By Joachim Klement, CFA

The second installment of this series presented evidence that a simple random walk forecast typically performs better than the amassed expertise of professional forecasters for short-term forecasts of about 12 months.

In this post, I argue that estimation uncertainty is not reduced for long-term forecasts either, because mean reversion cannot overcome the effects of compound interest. Luckily, there is a range of techniques, from simple to sophisticated, that can help long-term investors with this challenge.

**The "Muffin Top" Problem**

As most middle-aged people can confirm, age inexorably leads to a slowing metabolism. If you don’t change your diet, your waistline expands quite generously. In my case, I refused to notice these changes until I grew an undeniable "muffin top" of belly fat above my belt line. Chagrined, I changed my diet and stepped up my exercise, but so far — muffin doin’.

This little anecdote is a rather fitting (if unappealing) metaphor for long-term investing. What I tried to force my body to do was to revert back to its original state (the mean), but the forces of mean reversion were not strong enough to do so. This scenario can happen in the world of investing as well.

Imagine someone who wants to invest for the next 10 years and who is thus not interested in short-term forecasts so much as the long-term average expected returns of assets. Common wisdom states that, while return forecasts can be widely off the mark in any given year, in the long run, returns should converge towards a rather stable long-term mean. Because of mean reversion, it should be easier to forecast long-term returns than short-term returns.

**Compound Interest Ruins the Day**

In an important article in the *Journal of Finance*, however, University of Chicago economists Lubos Pastor and Robert Stambaugh showed that, in the presence of estimation uncertainty, mean reversion is not strong enough to reduce the volatility and uncertainty of long-term stock market returns.

The main reason is that an estimation error in the first year will propagate and compound over the subsequent nine years, an estimation error in the second year will compound over the subsequent eight years, etc. Take, for example, an investment you know will average an annual return of 10% per year over the next 10 years. If in the first year the return is -10%, the average return over the subsequent nine years needs to be about 12.48% per year to make up for this shortfall. In other words, a 20% estimation error in the first year requires a relative increase in annual returns over the next nine years of 24.8%.

If, on the other hand, the asset in the first year has a return of 0%, the average return over the subsequent nine years needs to be about 11.17% to make up for the shortfall. So a 10% estimation error in the first year requires a relative increase in annual returns of 11.7%. Half the estimation error requires less than half the relative return increase to make up for the shortfall.

The investment results of the first few years have an oversized influence on the long-term investment returns — something that retirement professionals know as "sequence risk." If you start saving for retirement and experience a major bear market in the first few years, you are much less likely to achieve your long-term financial goals than if you experience a rather benign environment at first and a bear market later.

While the research by Pastor and Stambaugh is theoretical in nature, there is empirical evidence that long-term return forecasts are, in fact, just as uncertain and "inaccurate" as short-term forecasts. Ivo Welch and Amit Goyal have looked at the predictive power of many different variables that are commonly used to forecast equity market returns. They find that the forecast error does not materially change for forecast horizons between one month and 10 years. In other words, despite the existence of mean reversion, the uncertainty about future equity returns does not decrease in the long run.

**Facing the Challenge**

If long-term return forecasts are just as difficult to make as short-term forecasts, what can long-term investors do to create robust long-term portfolios? After all, we know that traditional Markowitz mean-variance optimization is about 10 times more sensitive to return forecast errors than to forecast errors in variances. There are in my view several possibilities, increasing from least to most in degree of sophistication:

- The equal weight asset allocation discussed in the first part of this series does not rely on forecasts, and thus is a simple and effective way to create robust long-term portfolios.
- Minimum variance portfolios and risk parity portfolios do not require any return forecasts and, if done properly, can outperform traditional portfolios by a wide margin.
- More sophisticated methods like resampled efficient frontier methodologies or Bayesian estimators can include estimation errors into the portfolio construction process and thus create portfolios that are more immune to unexpected events.

Whatever technique one favors, there are ways to deal with forecast errors. Most critically, it is time investors take estimation uncertainty more seriously for the benefit of their clients and the long-term success of their portfolios.

**If you liked this post, don’t forget to subscribe to the Enterprising Investor.**

*All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author’s employer.*

Disclaimer: Please note that the content of this site should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute.