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Alpha (α)

Step-by-Step Guide to Understanding the Concept of Alpha (α) in Finance

Last Updated April 26, 2024

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Alpha (α)

What is the Definition of Alpha in Finance?

Alpha (α) refers to the incremental return achieved by fund managers in excess of benchmark returns.

If an investment strategy has generated alpha, the investor has “beat the market” with abnormal returns above that of the broader market.

Most often, the benchmark rate used to compare returns against is the S&P 500 market index.

Alpha (α) is a measure of an investment’s performance compared to a benchmark—such as a market index (S&P 500)—over a stated period.

In short, the concept of alpha reflects the “excess return” that an investment firm, like a hedge fund, generates above the expected return.

The expected return is estimated using the capital asset pricing model (CAPM), which states that the return on a security or a portfolio is a function of its systematic risk, or beta.

  • Positive Alpha (α) ➝ The return on investment outperformed the benchmark rate on a risk-adjusted basis.
  • Negative Alpha (α) ➝ The return on investment underperformed compared to the benchmark index.

If the investment manager of a fund can consistently generate positive alpha, the investor (and firm) is evidently skilled at selecting profitable investments and managing a portfolio.

Alpha Formula

In general, the formula for alpha can be explained as the difference between the return of an investment portfolio (e.g. stocks, bonds) and a benchmark return (e.g. S&P).

Alpha = Portfolio Return Benchmark Return

Alternatively, the difference between the expected return from the capital asset pricing model (CAPM) – i.e. the cost of equity – and the portfolio returns is known as “Jensen’s Alpha”.

The formula to calculate alpha using Jensen’s measure is as follows.

Jensen’s Alpha = rp [rf + β × (rm rf)]


  • Rp ➝ Return of Portfolio (or Investment)
  • Rf ➝ Risk-Free Rate
  • β ➝ Beta
  • Rm ➝ Market Return

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Alpha vs. Beta in Finance: What is the Difference?

Beta, in contrast to the concept of alpha, measures the risk/returns of the broader market, above which investors attempt to achieve returns.

In other words, beta is the minimum return for investors – or more specifically, the hurdle that “active” investors like hedge funds must exceed.

If not, investor capital would be better off being allocated to passive index investments (e.g. ETFs) that track the overall market performance.

Here, assuming the alpha is equal to zero, that would imply that the portfolio is tracking the broader market.

Active investment firms’ offerings should provide a benefit – either above-market returns or more stability (i.e. market hedge) – for their limited partners (LPs) to have an incentive to provide funding.

With that said, LPs of actively managed funds that prioritize high returns will gauge the investment acumen of a potential investment firm by tracking their historical alpha.

Stock Portfolio Alpha Calculation Example

For instance, if an investment strategy has generated an alpha of 2%, that means the portfolio outperformed the market by 2%.

Conversely, a negative alpha of 2% means the portfolio underperformed the market by 2%.

Considering the fee structure – which is particularly high in the hedge fund industry (i.e. the “2 and 20” fee arrangement) – active investors must reasonably outperform the market or have consistent returns independent of the market.

In the latter, certain investment strategies seek not to outperform the market but to have sustainable low-risk returns, regardless of whether it is a bull or bear market.

Alpha vs. Efficient Market Hypothesis (EMH)

For investors, alpha can stem from market efficiencies, irrational investor sentiment (i.e. herd-based mentality coupled with behavioral overreaction), or unexpected structural events (e.g. changes in rules and regulations).

The pursuit of alpha, generally speaking, tends to require a contrarian bet against the consensus and capitalizing on trends that most could not anticipate (i.e. Black Swan Event).

The efficient market hypothesis (EMH) states that alpha, at least over the long run, cannot be reasonably and consistently produced since the market on average is “correct.”

Based on that premise, active investing strategies are obsolete across long time horizons.

However, generating alpha is easier said than done, as confirmed by the wave of hedge fund closures in recent years.

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