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Sharpe (1964) had published his capital asset pricing model (CAPM), which indicates that a portfolio’s expected return will increase with its systematic risk (beta) according to the formula

E(Z_p) = z_f + β[E(Z_m) – z_f]          [1]

That is, a portfolio’s expected return  equals the risk-free rate  plus the portfolio’s beta β multiplied by the expected excess return of the market portfolio . Formula [1] defines the portfolio’s expected return as a linear polynomial of the market expected return.

According to CAPM, portfolios may randomly outperform or underperform the market from one year to the next. Over many years, the random good years will tend to cancel the random bad years, and the portfolio’s long-run performance will fall on the capital market line (if it is optimized under CAPM) or under the capital market line (if it is not)

Jensen was interested in whether mutual fund managers add value over the long-term. Could they through skill, privileged information or intuition outperform the market reasonably consistently, year after year? This was not about having randomly good or bad years, but about having good years with noticeable consistently. The CAPM formula [E(Zp) = zf + ß[E(Zm) – zf]] didn’t accommodate this possibility, so Jensen added a term to it that did:

E(Z_p) = α + z_f + β[E(Z_m) – z_f] [2]

and so alpha, α, was born. This allows for a persistent positive contribution to a portfolio’s expected return due to the manager’s skill.

A frequency distribution of the alphas Jensen estimated for 115 mutual funds based on at least ten years of data for each. The vast majority have estimated alphas that are less than zero. The average fund’s alpha was –.011, or –1.1%. Results are after fees but not including sales loads. Returns, and hence alphas, are with continuous compounding. Reproduced from Jensen(1986).

Jensen’s results lent strong support for the efficient market hypothesis, suggesting that no investment managers have positive alpha.

Alpha has become a symbol. It is a one-word moniker for investment managers’ belief they can outperform the market. Alpha is out-performance, and it is the job of an active manager to produce alpha.

Source: alpha