Modern Portfolio Theory

The Markowitz Efficient Frontier is a foundational concept in modern portfolio theory and a great starting point for investors thinking about diversification.

Developed by Harry Markowitz in 1952, the efficient frontier represents the set of "optimal portfolios" offering the highest expected return for a given level of risk, or the lowest risk for a given level of expected return, all with respect to a certain set of strict assumptions.

Here's how it looks. Imagine plotting the risk and expected return of all the available assets on a graph: expected return is on your vertical axis, risk (as represented by volatility) is on your horizontal axis. Next we can plot the risk and return of various portfolios that provide the best combinations of risk and expected return. These optimal portfolios form a curved line, which is the efficient frontier. According to the Markowitz framework, these are the portfolios you want to hold. Anything below that line would be considered inefficient.

The key insight here is that diversification really matters. By combining risky uncorrelated assets, investors can construct superior portfolios to any of the available assets in isolation.

It is important to note, however, that more recent research on multi-factor investing has demonstrated that the efficient frontier provides an incomplete view of the investment world.

Here's the limitation. The efficient frontier assumes all risk can be captured by a single dimension—volatility. Multi-factor research pioneered by Fama, French, and others has shown that multiple dimensions of risk drive expected returns. Factors like size, value, and profitability can explain differences in expected returns that the efficient frontier overlooks.

Despite its limitations, the efficient frontier remains valuable as a framework for thinking about diversification. Modern portfolio construction builds on Markowitz's foundation while incorporating factor exposures and realistic constraints. The core principle—that thoughtful diversification improves risk-adjusted returns—remains as relevant today as seventy years ago.

Not all index funds are passive. The definition of index funds has evolved over time. While they used to be broadly diversified and market-cap weighted, today many funds labeled as “index” actually hold concentrated portfolios that stray significantly from the market. So it’s important to look closely at what an index fund really holds.

Markowitz defined risk as the volatility of returns—specifically measured by variance or standard deviation. In simple terms, a riskier investment is one whose returns bounce around more unpredictably. If two investments have the same expected return, the one with lower volatility is considered less risky in the Markowitz framework. But here's where it gets interesting. Markowitz's key insight was recognizing that portfolio risk isn't just the sum of individual asset risks. It depends critically on how assets move relative to each other—their correlations or covariances. By combining assets that don't move in lockstep, investors can reduce overall portfolio volatility below what you'd expect from simply averaging individual risks. This covariance insight was revolutionary. It provided the mathematical foundation for why diversification works—not just holding many things, but holding the right combination of things that behave differently under various market conditions.

When modern portfolio theory first emerged, early research suggested that holding 20 to 30 stocks was enough diversification to achieve total volatility similar to the market. But later studies showed that even if expected volatility is similar, small differences can compound over time, creating significant realized tracking error. More recent research recommends holding at least 250 stocks to stay close to a market index. At Integrity, we view the market as just one premium among many an investor might want to capture. Depending on the strategy, we typically recommend portfolios with hundreds or even thousands of stocks to balance diversification, risk, and return potential.

In the investment world, there’s debate over what’s “active” versus “passive.” At Integrity, we see these terms as insufficient.

Investors used to align with either a market cap weighted index strategy because they believed all information is already priced or a concentrated active strategy that seeks to profit on unpriced information.

We now know that there can be good reasons to deviate from the market portfolio besides information arbitrage, like gaining exposure to new uncorrelated risk premium (which would not require taking on the costs and risks of information arbitrage).