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April 25, 2012 at 08:00 PM
From a purely mathematical point of view, the “stocks are safer over long periods of time” argument — before Paul Samuelson took an axe to it — went as follows. Historically, there was a 35% chance that a diversified portfolio of stocks would underperform safe cash during any one-year period. Moreover, the stock market’s behavior from year-to-year exhibited the same independence as consecutive coin tosses. The coin has no memory of its past behavior, and neither, so it was believed, did the stock market.
Put these two assumptions together and you get the following: Over a two-year period there is a (0.35)(0.35) = 12.25% Probability of Shortfall. Over a three-year period there is a (0.35)(0.35)(0.35) = 4.3% probability of shortfall, etc. Continuing this logic, by year 10, there was a 1 in 40,000 chance you would regret investing in a portfolio of stocks versus safe cash. This mathematically contrived justification was labeled time diversification, and became another rallying cry of the “buy, hold and prosper” crowd. A longer time period diversified away risk. The stock market was a casino in which the odds were heavily in the gamblers’ favor.
Enter Paul Samuelson who argued that if an investment was risky over one year, time didn’t make it any safer. The only safe asset for the long run was a risk-free inflation-adjusted government bond. Anything else carried risk, and that risk didn’t disappear in the long run, or even the very long run. It therefore didn’t matter how old or young you were. The fact that the probability of shortfall declined quite rapidly with time didn’t imply that you should skew your portfolio more heavily towards stocks when you were young vs. when you were old.
In many scholarly articles he argued that that very small shortfall probability was offset by the enormous pain and disutility of a loss. His great flash of genius was to demonstrate that these two effects exactly balanced themselves out. Ergo, the optimal amount of stocks vs. safe cash was time-invariant.
So — you might wonder — why is the financial industry encouraging people who are saving for retirement to invest more in the stock market and take on more risk? Is there any justification for this advice?
Human Capital
Despite Paul Samuelson’s warning about the riskiness of stocks, which I have taken to heart, I personally remain heavily invested in them, for better or for worse. The reason I have made this seemingly risky decision is because I am many years away from retirement. In fact, I have a very long time horizon before I plan to stop working at (planned) age 70, and start collecting my pension income from the university.
Now, if you have been paying any attention at all, your first reaction might be: “Didn’t he read anything he just wrote above? Professor Samuelson proved that time shouldn’t matter.”
But the fact is that I actually agree 100% with Professor Samuelson, and my behavior is perfectly consistent with his recommendations. The key to reconciling the above-stated ‘Samuelsonian’ time invariance and the investment advice doled out by industry — and my own behavior — is the concept of human capital.
There are two types of assets that a person might possess on their personal balance sheet. The first is financial capital, which is quite visible and market-based. Think of money in the bank, bonds in a retirement account or stocks in a portfolio. You can sell them anytime and immediately consume the proceeds. This is your financial capital.
But you also own another asset, and that is your income-earning ability. This asset is called your human capital value. Researchers such as Professor Gary Becker have computed how much an extra year of education can impact your earnings profile over your life. Evidently, the rate of return from investing in education is between 8% and 15% depending on your field and major. For now the important takeaway is as follows: If you define your wealth broadly enough to include both human and financial capital — and your human capital is relatively safe — then even Paul Samuelson will agree that it makes sense to have some money in the stock market even if you are very risk-averse. The question is how much.
The Equation Explained
Here are the six factors or variables that should determine how much money you should risk and invest in the stock market:
1. The amount of financial capital (i.e. money in the bank) that you have accumulated already, which is denoted by the letters FC. This is measured in dollars.
