Jeremy Siegel vs. Zvi Bodie: Does Equity Risk Decrease Over Time?

A Monte Carlo Simulation of Time Diversification

September 23, 2014

by David Blanchett, Michael Finke and Wade Pfau

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Stocks should be the asset class of choice for the long run, according to Wharton Professor Jeremy Siegel – and he has provided the data to prove it. But that paradigm has been challenged by Boston University Professor Zvi Bodie and others, who have shown that stocks become riskier the longer one owns them. Either view has profound implications for whether equity allocations should increase or decrease over time. Using Monte Carlo simulations, we provide guidance for the advisory profession.

In two recent articles, we have introduced the basics of Monte Carlo simulation and expanded on some of the practical applications of Monte Carlo analysis. In this article, we expand on a concept touched on briefly in both: time diversification. Time diversification has implications for how advisors build portfolios for clients and how we depict the probability of outcomes over longer investing periods.

The idea that stocks are good long-term investments is ubiquitous in financial planning, but it drives a lot of economists up the wall. Economists think that all things, including stocks and bonds, are priced fairly according to the risk preferences of buyers and sellers. Stocks are risky and therefore should have a higher average return. But risk means that sometimes stocks will have a lower return than bonds, even in the long term. Otherwise, they wouldn’t be risky. If we always did better investing in stocks over a 30-year time horizon, then only idiots wouldn’t buy them for retirement. And economists don’t like to believe that investment prices are set by idiots.

Many investors do appear to be idiots, unfortunately — or at least they were in the past. If you look at the historical data for developed countries, stocks have been less risky for long-run investors. And that’s not just some of the time, but pretty much all of the time.

We’re left with the very unsatisfying conclusion that stocks are the best asset class choice for long-run goals, even for risk-averse investors. Although unsatisfying for many economists and others who believe that it should be risk tolerance, not time horizon, that determines portfolio recommendations, it is best to at least understand how time diversification impacts optimal portfolios if future investments continue to behave as they have in the past.

Our Monte Carlo simulation results show how incorporating time diversification can have a large impact on portfolio recommendations compared to Monte Carlo simulations that ignore the effect. First, however, let’s look at the challenge researchers face when modeling time diversification. We’ll then turn to how Monte Carlo simulations can overcome those hurdles and how we constructed our model.

The role of Monte Carlo analysis

A simple Monte Carlo analysis assumes that returns are independent of one another. Simulated returns don’t include recessionary periods when stock prices fall too much and expansions when they rise too much. Some of the simulations will have the appearance of these scenarios (e.g., multiple consecutive negative returns). But there is no underlying force tethering the returns from getting too far out of line. Rising and falling stock prices in recessions and expansions create short-run volatility, but the cyclical nature of rising and falling valuation means that stocks aren’t too risky for long-run investors.

The ebb and flow of stock valuations results from mean reversion. Stock returns (or, more accurately, the excess return over bonds, known as the equity risk premium) go up and down with investor sentiment. This predictable short-term volatility gets smoothed out over the long term. So an investor who doesn’t care about short-run volatility gets rewarded with high returns and lower long-run risk.

The mean reversion and market sentiment story has been validated in finance literature. This is good news for investment advisors who can earn their fees by keeping clients from selling out of the market when valuations are most attractive (remember March 2009?). But it is bad news for Monte Carlo simulations if they are built on the assumption that mean reversion doesn’t exist. Estimations won’t give enough credence to what appears to be a very real phenomenon of time diversification.

Time diversification is the idea that stocks become less risky over the long run yet still earn a high risk premium. This is the part that most bothers economists who believe in efficient markets. If it were true, corporations could just issue long-term bonds, invest in stock mutual funds and earn a riskless profit. Bodie (1995) emphasized that time diversification violates the Black-Scholes option-pricing model and should show up in the prices of long-term stock options. But it doesn’t, leading him to conclude that stocks are indeed riskier over the long run. Despite Bodie’s research, there is a growing body of evidence that time diversification exists in the historical market-return data.

Siegel (2008) noted that stocks have been less risky over long holding periods based on historical equity returns in the U.S. going back to 1801. There is a growing body of literature dedicated to this topic, including our own research. The advantage of stocks as long-run investments may just be a historical anomaly, but it’s a historical anomaly that holds up in just about every country we looked at over a very long period of time.

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