Portfolio Theory

Modern portfolio theory (MPT)—or portfolio theory—was introduced by Harry Markowitz with his paper “Portfolio Selection,” which appeared in the 1952 Journal of Finance. Thirty-eight years later, he shared a Nobel Prize with Merton Miller and William Sharpe for what has become a broad theory for portfolio selection.

Prior to Markowitz’s work, investment theory focused on assessing the risks and rewards of individual securities. Standard investment advice was to identify those securities that offered the best opportunities for gain with the least risk and then construct a portfolio from these. Following this advice, an investor might identify a handful of railroad stocks all offered good risk-reward characteristics and invest in only these.

But this is not how investors actually behaved. In practice, investors tended to diversify their portfolios.

Markowitz bridged the gap between investment theory and investment practice by developing a mathematical model for diversification. This formalized what investors already knew intuitively: that they should focus on selecting portfolios based on those portfolios’ overall risk-reward characteristics instead of merely compiling portfolios from securities that each individually have attractive risk-reward characteristics.

In a nutshell, investors should select portfolios rather than select individual securities. Markowitz provided the mathematical justification.

If we treat single-period returns for various securities as random variables, we can assign them expected values, standard deviations and correlations. Based on these, we can calculate the expected return and volatility of any portfolio constructed with those securities. We may treat volatility and expected return as proxies for risk and reward. Out of the entire universe of possible portfolios, certain ones will optimally balance risk and reward. These comprise what Markowitz called an efficient frontier of portfolios. According to Markowitz, an investor should select a portfolio that lies on the efficient frontier.

James Tobin (1958) expanded on Markowitz’s work by adding a risk-free asset to the analysis. This made it possible to leverage or deleverage portfolios on the efficient frontier. This lead to the notions of a super-efficient portfolio and the capital market line. Because they are leveraged, portfolios on the capital market line are able to outperform portfolio on the efficient frontier.

Sharpe (1964) formalized the capital asset pricing model (CAPM). This makes strong assumptions that lead to interesting conclusions. Not only does the market portfolio sit on the efficient frontier, but it is actually Tobin’s super-efficient portfolio. According to CAPM, all investors should hold the market portfolio, leveraged or de-leveraged with positions in a risk-free asset. CAPM also introduced beta, and it relates an asset’s expected return to its beta.

Portfolio theory provides a context for understanding the interactions of systematic risk and reward. It has shaped how institutional portfolios are managed, and it motivated the use of passive investment techniques. The mathematics of portfolio theory is used in financial risk management and was a theoretical precursor for today’s value-at-risk measures.