Jan 17, 2009

The promise of equity investing: oversold to the public?

The conventional wisdom for personal investments is that the longer you have until you need the funds, the more risk you can afford to take. A young person with many years until retirement should put a larger percentage of his asset allocation (mix of stocks, bonds, and cash) into riskier asset classes such as equities. If we examine portfolio statistics, this appears to be a reasonable suggestion - while the S&P 500 may be up or down 40% in a year, over 10 or 20 years the average annual return approaches a more reasonable number, and the standard deviation of returns (how much do returns vary each year compared to the mean) also decreases. Since the standard deviation represents risk, people believe they are taking less risk by holding for the long term.

The problem here is that an individual is concerned with his portfolio's terminal value much more than the average of his returns. That is, when you retire in 40 years, how much real purchasing power does your 401(k) provide? Unfortunately, as time increases, the dispersion of your portfolio's terminal value increases, rather than decreases. This means the range of possible values, both extremely high and extremely low, is wider. The mean (expected) value looks pretty good, and there is a lot of upside, but if you end up in the bottom 3 sigmas, you may be disappointed. See graph from John Norstad below.

My argument is not that investors should eschew stocks in favor of something else. It's that average investors may not be fully informed about the risk that they are taking, and may be misled by the apparent effectiveness of time diversification. The investment community has put the best possible spin on portfolio statistics, but may not explain the nuances to an unsophisticated investor. Now that the primary burden of providing for one's retirement has been shifted from social security and pensions to 401(k)s and Roth IRAs, it is more important than ever that people understand what is going on in those accounts.

A detailed explanation and some other arguments are available here. He gets into some other interesting considerations, such as utility theory and the options pricing model. Regarding the latter - if the risk of stocks really declined the longer you held them, put options on the S&P 500 (the right to sell the index at a guaranteed price) should cost less the further out in the future they mature. This is basically a form of portfolio insurance - you buy the option and ensure that you will receive at least a certain price for your stocks. But we observe in the marketplace that the cost of such an option increases with the time to maturity. If you tried to insure the value of your portfolio for the next 10 years this way, it would be prohibitively expensive.

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