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Opinion

Thinking separately

Thinking separately
September 1, 2009
Thinking separately

Lord Turner advocates a so-called "Tobin tax" to help curb the excesses of the City. This device competes with Tobin's q as the US economist's best-know contribution to the dismal science. Still, we don't need to dwell on these two concepts. Rather, we should focus on that piece of Tobin's work that changed the face of investment; that every half-serious investor should know of (though few do); that simultaneously justifies the investment plans of the most aggressive and the most timid investors on the planet; and that prompts the question: why even bother to build investment portfolios?

It all started back in the mid 1950s when Tobin spotted a flaw in Keynes's General Theory of Employment, Interest and Money. Keynes had innovatively noted that interest rates were not just a reward for saving, which was conventional wisdom when he was writing his General Theory, they were also a reward for taking on risk. However, Keynes assumed that savers would either keep all their capital in cash or put all of it into risky assets, depending on how frisky they felt. Tobin thought this was wrong. Rather than adopt an either/or attitude towards using their capital, investors would take a more measured approach, he reckoned. If they were cautious and/or bearish, they would keep much of their capital in low-yielding but risk-free savings accounts. If they were more aggressive, or became more bullish, they would put more capital into risky assets. In other words, they would diversify in a way that Keynes ignored.

It was from this observation that Tobin's work on the subject got its name - the separation theorem. So called because each investor has two decisions to make. First, to decide what was his attitude towards risk. Second, to build the portfolio that was best aligned with that attitude.

So far, so obvious. However, at this point Tobin's work met research by another academic, Harry Markowitz, who was refining his ideas behind the effective diversification of portfolios. And this is where it really got interesting.

In the complex mathematics of his scheme, Dr Markowitz assumed that investors only choose between combinations of risky assets. He omitted - or forgot about - risk-free cash as part of the menu. Correct for that omission and the picture changes radically, at least in the theoretical world of Tobin and Markowitz. In that world, an investor can freely lend or borrow at the risk-free rate of return. That means he can slide smoothly from one extreme where he keeps all his capital in risk-free assets through to the other, where he borrows at the risk-free rate to buy still more risky assets.

Granted, this is theoretical and everybody knows you can't borrow at the risk-free rate. Yet, in fact, these assumptions are not that far removed from reality. Obviously, investors can lend at the risk-free rate - Treasury bills and various savings accounts fulfil that function. As to borrowing at the risk-free rate, there are other ways to achieve that end, which is to gear up the potential returns on a portfolio. Derivatives can do the job nicely - if an investor is feeling especially punchy, he buys call options on the FTSE 100, or whatever.

So, if we have established that something approximating to the theoretical world, where an investor can happily lend or borrow at the risk-free rate, applies in reality, then an important consequence ensues. In a nutshell, it is no longer worth the bother of selecting a portfolio of risky assets; all we need is an investment in the market. Sure, we can debate what, precisely, is this thing called "the market" and, in the abstract world of portfolio theory, it can stretch to include everything that can possibly be invested in. But the point is that each investor slides up or down this investment continuum – it's called the efficient frontier in portfolio theory – depending on his attitude towards risk and return. You want to target a 20 per cent annual return as opposed to 10 per cent? Easy, just move further along the efficient frontier by selling your Treasury bills, putting all your capital into a tracker fund and buying a few calls.

In this world, selecting an investment portfolio becomes otiose. What's the point of choosing between growth stocks and income stocks; value stocks and recovery situations; small cap and big cap stocks? None whatsoever. You can target the prospectively high returns from growth or recovery, or make do with the more modest returns from value stocks or big cap simply by gliding up or down the efficient frontier.

So why don't more of us do this? It's obvious why the fund-management industry doesn't - it would put most of them out of a job. They're not going to point out that there is no justification for charging expensive fees because the manager is wasting his time and your money. As to private investors? - vanity (we all think we can do better than average); stupidity (some of us even believe that); laziness (portfolio theory, of which this is a part, is tough to grasp); the entertainment value of selecting a portfolio. These may all be reasons why we ignore Tobin's separation theorem. Well, ignore it, if we will; but let's not pretend that it isn't persuasive.