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.

 

tobin_theorem

Tobin’s Separation Theorem

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.

In designing practical investment portfolios the risk-free bond allocation is usually expanded to include  short-term treasury securities (1 to 5 year maturities), or perhaps  to include federally-insured certificates of deposit, or even short-term investment grade corporate paper. It is sometimes suggested that the risk-free allocation should be made up of inflation indexed treasuries.
globe

In his  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  Dimson, Marsh, and Staunton paper, The Worldwide Equity Premium: A Smaller Puzzle.

The data rewards careful scrutiny. It covers 106 years of market history, not only for the US market, but also including foreign markets as well as the World Market and the World Market Ex-US.

The study 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, providing guidelines as to the required bond allocation, based on historical returns, for diluting the downside risk potential of equities. (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.


Table 1. Downside Risk Reduction
Maximum Loss Equity Allocation
35%
80%
30%
70%
25%
60%
20%
50%
15%
40%
10%
30%
5% 20%
0% 10%
About

Barry Barnitz, administrator of both the Bogleheads® wiki and of Financial Page, a Bogleheads® blog

Posted in Asset allocation
November 2015
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