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Building Your Optimum Portfolio

By: Frank Armstrong

*As seen on Forbes.

Somewhere out there is the perfect equity portfolio. Of the infinite number of portfolios you could form, the perfect equity portfolio is the one that generates the highest return per unit of risk. That’s the equity portfolio that everyone in the world would want to own. It wouldn’t matter if they were tycoons or tenant farmers, if they had a penny of equities then they would want that portfolio. The so called superefficient portfolio would dominate all others.

If you put a gun to my head I might guess that over the long haul that portfolio might return between 8 and 11 percent. Even at the low end that’s a healthy real return over inflation. Of course, in the shorter term returns may be radically different. You do remember 2009 don’t you?

Stock portfolios carry a substantial level of risk. And even the perfect equity portfolio is still going to carry the full measure of risk. Not everyone is going to be comfortable with that much risk. And, for good economic reasons some investors will need short term liquidity.

So, how much risk should you take? It depends.

Sleeping well at night is a legitimate financial objective, and if you plan to purchase your dream boat next year, send your daughter to medical school, or retire and need periodic withdrawals to support your lifestyle you will want to have the cash available without regard to what the market does in the next few months.

Another group of investors may not be satisfied with a measly 8 to 11 percent return. They want more and have a high appetite for risk.

So, how should investors balance their need for liquidity and their risk tolerance on one hand against their desire for superior long term return for something close to an optimum result? Economists struggled with this problem until James Tobin came up with an elegant solution. Tobin, an immensely influential economist, received the 1981 Nobel Prize in Economics in part for this work.

The old school approach

The old-school approach was to design an individual portfolio from scratch for each investor. This method of individual portfolio design has been called the interior-decorator approach to financial consulting. Investors were thought to require hand-tailored solutions constructed on a stock-by-stock basis. The widow, whose goal is safety of principal, might have been advised to invest in bonds, convertible stocks, utilities, REITs, and high-yielding blue-chip stocks. The corporate fast-tracker, meanwhile, might have been advised to purchase dot-com startups, small-cap stocks, and technology names to meet her growth goals.

This approach left both the widow and the fast burner with inefficient portfolios, though. Although the fast burner achieved her growth goal, she took on more risk than she needed to bear. Oddly enough, the widow did the same. By narrowly investing in assets with high correlation to one another (in other words, by favoring investments that behaved alike), both failed to maximize their return per unit of risk.

Tobin’s Separation Theorem

Tobin said investors should first determine their appetite for risk. With that level of risk tolerance in mind, investors can choose the equity portfolio from a Markowitz optimization. In other words, they’d choose the portfolio on the efficient frontier–or the line on a risk-return graph that includes all portfolios with the greatest expected return for a given level of risk–that has the highest return per unit of risk. Investors should then satisfy their liquidity and safety needs with another portfolio, called the zero-risk portfolio. In essence, investors have two buckets–an equity bucket for growth and a liquidity or safety bucket of lower-risk investments, such as cash or short-term bonds–and simply divide their assets between them. In this scenario, every investor, whether widow or corporate fast-tracker, owns the same equity portfolio; the investors temper liquidity needs and risk-reward profiles by adjusting their level of zero-risk assets.

In Tobin’s own words, “You would choose the same portfolio of nonsafe assets regardless of how risk-averse you were. Even if you wanted to change the amount of risk in the portfolio, you’d do it by changing the amount of the safe assets relative to the nonsafe assets, but not by changing the different proportions in which you held the nonsafe assets relative to each other.”

But what if a 100% equity portfolio fails to satisfy an aggressive investor’s need for risk-return potential? The investor could either leverage the portfolio or buy it on margin.

So, as you approach buying your dream boat, or as your daughter closes in on Harvard Medical School, your portfolio should hold greater liquidity in the form of more very safe assets. If you still can’t sleep at night, add a few more very safe assets until you can. The appropriate mix of the two buckets will provide an optimum solution for any investor’s risk tolerance and need for liquidity. 

A Few Problems

Tobin’s great advance left two problems unsolved. The first was the question of what exactly the dominant equity portfolio should be. The race to determine the superefficient portfolio was on. And then there was the problem of simplifying the math: Modern portfolio theory was so math-intensive at this stage that it didn’t offer much practical help to everyday investors. Markowitz had suggested an approach to the math as a footnote in his paper, but he left the problem for a student (Bill Sharpe) to solve. Simplifying the math eventually led to the solution for the superefficient portfolio. But that’s another story for another time.