Alpha in trading: formula and how it works

Achieving “excess returns” requires rare skills.

If you’re looking to invest in an actively managed fund, you probably have one goal in mind: beating the market. You’re looking for value beyond what a passive index fund can offer.

This added value comes in the form of a fund manager’s superior (or at least perceived) skills in selecting and managing stocks and other financial instruments. And there’s a word for that extra profit over and above the broader market’s return: alpha.

Investors often talk about alpha. The fund management industry is promoting alpha. But is it real, measurable and, above all, sustainable? Learn about the two types of alpha, how they are measured and used (and abused), and judge for yourself.

Important points

In its simplest form, alpha is an excess return above the return of a benchmark.
Jensen’s Alpha is an excess return above analyst expectations, risk-adjusted and relative to the benchmark.
True alpha – managerial skills – is difficult to measure and even more difficult to maintain.

Raw Alpha vs. Jensen’s Alpha

In its simplest definition, Alpha is the excess return over the return of a benchmark. This is also called raw alpha.

To illustrate, let’s assume the following:

The S&P 500 returned 10% in a given year.
One particular fund returned 12% in the same year.

That extra 2% is alpha, plain and simple.

But this is where things get a little more complicated. What if this fund took on more risk than the index itself? For example, what if the company held (or gave more weight to) more volatile stocks compared to the S&P 500?

In this case, analysts might have expected even more from the fund. What does that mean? Although the fund outperformed the S&P 500, it should have returned even more because it took more risk. There’s another term for this, and it’s called Jensen’s Alpha.

Simply put: Jensen’s Alpha is the excess return above what analysts expectedrisk-adjusted and relative to the benchmark. But how do you know what analysts expected? To do this, we turn to the Capital Asset Pricing Model (CAPM), William Sharpe’s Nobel Prize-winning formula that essentially states that stock returns are a function of market risk – nothing else.

Beta and the CAPM (Capital Asset Pricing Model) equation.

Going back to the previous example, suppose the fund that returned 12% took on twice as much risk (2.0 beta in the CAPM formula) compared to the market (which returned 10% and one had beta of 1.0). Assume a 10-year Treasury yield (the risk-free rate) of 4%.

With a beta of 2.0, the CAPM would assume a return (R) of 4 + 2 (12 – 4) = 20%.

However, since the return was only 12%, the fund’s Jensen alpha would be higher 12 – 20 = -8%.

Do you see the difference? With a return of 12%, the fund outperformed the market in terms of raw alpha but fell short of CAPM expectations.

Note: When funds report their alpha, they typically refer to Jensen’s alpha, not raw alpha.

Alpha as a leadership competency?

Funds list alpha to highlight the value their managers provide. The outperformance of a fund is attributed to its competence. Without the fund manager there would be no alpha.

As you might expect, funds with higher alpha tend to charge higher management or performance fees. But is a fund’s outperformance solely due to the skills of a manager? Not always. In fact, some critics argue that the term alpha is highly problematic. Let’s look at why.

Where Alpha may fall short

Although it is difficult for asset managers to achieve alpha, it can be equally difficult to find funds that, despite their alpha numbers, achieve “real alpha” on a consistent and sustained basis. This is where Alpha can get tricky.

The Sharpe ratio

Although he was best known for developing the CAPM, Sharpe’s later work went a step further. He suspected that many portfolio managers earned their returns by taking on a high degree of risk, but that their returns were not necessarily particularly high given the level of risk.

So he developed the Sharpe ratio to account for risk:

Sharpe ratio = (portfolio return – risk-free interest rate) ÷ portfolio standard deviation

Learn more about the Sharpe ratio and how it can be used in conjunction with (or instead of) alpha to assess manager skills.

CAPM can be misleading. The CAPM model is based exclusively on market risk (beta) when predicting returns, but other factors can also have an influence. A famous example is the Fama-French three-factor model, which adds market capitalization and book value to market risk as determinants of fund returns.
Excessive risk-taking. There are times when a fund manager achieves alpha by taking more risks And To be lucky. High-risk strategies can certainly increase returns if they work. However, critics would argue that increasing risk essentially means increasing beta, not alpha.
Consistency over a long period of time. A one-time alpha is not enough. But what is enough? Twice, three times, four times or more? Try a decade or two – long-term periods that can demonstrate a manager’s skills across multiple economic cycles and bull/bear markets.
Changes in manager and investment strategy. Funds change managers over time. Sometimes a new manager even changes strategy. If alpha is associated with skill-based outperformance, changes in manager or strategy may reduce the validity of alpha.
Manipulated benchmarks. Although cherry-picking and data manipulation should be disclosed to investors in the fund prospectus, portfolio managers have been known to switch benchmarks to deceptively increase the fund’s apparent alpha.

The end result

Discovering a fund manager that consistently generates alpha is like finding a unicorn, and the hunt for alpha has become an almost mythical task, like searching for the Holy Grail. That’s not to say that true alpha doesn’t exist, but it can be difficult to find and even more difficult to maintain over a meaningful period of time.

Always remember that past performance is not indicative of future results. Market conditions and economies are driven by dynamic, evolving and often unpredictable factors. And if you need a final reminder, remember that Bernie Madoff’s hedge fund investors thought he was a pure alpha generator, but it turns out he was running a huge Ponzi scheme.