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How Risky are Stocks in the Long Run?

October 7, 2014

by Michael Edesess

Reasons to doubt Siegel’s view

One reason to be skeptical of Siegel’s data is the time period that it covers. The period since 1800 has been unique in human history. During that period, growth of real global economic product has averaged about 2.7% annually. Prior to that time, for hundreds of years, according to economist Brad DeLong – indeed for millennia – growth averaged between zero and less than two-tenths of a percent per year.

Suppose that in the future, the pace of economic growth went back to the levels of the past, prior to the last 200 years. We assume this cannot possibly happen because we can’t turn the clock backward to pre-technology times. Yet prominent figures such as Northwestern University economist Robert J. Gordon have speculated that economic growth may be much lower in the future. Even GMO founder Jeremy Grantham, a long-time exponent of reversion to the mean, has warned that growth will abate dramatically in coming decades.

What would be the effect of that abatement – or more to the point, of the expectation of that abatement? A drop in the expectation of economic growth from the 2.7% of the last 200 years to well below 1% would have an immediate catastrophic effect on stock prices, causing them to fall by more than half. Indeed, when they did fall by half between 2007 and 2009, it could have been attributed to a sudden drop in the expectation of long-term economic growth. If that low expectation persists, stocks will remain depressed, as they did for many years in Japan.

Siegel’s history of stock-market returns is not enough by itself to ensure that future returns will be as good as in the past. In fact, there is ample reason to worry that they won’t. And if they are much worse because economic growth will be lower, then fixed income will be a safer haven.

Reasons to doubt Bodie’s view

Bodie’s view is also open to question. It is important to note what model Bodie used to calculate the cost of insurance: geometric Brownian motion.1 It is the basis for the vast majority of Monte Carlo simulations, and it is the fundamental assumption of most of Modern Portfolio Theory (MPT), including option-pricing theory.

But doubts have been aired for decades as to whether geometric Brownian motion correctly models real-world price changes. The first questions were raised by Benoit Mandelbrot more than 50 years ago, when the model was in its nascent stages. Mandelbrot observed that distributions of percentage price changes had “fatter tails” than the distribution2 assumed by geometric Brownian motion. That is, extreme price movements are more common than geometric Brownian motion assumes them to be. It is theoretically possible to alter the model slightly to incorporate these fat tails, but it is much easier mathematically to use geometric Brownian motion. That is why it continues to be used.

More recently, the focus of attention has been on a core assumption of the standard geometric Brownian motion model: that returns over different time periods are “independent and identically distributed” (IID).That is to say, the rate of return that actually occurs in one time period, no matter how high or low, cannot alter the probabilities of rates of return in subsequent periods.3

Recent objections to that assumption have often referred to “mean-reversion.” Mean-reversion of rates of return is the financial analog of the physics truism “what goes up must come down.” It implies that if a high rate of return occurs, then the likelihood increases that lower returns will follow, and vice versa. Indeed, mean-reversion would seem, on the face of it, to invalidate Bodie’s result.

However, as I will argue, the concept of mean-reversion in investment returns and most approaches that have been proposed to model it are flawed.

  1. Geometric Brownian motion assumes percentage price changes are lognormally distributed and that price changes in non-overlapping time periods are independent of each other.
  2. Namely, the lognormal distribution (or the normal distribution if percentage price changes are stated as continuously compounded returns).
  3. Assumings the time periods are not overlapping.