## Summary

- A new
*Journal of Financial Economics*paper examines equity returns over 170 years to test whether investing in stocks over long periods is risk-free. - It is not. Almost a fifth of diversified investors with a 30-year horizon will lose relative to inflation.
- US-based investors are less likely to experience a loss and are therefore more aggressive when investing in stocks relative to investors in other developed markets.

## Introduction

Investors with long horizons are often advised to invest heavily in stocks. This is because research has shown a relatively large historical equity premium in the US and infrequent long-term loss realizations. However, survivorship bias and imperfect data provide reason to question earlier findings.

A new *Journal of Financial Economics *paper uses stock markets from 39 developed countries, in some cases spanning 170 years, to estimate a distribution of buy-and-hold returns for different investment horizons. Their large coverage and treatment of returns data overcomes past data biases and provides a substantially broader view of risk over long horizons compared with past US-centric research. They find:

- The -21% real return realization in Japan over the past 30 years is not exceedingly rare – it lies within the ninth percentile of the buy-and-hold returns distribution.
- Left-tail events occur with a 12.1% probability when excluding transaction fees, and in some instances, a $100,000 investment would have shrunk to $14,000-47,000 after 30 years.
- However, a 30-year buy-and-hold strategy in the US is much less likely to incur a loss (1.2% probability), and achieving a substantial gain is highly probable.

## Data

The authors compile stock market index returns using the GFDatabase. The GFD provides data for diversified indexes that are created and calculated by stock exchanges, well-known index providers, or by GFD directly from original source documents. In all, they obtain index returns from 39 ‘developed’ countries, which are so classified through labour patterns pre-1948 and OEEC or OECD membership post-1948.

To calculate returns, the authors use four variables: (i) total return indexes that reflect both price changes and dividends; (ii) price indexes that measure capital gains; (iii) dividend yields at the index level; (iv) consumer price indexes (CPIs). To calculate a monthly nominal return, they use either a total return index or a combination of a price index and a dividend yield. Real returns divide nominal returns by CPI.

Overall, monthly returns are calculable for a significant proportion of ‘developed’ countries (Chart 1). The black dotted lines represent the time when a country was classified as ‘developed’ but lacked available index returns. This could be due to stock exchanges being temporarily closed (e.g., the NYSE in 1914), permanently closed (e.g., Czechoslovakia), a lack of historical data, hyperinflation (e.g., Germany), or short gaps in price or dividend yield data. In total, the final sample spans 36,786 months over 3,065 years, equivalent to 87% of the potential sample. Similar research covers just 1.7%.

## Methodology

For the main analysis, the authors use a bootstrap simulation method to estimate distributions of long-term, buy-and-hold stock market returns. Specifically, they adopt a stationary block bootstrap design, which can account for the negative serial correlation/mean reversion properties in returns. Mean reversion forms much of the basis for arguments that long-horizon stock returns are relatively safe.

## Investors Bear Considerable Risk of Loss

Chart 2 gives the distributions of real payoffs from a buy-and-hold strategy over one month, one year, five years, 10 years, 20 years, and 30 years. As past research has shown, the mean real payoffs increase over time – the average investor who starts with $1 can expect to have $1.01 after one month and $7.38 after 30 years. The skewness also increases over time, with average returns much closer to the mean over one-month and one-year horizons.

However, the results also highlight the substantial uncertainty over real investment outcomes faced by long-horizon investors. For a 10-year investor, for example, the first percentile of real payoff is just $0.13, whereas the 99^{th} percentile is $8.75. The dispersion in the payoff distribution is even more pronounced at the 30-year horizon, as the first and 99^{th} percentiles are $0.14 and $53.45, respectively. In terms of probabilities, the 20-year and 30-year investor has a 15.5% and 12.1% chance of losing money, respectively.

When accounting for the average expense ratio among active managers at a mutual fund (0.67-1.11%), the probability of loss for a 30-year investor increases to 17.5%. These results contrast past research, which states that the likelihood of losing money beyond 20 years is negligible. According to the authors of this paper, their findings show that ‘even at long horizons in the world’s most developed markets, investors bear considerable risk of loss’.

## Results by Country

The UK and US represent 4.9% and 6.7% of the total sample, respectively. Their results differ significantly from other developed countries (Chart 3). Over 30 years, a US investor’s mean payoff is $8.91 – 20% higher than the average for all developed countries. Meanwhile, a UK investor would earn $5.28, significantly below the overall mean.

Investors in both countries are, however, very unlikely to record losses in tail events. The fifth and 95^{th} percentile outcomes are $1.69 and $24.30 in the US, and $1.24 and $12.97 in the UK, respectively. More specifically, the probability of incurring a loss after 30 years is just 1.2% in the US and 3% in the UK. Overall, these results imply greater certainty for those investing over long periods in the US and UK.

The authors note, however, that future US returns are unlikely to follow the same probability distribution. The higher average payoff and lower probability of loss reflect a large, unexpected increase in equity valuations over the past century and a relatively short return history. They advise instead using the developed country distribution as a more plausible indicator.

## Asset Allocation Implications

The authors examine the implications of the above results in a simple portfolio choice problem with a single risky asset (the domestic stock market index) and a risk-free asset. The risk-free asset is either inflation protected or cash. The inflation-protected risk-free asset maintains its real principal balance but earns no interest, while a cash investment can lose its value over the holding period (not inflation-protected).

The results show that investors using the developed country sample invest less in stocks relative to the US sample investors. At the 30-year horizon, for example, the developed country investor with access to the inflation-protected risk-free asset chooses an optimal weight of 43% in stocks compared with a weight of 75% for the US investor. In other words, non-US investors are more conservative over their stock investments because of a higher sense of risk.

## Bottom Line

Investing over longer horizons can significantly improve retirement savings. However, as this research shows (and past research has insufficiently highlighted), there is almost a one-in-five chance that investors lose money in real terms from investing during their working years. And so, any young person deciding where to invest might consider a more conservative portfolio allocation over long horizons because remember, you only have one lifetime in which to save for retirement.

## Citation

Anarkulova, A., Et Al., (2021), Stocks for the long run? Evidence from a broad sample of developed markets, *Journal of Financial Economics*, https://www.sciencedirect.com/science/article/abs/pii/S0304405X2100310X

## Authors of Working Paper

Aizhan Anarkulova is a Ph.D. candidate in Finance at the University of Arizona. Her main research areas are asset pricing, investments, portfolio allocation, asset management, retirement planning, and price informativeness.

Scott Cederburg joined the Eller College of Management in 2011 after earning his PhD in Business Administration (Finance) from the University of Iowa in 2011. Prior to academia, he was a senior financial analyst with Ethanol Capital Management and an investment analyst with Schwendiman Funds. A Chartered Financial Analyst, Cederburg’s research interests include asset pricing, cross-sectional anomalies, long-run risk, asset allocation and applied Bayesian econometrics.

Michael O’Doherty is an Associate Professor of Finance and the Charles Jones Russell Distinguished Professor in the Finance Department at the Robert J. Trulaske, Sr. College of Business, University of Missouri. Dr. O’Doherty’s research interests include asset pricing, investments, financial econometrics, mutual funds and hedge funds.