**Stocks for the long run? Evidence from a broad sample of developed markets (2022a)***Aizhan Anarkulova, Scott Cederburg, Michael S. O’Doherty*

Journal of Financial Economics 143(1), URL/SSRN

**Long-Horizon Losses in Stocks, Bonds, and Bills: Evidence from a Broad Sample of Developed Markets (2022b)***Aizhan Anarkulova, Scott Cederburg, Michael S. O’Doherty*

SSRN Working Paper, URL

*Stocks for the Long-Run* – this is not only the title of Jeremy Siegel’s popular book but also a well-established idea among investors. If you can wait long enough and don’t need your money on the way, just put it in a diversified index fund and wait. This week’s AGNOSTIC Paper challenges this simple advice and shows that even over very long periods, the chance of losing money with stocks can be higher than many people may think…

Everything that follows is only my summary of the original paper. So unless indicated otherwise, all tables and charts belong to the authors of the paper and I am just quoting them. The authors deserve full credit for creating this material, so please always cite the original source.

## Data and Methodology

To determine the risk of long-term losses from stocks, the authors construct a very comprehensive dataset from a variety of sources. In total, they cover equity-index returns from 39 developed countries between 1841 and 2019. Constructing such a dataset obviously involves a lot of nasty details which are beyond the scope of this summary. However, it is worth mentioning that the authors particularly focus on preventing survivorship bias and properly consider some really scary periods of historical wealth-destruction (see below). The following table summarizes the sample.

In addition to that, the authors focus their analysis on real returns because inflation has a tremendous impact on investors’ wealth over long time horizons.^{1}Even the 2% inflation target of most central banks erodes about 45% of buying power over a 30-year period. They further assume reinvested dividends and calculate all performance as *gross total return*. The authors also calculate real returns from the perspective of a global USD investor to control for the impact of exchange rates.^{2}For example, that is the real return of an investor who invests in Germany and converts his assets into USD without any FX hedging.

*Long-term* in the sense of the paper corresponds to a period of 30 years as this is close to the typical “safe-for-retirement” time horizon. To determine the chance of losing money over such a period, the authors employ a historical bootstrapping simulation. The idea is straightforward. Even with >150 years of data, we unfortunately don’t have too many unique 30-year periods to look at. But we can use the data to simulate alternative paths of history. This is of course theoretical and “after-the-fact”, but it gives a perspective on what could have happened compared to just analyzing what actually happened. Mathematically, the authors randomly select a series of 360 monthly returns from their dataset and repeat this process 1M times. The result are 1M hypothetical 30-year returns that give us a distribution of historical outcomes. This methodology and the corresponding results are the heart of the paper.

## Important Results and Takeaways

### History offers some scary events of wealth-destruction

Before going into the results of the simulation, the authors provide anecdotal evidence of some interesting times for stock investors. The following table shows returns during the two World Wars, country-specific revolutions, financial crises, and labor strikes.

These numbers are a first attempt to show that the extraordinary history of the US market is not necessarily representative for the rest of the world and stock markets in general. For example, German and Japanese stock investors lost 91.10% and 87.15% of their real wealth during World War II, respectively. It is of course not surprising that losing a world war doesn’t lead to good stock performance and it looks obvious in hindsight. Going forward, however, we simply don’t know if there will be another World War. The potential disasters from investing in “losing” countries’ stock markets are therefore a tail risk which most likely doesn’t show up in realized historical returns of “winning” countries like the US.

### The US equity market is not necessarily representative

After this warm-up, the following table now summarizes the key results of the paper and shows the simulated distributions of cumulative real stock returns over different time-horizons. Just to get everyone on the same page: The mean of $7.38 in Panel A represents the average real payoff after 30 years. So a buy-and-hold investor who invested in the “average” developed stock market turned $1 into $7.38 after adjusting for inflation. That corresponds to a (very good!) real return of about 6.9% per year. Note that this analysis assumes that investors put their money in *exactly one* domestic stock market. I will cover the role of international diversification later.

More interesting than the average payoff is (in my opinion) the distribution of the simulated outcomes. There are a couple of observations. First, payoffs and the probability of making money in real terms increase with the length of the investment horizon. I think that is not too surprising and in-line with *Stocks for the Long-Run*.

Second, the range of possible outcomes is very wide. For example, the median payoff over 30 years is $4.16 while the 90%-percentile is a staggering $15.58. Converting those wealth-multiples into annual real returns reveals a substantial difference of almost 5%-points (4.86% vs. 9.58%) per year. Such numbers once again highlight the tremendous upside that comes with equity investments.

On the other end, there are also some really disastrous outcomes. Most importantly, the authors estimate a 12.1% probability of losing money with stocks over a 30-year horizon after adjusting for inflation. Investing for three decades without any real return is already a really bad outcome. But the lower percentiles of the distribution suggest that it can get even worse. Based on the simulation, there is a 10% chance of losing at least 15% of purchasing power, a 5% chance of losing 53%, and a 1% chance of losing 86%. Those are of course very extreme cases, but there is always a chance that you invest in a country that loses a world war or goes through other catastrophic times.

Using these insights, the authors next compare the US stock market with the rest of their sample. As the dark-blue histogram above shows, running the same simulation with just the US-sample generates a considerably different distribution of long-term returns. Most importantly, the estimated probability of losing money with a 30-year investment in US equities drops to 1.2%. This is only one tenth of the result for the global sample and strongly suggests that we shouldn’t just look at the history of the US market to form our expectations for the future…^{3}Note that there can be plausible reasons why the US stock market is superior to others. The results just show that its history was very different compared than that of other developed markets.

### Global diversification helps tremendously

The results so far are pretty clear. Even if you go into stocks for the very long-run, there is no guarantee to make a real return and the chance of losing is probably higher than what the history of the US market suggests. In a not yet published follow-up paper, the authors take the next logical step and look at the same analysis from the perspective of an investor who invests in a globally diversified equity portfolio. The following table again summarizes the results.^{4}The follow-up paper also covers the distribution of bond and bill returns. Although also interesting, I will just focus on equities in this post.

Panel A corresponds to the previous analysis in which the authors assume that investors put their money into exactly one developed equity market. The numbers are slightly different because the authors run 10M iterations of their simulation in the second paper, but the overall pattern remains very similar. Even over 30 years, there remains a considerable 12.6% probability of losing money after adjusting for inflation.

In contrast, Panel B takes the perspective of an investor who puts her money into a market-cap weighted portfolio of all developed markets except her home country and without any currency hedging. For example, that would be the MSCI EAFE Index from the perspective of a US investor. The results are very interesting! Compared to only investing in one particular market, the probability of losing real wealth over 30 years strongly decreases from 12.6% to 4.2%.

And while still painful, even the 1%-percentile is with a real payoff of $0.58 now considerably better than the $0.13 for just one domestic market. This downside protection comes at the cost of somewhat lower payoffs in the upper half of the distribution. Overall, however, I think global diversification delivers on its promise and offers an attractive ratio of risk and reward. Panel A of the following chart summarizes the different distributions again graphically.

In addition to the global diversification of equities, the authors find that investing in international equities without currency hedging acts as “natural” protection against domestic inflation. More specifically, they explain that domestic currencies tend to depreciate when a country suffers from high local inflation. In such a situation, investors holding international equities in foreign currency benefit from exchange rate movements. In fact, the last year was a prime example for this mechanism. Through much of 2022, inflation was considerably higher in Germany than in the US and the USD massively appreciated against the EUR. German EUR-investors with USD-denominated international equities therefore enjoyed a positive performance from exchange rate movements of about 5%.

## Conclusions and Further Ideas

I really like the paper because the authors go through a lot of effort to create this unique ultra-long-term dataset. I also like how they use their straightforward simulation method to examine the very popular mantra of *Stocks for the Long-Run*. As you might have recognized from this website, I usually prefer data over stories and I think it is really useful to see that not all equity markets have such an extraordinary history as the US. In my opinion, the paper is therefore a very important reference that helps to form realistic expectations about the long-term performance of equities.

Having said that, there are two important points where I think the paper sets a somewhat unlucky focus. First, the authors primarily highlight the possible downsides of long-term equity investments. The 4 to 12% probability of losing real purchasing power over 30 years is of course very relevant and scary. However, I think we shouldn’t forget that most of the time, stocks produced very decent real returns over long periods. In addition to that, the positive outcomes on the right tail of the distribution are simply phenomenal. Especially when combined with international diversification to protect the downside.

The second point is in my opinion even more important. Yes, a 30 year investment that doesn’t produce any real return is scary and most of us probably don’t have too many 30-year periods in their life to just say *“Bad luck, let’s start again.”* However, I would argue that most people don’t save for retirement with a one-shot 30-year investment, but rather gradually over their working life. Continuous investing over time could reduce the probability of catching a really bad outcome, but I am speculating here. Therefore, it would be great to see the authors’ analysis under the assumption of a regular savings plan over 30 years.

Despite those two points, I believe the paper is a great reference and offers very important and practical insights. I think it is always great when people challenge a seemingly undisputed “truth” like *Stocks for the Long-Run* with comprehensive data and creative methodology. But despite more risk than suggested by just looking at the historical performance, I don’t see many alternatives to *Stocks for the Long-Run* for most investors. For me personally, the most relevant takeaway is therefore the importance of global diversification to protect the downside. More about this next week.

- AgPa #82: Equity Risk Premiums and Interest Rates (2/2)
- AgPa #81: Equity Risk Premiums and Interest Rates (1/2)
- AgPa #80: Forget Factors and Keep it Simple?
- AgPa #79: The Momentum OGs – 30 Years Later

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## Endnotes

1 | Even the 2% inflation target of most central banks erodes about 45% of buying power over a 30-year period. |
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2 | For example, that is the real return of an investor who invests in Germany and converts his assets into USD without any FX hedging. |

3 | Note that there can be plausible reasons why the US stock market is superior to others. The results just show that its history was very different compared than that of other developed markets. |

4 | The follow-up paper also covers the distribution of bond and bill returns. Although also interesting, I will just focus on equities in this post. |