Milevsky: How Much in Risky Stocks vs. Safe Cash?

2. The value of your human capital, which is measured in dollars and denoted by the letters HC. Make a conservative estimate of what you think you will earn between now and retirement ­— net of any income taxes and required expenditures — and then compute its present economic value. For young college graduates, this number could be in the millions.

3. Your expectation of the rate at which you (or the experts) think stocks will grow over time, denoted by the letter mu (μ). Historically this number has been around 7% for stocks, once inflation is accounted for, although it might be as low as 5% in today's economic environment.

4. Your expectation for the volatility of stocks, denoted by sigma (σ), which has been around 20% for a well-diversified portfolio of stocks. This is a purely objective number, best determined by a statistician. Some argue that it might be as high as 25% or even 30%.

5. The risk-free rate (r), which has been between 1% to 4%, and probably closer to the low-end of the range today. It represents the alternative to stocks.

6. Your risk aversion, denoted by (γ), is a purely personal value that only you can determine.

Notice that this equation says nothing (explicitly) about age, time horizon, mortality rates, or even if stocks have been doing well recently. Whether you are 20, 50 or 80, Samuelson's asset allocation equation tells you to consider your attitude towards risk, your total wealth and the long-term view of the market — but not the time horizon. It is nowhere to be found explicitly in the equation.

When you think about it though, time is really embedded inside of Samuelson's equation, because the human capital value gets smaller, and eventually hits zero, as you age. Once you reach retirement — defined as the date when you stop working, permanently — and you have no more human capital, and all your wealth is tied-up in financial capital, then perhaps stocks really are too risky for you. This is your call.

Samuelson's Life and Impact

Paul Samuelson was born on May 15, 1915 in Gary, Indiana, and died on Dec. 13, 2009. He eventually enrolled at the University of Chicago, home of Milton Friedman and other conservative economic theorists. Although he was turned off by the Chicago school's blind defense of free and efficient markets, his friendship and intellectual rivalry with Milton Friedman continued for the rest of his life.

In 1935 he earned his B.A. degree and headed east to Harvard University, where he earned his Master's degree in 1936 and his Ph.D. in 1941. During his time at Harvard he fell under the spell of the Keynesian approach to economics, which argues that governments should get involved in financial markets and not leave economic affairs to Adam Smith's invisible hand. Samuelson often called himself and used the term "cafeteria Keynesian," claiming to pick and choose only what he liked from the theory. In fact, in 1960 he advised newly elected John F. Kennedy — as the U.S. was heading into a recession — to reduce taxes. Kennedy the Democrat was shocked at the advice, but was convinced of the merits by Samuelson.

Paul Samuelson was recognized as an economics prodigy from very early on in his career. In 1947, the American Economics Association awarded him the (inaugural) John Bates Clark medal, which is bestowed to economists under the age of 40 and considered to be the second most prestigious award in the field. The first most prestigious award is the Nobel  Memorial Prize in Economic Sciences, which he was awarded in 1970.

Remarkably, it was only in his 50s that Paul Samuelson turned his research attention to matters of finance, the stock market and asset allocation. In articles  published in the late 1960s he laid the foundations upon which Robert Merton and Myron Scholes built their famous option pricing equation, which garnered their own Nobel prizes. Indeed, if anybody deserved a second Nobel award, it would have been Paul Samuelson.

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Reprinted by permission of the publisher, John Wiley & Sons Canada, Ltd., from The 7 Most Important Equations for Your Retirement, by Moshe A. Milevsky. Copyright © 2012 by Moshe A. Milevsky.