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Tobin’s Separation Theorem

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Tobin’s Separation Theorem

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A young widow struggling to get by will most likely need a different portfolio than her single girlfriend on the corporate fast track. But, how should their investments differ? And, how can they best achieve their varying needs for safety, income and capital appreciation?

The old school approach

The old school approach was to design an individual portfolio for each from scratch. This method of individual design for each client has been called the “interior decorator” approach to financial consulting. Investors required a unique “hand tailored” solution constructed on a stock-by-stock basis. The widow might have been advised to meet her needs for income and safety through bonds, convertible bonds, convertible stocks, utilities, REITS, and high yielding blue chip stocks. The corporate fast burner might be counseled to purchase dot.com startups, small cap and tech stocks.

The old school approach left both the widow, and the fast burner with inefficient portfolios. The widow achieved her income goal at the cost of much more risk than she needed to bear. Surprisingly, the fast burner was in the same position. By narrowly investing in risky assets with high correlation to one another, she too failed to maximize her return per unit of risk.

Markowitz’ original paper wasn’t much help. He had assumed an investor with no need for liquidity, and an infinite time horizon that was either 100% in or out of the market. Markowitz’ investor was concerned solely with maximizing his return at a particular level of risk while choosing only from a universe of “risky” investments. In short, this investor didn’t live in the real world with the rest of us.

James Tobin, who considered himself an ivory tower economist, solved this real world problem with an elegant and powerful insight. He realized that investors have a full range of liquidity preferences, and expanded potential investor choices to include low risk assets.

Tobin stated that investors should first determine their appetite for risk. This appetite should be satisfied from the one dominant equity portfolio determined from a Markowitz optimization (the single portfolio on the efficient frontier with the highest return per unit of risk). Then the liquidity and safety needs are satisfied with the local zero risk portfolio. In essence the investor has two buckets and need only choose how to divide his assets between them. So, each investor owns the same equity portfolio, but tempers the liquidity needs and risk-reward profile with different proportions 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.”

What’s in it for you?

By using the “two bucket” approach, each investor can easily tailor her investments at the portfolio level to best meet her needs. Not only did Tobin greatly simplify the portfolio construction process, he increased its efficiency. Now all investors can achieve the maximum return per unit of risk assumed, and the choice set of optimum risk-reward profiles is virtually infinite.

In the event that a 100% equity portfolio fails to satisfy an aggressive investor’s need for risk-return potential, the appropriate solution is to leverage the portfolio, or buy it on margin. We oversimplify here by presuming availability of credit.

A few remaining problems

Tobin’s great advance left unsolved the question of what exactly should be the dominant equity portfolio. The race to determine the “super efficient” portfolio was on. And, we still had the problem of simplifying the math. Modern Portfolio Theory was still so math intensive at this stage that it wasn’t much practical help yet. Markowitz had suggested an approach to math as a footnote in his paper, but left the problem for a student to solve. Fortunately, Bill Sharpe was up to the task. Simplifying the math also led to the solution for the super efficient portfolio. But, that’s a whole ‘nother story.

Epilogue

In 1981 James Tobin was awarded the Nobel Laureate in Economics for his analysis of financial markets and their relations to expenditure decisions, employment, production and prices.

Coming up

Does a company’s dividend indicate anything about the value of the stock? Is there an optimum ratio of stocks, bonds, and bank loans for a company? Should investors prefer companies with high leverage or “strong” balance sheets? Merton Miller and Franco Modigliani proved that everything I thought I had learned about this in college was dead wrong!

References:

James Tobin, “Liquidity Preferences as Behavior Toward Risk”, The Review of Economic Studies, February 1958

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