Malkiel Understates the Risk of Long Term Investing

Malkiel’s “Random Walk down Wall Street” offers very practical advice for household investors, but is dangerously misleading on the risks of long term investing.

The book starts out with a behavioral bent, pointing out all the times in which markets have gone crazy. I personally found the coverage of how simple name changes during the dot com bubble would cause certain stocks to zoom higher in value — a smoking gun for irrationality. Yet in spite of this behavioral bent, Malkiel is very down to earth about how many opportunities are available for people to beat the market. In the end of the first part of the book, Malkiel notes:

Markets are not always or even usually correct. But NO ONE PERSON OR INSTITUTION CONSISTENTLY KNOWS MORE THAN THE MARKET.

But even if people can’t beat the market, that doesn’t mean that there aren’t a lot of ways to underperform dramatically. I view his chapters on diversification in this light. He does a good job of introducing what can be very difficult mean-variance theory. Instead of using matrix algebra, he goes through an toy example of umbrella manufacturers and a resort owner and shows how it can be valuable to spread a nest egg across investments that, as a collective portfolio, can perform well come rain or shine.

When it comes to implementing investment advice, I also wholeheartedly agree with his argument for sticking with indexed funds. I enjoyed his statistical treatment of why reported mutual fund returns over-predict the actual investment opportunities available to investors due to survivorship bias. And whenever he brought up market “anomalies” such as the January effect or waiting for low price to earnings ratios to get higher returns, he was sure to note the uncertainty behind these signals, and to push people towards a passive investment strategy.

However, while I agree with the general message that households should be investing more into the stock market, both domestic and international, I think Malkiel substantially understates the true risks of investing in the stock market. In particular, he engages in the fallacy of time diversification when he tries to convince the reader that stocks are safer in the long run. The core of his argument centers around this chart:

Based on this chart, he argues that “A substantial amount (but not all) of the risk of common-stock investment can be eliminated by adopting a program of long-term ownership and sticking to it through thick and thin (the buy-and-hold strategy discussed in earlier chapters).”

But this relies on an empty notion of risk. The risk that is relevant for retirement investors is not the risk that their investment earns an average return above some other investment, for example long term bonds, but rather whether, at retirement, there is enough wealth left over to carry them through their golden years. As such, it’s not the average return that matters, but rather the total return over an entire working life!

And when it comes to this, the longer your investment horizon the larger the variance of the total return! If returns are independent over time, variance scales linearly. While there may be some mean reversion in the long run, as Malkiel notes in his discussion on PE ratios, this mean reversion can be very slow and doesn’t change the thrust of the analysis.

The risk from stock investment might be better visualized by thinking about what are the range of possible outcomes after 40 years in the stock market. Suppose each year stocks return 8% on average with a standard deviation of 20%, and that returns are independent (adding plausible levels of dependence does quantitatively little to the results). Suppose further that the investor’s utility is log, so that negative outcomes hurt a lot and extremely positive events aren’t that positive. Then the potential life paths for utility are summarized in the chart below. Each black line represents one potential history of an investor going 40 years in the stock market.

From this diagram it’s clear that risk rises over time. Sure, you have a tendency to drift up, but the bad outcomes get very bad. So even if the variance of the average return goes down, the variance of that average return multiplied by the investment timescale keeps on going up.

2 thoughts on “Malkiel Understates the Risk of Long Term Investing

    1. Yichuan Wang Post author

      So a lot of the asset pricing literature has focused on the notion of “long run risk”. What if the economy just slightly underperforms going forward, but that this underperformance is persistent? Not only are you earning less income because the economy is worse, all of your leveraged assets are doing worse as well! I’m not trying to say that investing in stocks is a bad retirement idea, but rather that there’s no magic of averaging that makes long run investing safer. Rather, it has something deeper to do about life cycle investing.

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