Saturday, January 27, 2007

Tobin's Separation Theorem : The Dilution of Risk

Ever since the 1957 publication of James Tobin's seminal paper on what has become known as "The Separation Theorem" (Liquidity Preference as Behavior Towards Risk for those intrepid souls willing to sample it) , investors have had the theoretical basis for modulating portfolio risk.

In essence, the Theorem postulates that an investor can control the risk of a basket of risky investments by either borrowing at the risk free rate and leveraging the portfolio (and its risk), or alternately, lending at the risk free rate and tempering risk. Since most investors are risk averse, the clear preference of most investors is to combine the risky basket of securities with risk free bonds, and thereby lower the downside risk of the portfolio. In common parlance, we would term this the stock/bond asset allocation decision.

The risk free bond allocation is usually defined as short-term treasury securities (1 to 5 year maturities), or perhaps expanded to include short term investment grade corporate paper. It is sometimes suggested that the risk free allocation should be made up of inflation indexed treasuries. (My personal individual preference is to combine both securities for risk dilution by dividing the risk free allocation between the two.)

In his excellent paper, The Long-Term Risks of Global Stock Markets, Phillipe Jorion finds that "a globally diversified portfolio would have displayed much less downside risk than any single market." The global equity portfolio is therefore a proxy for the risk basket of securities.

We can derive a notion of the downside risk for this risky basket by reference to the superb Dimson, Marsh, and Staunton paper, The Worldwide Equity Premium: A Smaller Puzzle, a table from which is reproduced in the following pdf. file.

The table rewards careful scrutiny. It covers 106 years of market history, not only for the US market, but also including four foreign markets (UK, France, Germany, and Japan) as well as the World Market and the World Market Ex-US. The table provides real rates of return for various market episodes; highest and lowest period returns; and longest runs of negative real returns. The rewards and risks of equity investment are manifestly apparent. Although future returns and economic episodes are uncertain as to limits, the historical record does demonstrate that the world equity portfolio has surrendered as much as 50% of its real value during past down market cycles.

The following table (courtesy of William Bernstein, The Intelligent Asset Allocator) puts the Separation Theorem to practical use, showing the required bond allocation for diluting the downside risk potential of equities to tolerable levels. (The choice of maximum loss preference would, of course, depend on the risk tolerance of the individual investor). One must also caution that, as the Dimson, Marsh, and Staunton paper reminds us, hyperinflation can render even risk-free assets worthless, a reminder that uncertainty is an inescapable fact of life. An allocation to commodities might be advisable to hedge this risk.

Table 1. Downside Risk Reduction
Maximum Loss
Equity Allocation

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