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.

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 use a comprehensive new dataset to study long-horizon returns of domestic stocks, international stocks, bonds, and bills in developed countries. The dataset covers 38 countries over the period from 1890 to 2019, and our sample formation procedures mitigate survivor and easy data biases. Bootstrap estimates of 30-year real loss probabilities are high for domestic stocks (13%), bonds (27%), and bills (37%), whereas exchange-rate fluctuations offset inflation risk to produce a low loss probability for international stocks (4%). Long-horizon losses in domestic stocks are often driven by catastrophic outcomes for real cash flow growth, whereas inflationary periods are devastating to fixed income investors.

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). 

Target date fund (TDF) providers claim to provide value for investors through glide path design, implementation, and tactical asset allocation. We study TDFs’ tactical asset allocations, or glide path adjustments, and find that those adjustments lead to underperformance. Underperformance is concentrated in TDFs that most actively change their glide paths. We also find that TDFs tend to adjust their equity allocations similarly and that those adjustments are highly correlated with S&P 500 returns. Underperformance is highest during and after periods of correlated adjustments, suggesting TDFs’ tactical asset allocations may be impacting asset prices.

Campbell and Shiller (1988) introduce a linear approximation of the valuation relation between returns, dividends, and prices using logs. Vuolteenaho (2002) customizes this method for the firm-level return decomposition. The return decomposition relies on the accuracy of a log-linearization technique to determine returns' driving forces. I argue that this technique in the firm-level decomposition is problematic because of a high degree of bias in how expected log returns correspond to expected returns. Accounting for the variation in return volatility can help get better estimates of stock return shocks: cash-flow news and expected-return news. Based on the test results, there are important differences between the estimates in this paper and what has been found in the prior literature. The variance of cash-flow news increases by 54% under my method compared to the existing method.