James Tobin (1958) added the notion of leverage to portfolio theory by incorporating into the analysis an asset which pays a risk-free rate. By combining a risk-free asset with a portfolio on the efficient frontier, it is possible to construct portfolios whose risk-return profiles are superior to those of portfolios on the efficient frontier. Consider Exhibit 1:
In Exhibit 1, the risk-free rate is assumed to be 2%, and a tangent line—called the capital market line—has been drawn to the efficient frontier passing through the risk-free rate. The point of tangency corresponds to a portfolio on the efficient frontier. That portfolio is called the super-efficient portfolio.
Using the risk-free asset, investors who hold the super-efficient portfolio may:
- leverage their position by shorting the risk-free asset and investing the proceeds in additional holdings in the super-efficient portfolio, or
- de-leverage their position by selling some of their holdings in the super-efficient portfolio and investing the proceeds in the risk-free asset.
The resulting portfolios have risk-reward profiles which all fall on the capital market line. Accordingly, portfolios which combine the risk free asset with the super-efficient portfolio are superior from a risk-reward standpoint to the portfolios on the efficient frontier.
Tobin concluded that portfolio construction should be a two-step process. First, investors should determine the super-efficient portfolio. This should comprise the risky portion of their portfolio. Next, they should leverage or de-leverage the super-efficient portfolio to achieve whatever level of risk they desire. Significantly, the composition of the super-efficient portfolio is independent of the investor’s appetite for risk. The two decisions:
- the composition of the risky portion of the investor’s portfolio, and
- the amount of leverage to use,
are entirely independent of one another. One decision has no effect on the other. This is called Tobin’s separation theorem.
William Sharpe’s (1964) capital asset pricing model (CAPM) demonstrates that, given strong simplifying assumptions, the super-efficient portfolio must be the market portfolio. From this standpoint, all investors should hold the market portfolio leveraged or de-leveraged to achieve whatever level of risk they desire.
- Sharpe, William F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance, 19 (3), 425-442.
- Tobin, James (1958). Liquidity preference as behavior towards risk, The Review of Economic Studies, 25, 65-86.