Practical analysis for investment professionals
19 January 2016

Dumb Alpha: The Drawbacks of Compound Interest

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.

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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.

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About the Author(s)
Joachim Klement, CFA

Joachim Klement, CFA, is Head of Investment Research at Fidante Capital and a trustee of the CFA Institute Research Foundation. Previously, he was CIO at Wellershoff & Partners Ltd., and before that, head of the UBS Wealth Management Strategic Research team and head of equity strategy for UBS Wealth Management. Klement studied mathematics and physics at the Swiss Federal Institute of Technology (ETH), Zurich, Switzerland and Madrid, Spain, and graduated with a master’s degree in mathematics. In addition, he holds a master’s degree in economics and finance.

7 thoughts on “Dumb Alpha: The Drawbacks of Compound Interest”

  1. ashok says:

    How about a simple dollar cost averaging over the initial years?

  2. Adam Wright says:

    Please note: I did not read the underlying article.

    All else equal, as price goes down expected return goes up. Therefore, it is reasonable that future returns post an initial -10% may be high enough such that you hit your average return over the long-term.

    If you can suffer short-term forecast errors patiently and not over-react or even react to this noise then you should hit your long-term goals. It’s the people that don’t just sit there and do something that end up buying high and selling low. For these people it is quite obvious they won’t make the mean return. Volatility is only a risk if you let it.

    For instance, say you find a business capable of returning 10% on capital employed for the foreseeable future and you buy it at what appears to be a very fair price. Now, this is hypothetical of course, the average underlying return line is straight with each year successively higher. Since this business is traded the actual stock price will experience volatility such that the return in any given year is above or below that 10%. A good investor would add to their position in years when the return is below 10% and sell pieces when the return is over 10%. So that over a long-term horizon the return achieved is basically 10%. It is the investors job to not let the changes in market price confuse them into thinking that the market is always accurately reflecting the changes in true value.

    As far as the point about sequence risk is concerned it would reasonable that a properly allocated portfolio mitigates the problem of having to sell low in retirement to meet income needs. It would be of little issue if the overall portfolio drops 5% in the first year if you can sell stable assets that did not decrease in value. The remaining assets are thus the major contributors to the negative performance which you leave invested. This re balancing, if you will, enables the investor to hit those averages.

    The problem which I believe you are addressing only makes sense if you hold 1 asset in your retirement account. For example a 2017 target date fund.

  3. Joe Christianson says:

    I appreciate your columns, Joachim, but unfortunately the discussion of sequence risk is incorrect. Assuming that someone just starting to save for retirement is starting with little or no money, and that they consistently add to their retirement account, they would prefer to have the bear market early. If you are just starting your career and have only saved up $10,000, then a -50% bear market costs you $5,000. If you are at the end of your career and have saved up, say, $3,000,000 and you hit the -50% return, it will cost you $1,500,000.

    Even taking into account the compounded returns on the $5,000 loss early in your career, you are better off taking the loss early.

  4. Alex says:

    It would be really great it there was a link the first part of the article each time you mention it so people coming in late (like me) are able to skip back and start from scratch.

    Just a thought.

    Great post.

  5. ganesh says:

    Equal weight portfolio is better suggestion.
    But when a stock runs and gets weightage more compared to others, it needs to be rebalanced.
    But winners never to be cut short. Keeping losers is not as severe.
    The only mistake which can ruin long term wealth.

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