# Modern Portfolio Theory & Modern Real Estate Investing

*This learning series on Modern Commercial Real Estate Investing first appeared on the **EquityMultiple blog**. Please check in there for updates and additions to this series.*

We spend countless hours analyzing the relative risk and return potential of *individual* real estate investments. But what of the broader picture of an investment portfolio? What is the analytic case for allocating a greater share to real estate than reflected in portfolios of most individual investors? Modern portfolio theory can provide a useful guiding framework for asset allocation, not just for large institutional investors but for individuals as well.

Modern portfolio theory refers to the quantitative practice of asset allocation that maximizes projected (ex-ante) return for a portfolio while holding constant its overall exposure to risk. Or, inversely, minimizing overall risk for a given target portfolio return. The theory, first put forth by Harry Markowitz in his paper “Portfolio Selection” in the 1952 Journal of Finance, prescribed diversifying across uncorrelated assets to reduce the overall risk exposure of the portfolio.

The theory uses a mathematical process called “mean variance optimization”, thereby considering the covariance of constituent assets or asset classes within a portfolio, and the impact of an asset allocation change on the overall expected risk/return profile of the portfolio.

# Modern Portfolio Theory and Investment Analysis

Consider a hypothetical fictional investor (let’s call him Steve, a lawyer in his early thirties). Steve currently holds a large amount of Apple stock, just received his holiday bonus, and is looking to grow his portfolio wisely. He does not want to put more money into Apple (though the stock is performing well) because he understands that he should diversify his portfolio as it grows. Steve is deciding between putting his money in Facebook — a stock that appears safe and stable — and devoting his bonus to passive real estate investments.

In order to employ modern portfolio theory to inform his allocation choices, he’ll need to gather a set of estimated asset performance figures: the expected return of each asset within his potential portfolio; the volatility of each asset class (as represented by their standard deviation from their expected mean return); the correlation between these asset classes; and their covariance with one another (as defined by the product of their volatilities and correlation with one another).

Steve arrives at the following regarding the expected return, volatility, and correlations of his portfolio’s constituent asset classes:

From here, Steve can further calculate the covariance of these assets using the formula **COVij=SiSjCij **where S is the time-series standard deviation of periodic total returns (volatility), and C is the covariance between the two assets i and j. As such, Steve arrives at the following covariances for the constituent asset classes of his portfolio.

To capture the true impact of Modern Portfolio Theory is it important to examine what the expected return and standard deviations of portfolios with these potential allocations would be. Below are the expected return and standard deviations of Steve’s two portfolio options. Portfolio A consists of 70% Apple stock and 30% Facebook. Portfolio B consists of 70% Apple Stock and 30% real estate.

Despite the fact that Facebook stock and Steve’s real estate holdings have the exact same expected return and risk profile, the portfolio containing real estate has a significantly lower overall risk profile than the portfolio containing Facebook, an asset that is similar in nature and highly correlated to Steve’s main holding of Apple. True diversification considers not just the risk/return profiles of asset classes and assets within the portfolio, but also the correlation of the *individual* assets within the portfolio.

The figures above, albeit simplified, make clear the impact that modern portfolio theory practice can have. As you can imagine, the larger and more varied the portfolio, the more complex the calculations and the more powerful the output can be. Excel and other software can assist with more complex mean variance optimizations.

Like David Ricardo’s theory of comparative advantage in trade, modern portfolio theory is a simple, elegant concept with profound real-world implications. While it may not be practical or feasible to employ sophisticated formulas to rebalance your portfolio, the take-home principals of Modern Portfolio Theory are worth keeping in mind when any new asset or allocation mix is considered: **for any level of expected aggregate return, the degree of correlation between assets and asset classes within a portfolio should be minimized.**

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# Limitations of Modern Portfolio Theory

In Markowitz’s original conception, standard deviation is used as a proxy for volatility, which in turn is a stand-in for risk, which investors seek to mitigate within the framework. Upon examination, the issue with this proxy is apparent: using standard deviation as a measure of risk implies that a better-than-average return is as undesirable as a worse-than-expected return of the same magnitude. Furthermore, using the normal distribution to model the pattern of potential investment returns makes investment results with more upside than downside appear more risky than they really are, with the opposite true as well. This can lead investors to misunderstand the potential ‘upside’ or ‘downside’ of a particular investment when considering only traditional modern portfolio theory methodology.

Some academics and portfolio managers have taken to incorporating a metric called ‘Downside Risk’, which incorporates an investor’s goal return and defines risk as those outcomes that do not achieve that goal. The statistic is calculated in a similar manner to standard deviation, however only accounts for results that lie below the investor’s desired return hurdle. The metric measures the volatility of results below the target return. This modified framework is sometimes referred to as “Post-Modern Portfolio Theory”.

# Modern Portfolio Theory and the Current Landscape of Alternative Investments

Diversification across uncorrelated assets is the cornerstone of Modern Portfolio Theory, so it’s no surprise that acolytes of MPT have taken an active interest in diversifying across a growing spectrum of alternative assets.

While there is no one definition to encompass alternative investments, they are broadly defined as securities constituent of private, less efficient markets. They are typically less liquid than public market offerings. While public market vehicles like index funds can offer access to “beta” (an investment in the broad health of the economy or sector of the economy), private-market alternatives offer access to “alpha”, or return potential derived from skill in management and the exploitation of market inefficiencies.

Performance of a privately-held commercial real estate asset, for example, tends to depend on the soundness of location and business plan and the skill and resources of the Sponsor and/or developer, rather than market swings. By definition, then, alternative assets exhibit low correlations with traditional assets, making them attractive additions to a portfolio when evaluated through the lens of Modern Portfolio Theory.

Studies have supported this assertion, including a Blackstone study that analyzed performance of a portfolio with a 20% allocation to alternative investments (including private real estate) over a 20 year period:

Two aspects of the current traditional asset environment have also pushed many institutional and individual investors toward greater alternative asset allocations:

**A Low-Yield Environment Among Traditional Assets:**In the past several years, yields on bonds have dwindled to close to zero. Even if and when bond yields pick up, gains may be tempered by a concomitant increase in inflation. Meanwhile, a combination of high valuations (the price-earnings ratio of the S&P 500 is 550 basis points higher over the period of 2008–2016 than during the years between 1985 and 2007).**Higher Correlations Among Traditional Assets:**Between the years 2001 and 2011, cross-asset correlations roughly doubled among traditional assets due to more integrated global securities markets, and heightened global volatility.

These factors both point toward the growing appeal of alternative assets, like private real estate, when considered within the Modern Portfolio framework. Unfortunately, individual investors remain severely under-allocated vs. institutional investors like pensions and endowments.

The JOBS Act, and subsequent online platforms like **EQUITY**MULTIPLE, have begun to level the playing field by offering similar private-market alternative assets at relatively low minimums.

It should be noted that alternative investments still carry risk, not least of which liquidity risk. Again, alternative assets exhibit a greater Alpha, so it’s important for investors to understand the quality of management and the underlying asset, as well as all risk factors.

- Low growth prospects in equities and the bond market point to investors seeking yield in alternatives
- Alternatives, characterized by less efficient private markets, and less liquidity — amounting to relatively low correlations with traditional assets

“returns tend to be less correlated to the beta of traditional market investments and are more dependent on the individual manager’s skill.”