Stocks for the Long Run
(6 min read)
(6 min read)
Do stocks outperform bonds in the long run? Yes, according to a recently published paper in the highly rated Journal of Banking and Finance. It states that ‘any investor would be better off investing in stocks rather than in risky bonds, as long as the portfolio included a riskless asset – a Treasury Inflation-Protected Security (TIPS)’.
This result gives weight to a famous idiom, ‘stocks for the long run’, which papers have previously struggled to justify empirically. Why? They have been measuring risk inappropriately. They tend to use the variance of returns, or of log-returns, which only works if returns are normally distributed.
In the long run, returns are not normally distributed, especially annual returns. They do not even follow any specific parametric form. So, the authors use a distribution-free Stochastic Dominance approach to capture the possibility that investors may prefer an investment with a higher variance over one with a lower variance. They find:
Bear with me – some simple distribution theory will help us through this paper. Let B and S denote the cumulative distributions of the returns of a risky bond-only (B) and stock-only (S) strategy. Then, a stocks strategy is preferred to a bonds strategy by all investors if S is below B. In other words, loosely speaking, stocks provide a better chance of higher returns at any point along the distribution. And so, any rational investor would choose a portfolio of stocks over bonds. If the distributions cross, neither dominates (Chart 1).
The paper argues that when they add US TIPS to a portfolio of stocks (say 40% stocks, 60% TIPS), the three-year+ return distribution is always lower than the one with bonds. This dominating portfolio has a higher Sharpe ratio, and it remains higher for any combination of stocks and TIPS.
To get the results, the authors must generate the cumulative distributions. First, they create empirical return distributions from the annual real returns on the S&P500 (including dividends) and US 10-year bonds between 1928 and 2019. For the riskless asset, they obtain the returns on TIPS with one- to 30-year maturities.
With the empirical return distribution to hand, they randomly draw annual returns 100,000 times to build the cumulative return distributions for investment horizons of between one and 30 years. Intuitively, this simulation gives the ex-ante annual returns an investor could have expected to receive at any point over the last 90 years when investing in stocks, bonds, or any combination of stocks and bonds with a riskless asset.
Using this information, and eyeballing Chart 1, we could say the following. An individual investing only in stocks could have expected to achieve annual S&P500 real returns of over 50%, roughly 40% of the time. A bonds-only investor could have expected to achieve the same annual returns less than 5% of the time. Equally, a bonds-only investor was less likely to have experienced large negative annual returns.
First, the authors examine the cumulative return distributions of stock- and bond-only investments over increasing time horizons. They find, as in Chart 1, the distributions cross in all horizons. Therefore, neither strategy dominates the other. This is mostly because the minimal return on stocks is always lower than the minimal return on bonds. Notably, however, the mean return on bonds is always smaller than on stocks.
Under what circumstances, then, could a portfolio of stocks always beat a portfolio of bonds? At shorter-term investment horizons, like one year, the authors find that a portfolio with equities requires 70% in TIPS to ensure that the chance of low returns in the worst-case scenario is lower than in a portfolio with bonds. However, by removing downside risk, the upside probability is actually higher in a risky bonds portfolio, which is hardly appealing.
So, while there is no combination of stocks with a riskless asset that dominates at a short-term horizon (less than three years), there is when the investment horizon increases. At a five-year horizon, the authors find a portfolio with 40% stocks and 60% TIPS dominates any combination of bonds with a riskless asset. As the horizon increases from there, any combination of stocks and TIPS (e.g., 90% stocks, 10% TIPS) outperforms one with bonds and TIPS.
In reality, however, portfolios usually contain a mix of risky stocks and bonds. In this scenario, as the investment horizon increases, the most dominant strategy is one with a higher percentage of stocks in the portfolio (Chart 2). For example, if an investor’s horizon is 15 years or more, the investor should invest at least 60% in stocks and 40% in bonds, irrespective of the proportion of TIPS included – so, say 10% TIPS, 54% stocks, and 36% bonds.
In essence, the paper says that the longer the investment horizon, the more an investor should include stocks into the portfolio, as long as a riskless asset is included. This is because, in expectation, they will achieve higher returns with a higher probability than one with a higher allocation of bonds.
Crucially, the result is robust even when the authors look at the most recent 30-year period. Indeed, when dividing the sample into three sets of 30 years (1928-1957, 1958-1987 and 1988-2018), stocks are still preferable to bonds in the long run when a riskless asset is included.
The result is also robust for periods where the annual expected returns on stocks are lower. ‘If the annual expected return on stocks is 2.30-2.86% lower than the average real return of 8.1% in the 1928–2018 period, stocks still dominate bonds.’
Interestingly, the result does not just hold when expected returns are lower, but also in rare disaster events, like the GFC. For example, for a disaster return of -30%, stocks continue to dominate bonds for horizons of three or more years. So, by adding a reasonable probability of large crashes during the investment horizon, the authors still find that a portfolio of stocks with a riskless asset dominates bonds with a riskless asset.
For investors deciding on an asset allocation framework, the paper helps confirm one thing – holding a larger share in equity indices is more fruitful over time, even when adjusting for risk. By doing so, you can trump the alternative of a bonds-heavy portfolio in periods of both market tranquillity and chaos. The key is to ensure you include a risk-free asset, otherwise, there is no guarantee holding more stocks than bonds yields higher returns in the long run.
Levy H., Levy M. (2021), Stocks versus bonds for the long run when a riskless asset is available, Journal of Banking & Finance, (Volume 133), https://www.sciencedirect.com/science/article/abs/pii/S0378426621002314