### Is Alpha Dead?

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*“While there's life, there's hope.” – Cicero*

**Introduction**

We live in an alpha-centric world. Active investment managers – “alpha hunters” – seek to generate superior risk-adjusted returns, which many investors accept as synonymous with “alpha.”

It is not my intent to pile onto the extensive empirical literature about actual success or failure in the quest for alpha, but I will explain why alpha does not automatically result in superior risk-adjusted returns and is not a suitable performance metric, except for investors with an unlimited appetite for leverage.

While beta has been declared dead several times in the past, alpha is a survivor. My diagnosis is that alpha, however, is in very critical condition itself, even under the most optimistic interpretation. A more realistic assessment is that alpha is dead.

**Defining alpha**

The “alpha” measure of performance has been part of the established body of knowledge for several decades. It was developed and discussed in the 1960s as a means of assessing mutual fund performance with the tools of the then-newly-developed Modern Portfolio Theory.

Typically, alpha is calculated as the intercept in a linear regression of portfolio returns on an index. This regression is commonly known as the single-index-model:

r_{p} stands for the excess portfolio return over the returns of a risk-free asset; r_{b} is the index’s excess return; and e_{p} is a noise term that is assumed to be normally distributed with an expected return of zero and a positive volatility. As in the standard linear regression model, the noise term is assumed to be uncorrelated with r_{b}. β_{p} is commonly referred to as a portfolio’s beta, which captures the sensitivity of portfolio returns relative to the index returns and determines the proportions of the portfolio’s systematic and unsystematic risk, relative to the index chosen.

Conceptually, alpha can be interpreted as a residual return: On average, it is the portfolio return component that is not explained by the exposure to the index.

The CAPM predicts that in financial market equilibrium, all asset alphas must be zero; equilibrium returns are fully determined by the economically relevant risk component, which is systematic risk. (The diversification of unsystematic risk is a free lunch.) In light of this, significant positive alpha values on portfolio level can be interpreted as excess returns over an efficient passive market arising from superior skill.

Alpha is not modeled directly, but derived from a “budget constraint” that requires all return components to sum up to the portfolio return. This has important implications; later on, I will discuss an extreme case in which alpha consists of model misspecifications only.