Having the right plan and sticking to it means understanding how returns really work.

One of the more common mistakes many investors and even some financial advisors make when developing an investment plan is in** **treating the expected return of a portfolio as “deterministic.” They tend to think about expected returns in terms of a specific figure that a portfolio is anticipated to earn.

Expected returns, however, are simply the mathematical mean of a potentially very wide dispersion of prospective outcomes. The mistake occurs in supposing they are exact projections.

That error can prove very costly because it may lead investors to assume more risk than they have the ability, willingness or need to take. As the late Peter Bernstein once explained, “The greatest risks we take are when we are certain of the outcome.”

The graph below demonstrates the correct way to think about the expected return of a portfolio, an asset class or an individual stock.

**Understanding Distribution Of Possible Returns**

Although expected returns are not actually normally distributed, I believe this illustration is helpful in explaining a framework for how to consider them. Think of Portfolio A as marketlike, such as a total stock market fund. The illustration shows that the expected return is 7 percent. But it also shows that the 7 percent return is just the mean (and in this case, the median) of a wide dispersion of possible outcomes.

In other words, there is a 50 percent chance the return will be above the expected 7 percent, perhaps a 30 percent chance it will be above 9 percent, a 10 percent chance it will be above 12 percent and a 5 percent chance it will be above 13 percent. There is a similar potential that returns will fall on the left side of the distribution.

Possible outcomes may well be below, and even well below, the expected rate of 7 percent. Please note that the numbers in this example are for illustration purposes only, and are not based on any actual distribution.

Investors should design investment plans that incorporate the potential for years, and perhaps even longer periods, of negative returns. They should also consider the possibility of so-called black swans, or major market-moving events considered so unlikely that investors make the mistake of confusing the improbable with the impossible.

**Distributions Are Estimated, And Not Known**

This raises the issue of another prevalent mistake made by investors. Even among those who view expected stock returns to stocks correctly, many make the additional mistake of treating the potential distribution of outcomes as if they are *known*, when they can only be *estimated*.

A good example of this problem arises when advisors discuss the outcomes of Monte Carlo simulations with clients. I often hear statements such as, “The odds of success of this portfolio are 85 percent under this withdrawal assumption.”

Unfortunately, we don’t *know* the odds—we can only *estimate* them. And that’s an important distinction because we know that shocks to the uncertainty premium help explain asset price fluctuations, business cycles and financial crises. Thus, the advisor’s statement should be something similar to, “Based on our current assumptions, we estimate that the odds of success are ….”

**Black Swans**

Anna Orlik and Laura Veldkamp—authors of the 2014 paper, “Understanding Uncertainty Shocks and the Role of Black Swans”—show how shocks (often caused by black swan events) lead to dramatic changes in our estimates of the potential future dispersion of returns.

The authors note that: “[R]eal people do not know what the true distribution of economic outcomes is, when it changes, or by how much. They observe economic information and, conditional on that information, estimate the probabilities of alternative outcomes. Much of their uncertainty comes from not knowing if their estimates are correct.”

A problem for investors is that the *perception* of the potential for black swans to occur varies over time. Periods of relative stability can lead to investors becoming less risk averse and more confident in their ability to estimate returns and the potential distribution of the returns.

Thus, they understate the potential for black swans. And when black swans do occur, we see shocks to the uncertainty premium in stock prices. Panic often sets in, causing even well-thought-out financial plans to end up in the trash heap of emotions.

It’s important for investors to understand that, at best, we can make reasonable estimates regarding expected returns and the potential distribution of outcomes different from the mean. We cannot *know* the potential distribution, or even the odds. In other words, investing is always about dealing with uncertainty as opposed to risk.

**Uncertainty Vs. Risk **

With risk, we either know the odds, like at the roulette wheel, or we can make confident estimates, like with mortality tables. With that understanding, it’s important that investors not assume more risk than they have the ability, willingness or need to take.

Investors and their advisors should build into investment plans specific actions to be taken (what I refer to as a plan B) if a black swan event appears and it looks likely to cause that plan to fail. Battles are often won in the preparatory stage, not on the battlefield itself.

For investors interested in building a portfolio that addresses the risk of black swans in an efficient manner, my colleague Kevin Grogan and I discuss a strategy we recommend you consider in our book, “Reducing the Risk of Black Swans.”

Larry Swedroe is the director of research for the BAM Alliance, a community of more than 140 independent registered investment advisors throughout the country.