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# The Confusing Relationship Between Alpha and Beta, Active and Passive Management

Without a doubt, the widespread use of the terms alpha and beta, and the related terms active, passive and index investing, has done more to confuse investors than to enlighten them.  Alpha and beta are mathematical terms that come from a linear regression equation, of the form Y = bX + a.  In the commonly used case, “X” is an appropriate asset class or sub-asset class benchmark, and “Y” is the return on an actively managed fund.  The equation shows that this return is a function of both exposure to the overall market (measured by beta, in the “bX” term), as well as a residual, termed “alpha”, which active managers like to use as a measure of their skill. A related measure is the so-called Information Ratio, which divides average alpha by the standard deviation of (active portfolio return less benchmark return).  The Information Ratio measures the amount of risk (relative to the benchmark) that is taken to achieve a given level of alpha.  So far, so good.

Now let me briefly define our view on how to apply these concepts.  In our view, there are two basic investment strategies: passive and active.  Passive investors hold portfolios whose composition does not depend on a forecast. Logically, the passive portfolio must be a portfolio that every investor could hold if he or she chose to do so.  The only portfolio that meets this test is the market capitalization weighted portfolio.  Any deviation from this portfolio implies a forecast of one type or another.  An investor who believes that markets are usually close to efficient (i.e., with asset prices generally close to their fundamental values) would deviate from the market cap weighted portfolio in the expectation of earning either higher returns with higher risk than the passive portfolio, or lower returns with lower risk.

In contrast, an investor who deviates with the expectation of earning higher returns with lower risk than the passive portfolio makes a different set of assumptions: (1) that some investors will consistently make valuation mistakes, or, in the case of public investors, make investment decisions on the basis of considerations beyond or besides profit maximization; (2) that these deviations can be forecast, to a degree beyond luck; and that (3) they can be exploited at a cost that is lower than the expected return from doing so.  Some of these deviations from the passive portfolio have been embodied in index products that reduce the cost of implementing them. Examples of these include large capitalization stocks, value stocks, or stocks from a given country, region, or industry sector.  Confusingly, the return on these low cost, index-based deviations is also referred to as “beta”, because such products are the benchmark against which the returns of active managers’ who invest in these types of stocks (e.g., small caps) are regressed to identify their “alpha.”

The logic here is that an active manager must add cost and risk adjusted value beyond what an investor could obtain simply by investing in the relevant index product.  However, what is often overlooked in this analysis is that both the decision to deviate from the passive market portfolio and the decision to use an actively managed fund rather than an index product are based on forecasts.  So, to put it differently, in our view this deviation involves one type of beta and two types of alpha (call them cheap and expensive), rather than two types of beta and one type of alpha.

Disclosure: No positions