We characterize the distribution of long-term equity returns based on the historical record of stock market performance in a broad cross section of 39 developed countries over the period from 1841 to 2019. Our comprehensive sample mitigates concerns over survivor and easy data biases that plague other work in this area. A bootstrap simulation analysis implies substantial uncertainty about long-horizon stock market outcomes, and we estimate a 12% chance that a diversified investor with a 30-year investment horizon will lose relative to inflation. The results contradict the conventional advice that stocks are safe investments over long holding periods.

We use a comprehensive new dataset of asset-class returns in 38 developed countries to examine a popular class of retirement spending rules that prescribe annual withdrawals as a constant percentage of the retirement account balance. A 65-year-old couple willing to bear a 5% chance of financial ruin can withdraw just 2.26% per year, a rate materially lower than conventional advice (e.g., the 4% rule). Our estimates of failure rates under conventional withdrawal policies have important implications for individuals (e.g., savings rates, retirement timing, and retirement consumption), public policy (e.g., participation rates in means-tested programs), and society (e.g., elderly poverty rates). 

We challenge two tenets of lifecycle investing: (i) diversify across stocks and bonds and (ii) reduce equity allocations with age. An optimal lifetime allocation of 33% domestic stocks, 67% international stocks, 0% bonds, and 0% bills vastly outperforms age-based, stock-bond strategies in building wealth, supporting retirement consumption, preserving capital, and generating bequests. Our lifecycle model preserves crucial time-series and cross-sectional dependencies in asset returns and addresses small sample issues in US data. Our investors prefer diversifying with international stocks, not bonds. Target-date fund investors need 61% more pre-retirement savings to match the all-equity strategy’s expected utility over retirement consumption and bequest.

A positive relation between risk and return is a fundamental tenet of finance. Despite the theoretical prediction of a positive time-series risk-return relation at the market level, empirical evidence is mixed, with studies finding evidence of positive, negative, or insignificant relations. Due to low test power, using small samples can result in negative or insignificant coefficient estimates on the conditional variance—even when the true relation is positive. I pool data across 33 developed countries, covering almost 2,600 years of market returns, which provides the most comprehensive test of the time-series risk-return relation to date. Using the full sample of developed country returns, I confirm the fundamental prediction about risk and return: the estimated mean-variance coefficient is positive with strong statistical significance.  The regressions with individual country returns yield insignificant results with few exceptions, highlighting the need for an expanded sample. 

We study long-horizon returns of domestic stocks, international stocks, bonds, and bills with a focus on periods with real losses in each asset class. Our dataset construction and estimation methods mitigate survivor bias and offer novel, quantitative evidence on the joint distribution of asset class returns. We find that (i) 30-year real loss probabilities in domestic markets are high for stocks (13%), bonds (27%), and bills (37%); (ii) exchange-rate fluctuations offset local inflation to produce a lower loss probability for international stocks (4%); and (iii) equity losses are driven by negative real dividend growth attributable to declining profit shares.