Diversification and the Market Portfolio

Diversification and the Market Portfolio

This is the second in a ten-part series exploring the implications of modern portfolio theory (MPT) for common investment decisions faced by individuals. This part focuses on two ma¬jor concepts: diversification and the market portfolio.

by Donald R. Chambers

Modern Portfolio Theory pro¬vides a rigorous understand¬ing of what diversification is and how it works to improve investment opportunities. MPT also shows how to create the portfolio that contains as much diversification as possible: the market portfolio. In doing so, MPT provides a powerful prescription that is applicable to virtually every investor. MPT tells us exactly which risky assets we should hold and in which proportions we should hold them!

Briefly, the market portfolio is that portfolio that contains all investable assets that contain risk— and holds them in proportion to their size.

An investor who implements this prescription from MPT for her in¬vestment decisions can ignore over 90 percent of the complexities, deci¬sions, and wasted time of traditional investment analysis and can focus on the one unambiguously beneficial objective: diversification.

Market and Idiosyncratic Risks. Part 1 of this series introduced MPT’s distinction of two types of risk: idiosyncratic risk and market (systematic) risk.

Idiosyncratic risk is also known

as diversifiable, non-systematic, non-market or unique risk. Idiosyn¬cratic risk is any fluctuation in an as¬set’s return that is not caused by (or at least correlated with) the move-ments in the overall market. An ex¬ample of idiosyncratic risk is when

a firm drops 10 percent because it announces bad earnings. When a firm drops 10 percent because the overall stock market plunged, it is market or systematic risk.

Market risk is also known as non-diversifiable, systematic or beta risk. The market risk of an investment is all fluctuations in the investment’s value that are caused by or correlated with movements in the overall market.

Virtually all stocks of individual firms have both market risk and idiosyncratic risk—which combine to form their total risk. For most stocks, the idiosyncratic risk is substantially larger than the market risk. The market portfolio contains market risk—but by definition con¬tains no idiosyncratic risk.

Diversification Defined. Most investment professionals use the term “diversification” to represent the spreading of one’s wealth into a variety of investments. For example, a broker might say “I think stocks are getting a little overvalued now and it is time to diversify a little by placing some money in Treasury bills.”

MPT uses a more precise definition of diversification that is more useful for this analysis. Diversification is the spreading of one’s wealth into risky assets that have some level of imperfect correlation. Imperfect cor-relation is when two variables have at least some chance of not always moving in the same direction and in the same proportion to each other.

Virtually all stocks are imper¬fectly correlated with each other and therefore provide at least some level of diversification when combined into a portfolio. The imperfect cor¬relations mean that their differences in returns may at least occasionally offset each other to some degree if the assets are combined into a portfolio. That is the essence of diversification.

Putting it another way, diver¬sification is unambiguously good. The idea is that the idiosyncratic risk (i.e., the diversifiable risk as introduced in Part 1) of one asset offsets at least some of the idiosyncratic risk of another asset—causing idiosyncratic risk to disappear from the portfolio.

MPT predicts that investors can lower their risk without lowering their expected returns through diversifica¬tion. It is the closest thing to the pro¬verbial “free lunch” that a financial economist can find.

That is why diversification should be the primary goal of the investor.

The Riskless Asset Reduces Risk but Does Not Diversify. As explained in the first part of this series, MPT prescribes that investors should hold only two assets: the market portfolio and the riskless asset. (Formally, this idea is often referred to as the “two fund separa¬tion theorem.”)

Investing in T-bills (U.S. Trea¬sury bills), money market funds, or money market accounts (i.e., riskless assets) reduces risk. But the returns of riskless assets are fixed (in the short run) and therefore they do not ever have unexpectedly high returns and—in the pure sense of the word—cannot provide diversifica¬tion.

A T-bill might offer a posi¬tive return when all other risky assets decline, but it can not offer an unexpectedly high return. This seemingly minor point is actually an essential observation in estab¬lishing the enormous breakthrough in MPT that investors can optimize their portfolios by selecting from only two investment alternatives (the market portfolio and riskless assets).

Riskless assets such as T-bills do not have idiosyncratic risk. There¬fore, riskless assets cannot offset the idiosyncratic risks of risky assets and make the risk “disappear” in a port¬folio. Simply put, riskless assets do not provide diversification. Diversifica¬tion can lower risk without lower¬ing expected returns. MPT predicts that investing a riskless asset will lower risk, but only at the expense of lowered expected returns.

Perfectly Positively Correlated Assets Do Not Diversify. Usually, combining risky assets into a portfo¬lio provides diversification. But to il¬lustrate the principles involved, let’s first look at the extreme case where returns are perfectly correlated and there is no diversification.

The returns of one share of IBM are perfectly correlated with the re¬turns of another share of IBM since they are identical. Any unexpectedly high or unexpectedly low outcomes in the one share are identical to the unexpected outcomes in the other share. Thus, holding a portfolio consisting only of many shares of the same stock does not provide diversification.

A less trivial example would be the combination of mutual funds or other products that closely track the same index such as an index of pharmaceutical stocks. Since those assets are nearly perfectly positively correlated, there would be virtually no diversification from combining them into a portfolio.

The idea that perfectly positively correlated assets do not provide diversification is illustrated with a solid line in Figure 1. Asset A has relatively low risk and low expected return. Asset B has higher risk and higher expected return. Perhaps as¬set A is an unleveraged investment in an S&P 500 fund and Asset B is an investment that uses leverage

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