Risk is often characterized by a probability distribution of returns around an average return. Risk averse investors do not like a lot of variation from the mean, particularly on the downside. With the bell-shaped normal distribution often assumed in models, that variation is given by the standard deviation. But repeated evidence (and experience!) has shown that the normal distribution does not depict the risk: Typically, there are more extreme returns, both positive and negative, relative to their probability given by the normal distribution (see chapter 8). Those extremes are called the “tails” of the distribution. The observation tells us that the best way to view the risk of investing in equities is to see it as good upside potential but with severe downside risk.
Beware of assuming a probability distribution and of models that assume a particular distribution. Rather go through the fundamental analysis asking: What is the upside potential in this business. What is the downside? Value added (residual income) is at risk: What is the upside and the downside?
Why do theorists use assumed probability distributions in their modelling? To get what they call “closed-form solutions.” That is, they want to get to a formula. But formulas are always suspect, as chapter 3 pointed; they can leave you into thinking that valuation is just a matter of plugging into formulas. Formulas sometimes help your thinking, but only if they are based on reasonable assumptions. The residual income model is one: The two assumptions underlying it are palatable. First, investors invest to get dividends: quite reasonable. Second, the clean-surplus equation by which successive book values are increased with earnings and reduced by dividends: That’s how accounting actually works!