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.

## References

- 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.