investment decision making and investment outcome evaluation processes. Very often, a flawed decision making process somehow yields satisfactory, or even superior outcome, compared to that of a better and well thought-out decision making process. However, human nature inevitably makes us automatically equate heroic investment results to the upshot of a sound investment process.
In the world of value investing, most decisions are made based on the perceived level of margin of safety. However, the calculation of margin of safety, which is of utmost importance, is often carried out inappropriately. In most cases, the failure to incorporate an expected return mindset, or the inadequate application of an expected return mindset, attributes the most to a flawed margin of safety calculation. Renowned value investor Michael Mauboussin once said that “investors, like most of the general population, inevitably encounter pitfalls based on human behavior. As an example, overconfidence results in too narrow an outcome range, and the confirmation trap compels us to seek confirming information and dismiss or discount that which disconfirms.”
Let me use an example from articles posted on gurufocus to illustrate this point.
Here is how an investor reached his or her intrinsic value of MasterCard in an article titled “MasterCard: A Steady Wealth Creator.”
In the last three years the earnings have grown at a CAGR of 22%. If we consider a conservative estimate of 18% forward EPS growth rate and a PE of 29 and assuming all goes well and the company earns $15 EPS in the next 10 years, then I believe the stock should be worth $108, which gives us a return of 42% from the current price.
Here the author’s return calculation is arguably inadequate as his conclusion implies that a $108 price tag for MasterCard is the the only, or what the author considered the most likely outcome of an investment in MasterCard. The author then used this $108 to arrive at margin-of-safety equivalent of 42% (this implies MasterCard was at $62.64 at the time the article was written).
What is missing in this investor’s process is setting probabilities and considering outcomes, and then calculate the expected value as the weighted average value for a distribution of possible outcomes. Using a overly simplified matrix below, we can see how by incorporating the expected return can change how one looks at the margin of safety.
| Scenario | Probability | Outcome | Weighted Average Outcome |
| All Goes Well | 0.25 | 108 | 27 |
| All Goes Phenominal | 0.25 | 120 | 30 |
| All Goes So-So | 0.25 | 90 | 22.5 |
| All Goes South | 0.25 | 70 | 17.5 |
| Expected Value | $97 | ||
| New Margin of Safety | 35% |
Of course, the expected value and accordingly, the margin of safety, depend on the “rosiness” or “gloominess” of an investor’s expectation. Someone who has a less bullish view of MasterCard will naturally assign higher probabilities and lower values to the less favorable outcomes and lower probability and lower values of more favorable outcomes, such as the result shown in the following matrix:
| Scenario | Probability | Outcome | Weighted Average Outcome |
| All Goes Well | 0.20 | 100 | 20 |
| All Goes Phenominal | 0.15 | 115 | 17.25 |
| All Goes So-So | 0.40 | 80 | 32 |
| All Goes South | 0.25 | 60 | 15 |
| Expected Value | $84.25 | ||
| New Margin of Safety | 26% |
Now the margin of safety has been reduced to 27%, compared to the original 42%. If one share of MasterCard’s common stock subsequently reaches a price tag of $108, the investor who didn’t make the purchase may look stupid as he seemingly missed out. But if the same share subsequently dropped to $60, the same investor may get some applause and respect.
I want to add that the omission of expected value is not just among non-professional investors. Sell-side analysts and even many buy-side analysts base their recommendations on bear case, base case, and bull case. What’t missing in their analysis is the probability of each outcome. A report that shows a stock with a bear case of $50, a base case of $150, and bull case of $320 will have vastly different implications if the probability of bear case is 70% versus 10%.
Sound simple? Yes. But it is far from easy. Our brain is wired to take shortcut when it comes to complex decision making process such as making multiple assessment of both the probabilities and outcomes of an investment. So we have to overcome this biological hurdle before we can even move on. Secondly, both estimating the probabilities and outcomes involve a great deal of judgment and better judgment comes from knowledge compounding and experience accumulation. Unfortunately (and fortunately for those who are more determined), there is no shortcut to knowledge and experience accumulation.
To conclude, let me quote Michael Bauboussin again:
“Investing is probabilistic and that expected value is the right way to think about security prices. Investors encounter many pitfalls in objectively assessing probabilities and outcomes. Unless we practice mental discipline, we will lose in the long term to those who can.”
