Alpha is known as the difference between a fund’s expected returns and its actual returns. Alpha has a very close relationship with another financial term known as beta. Beta is a measure used to determine a fund’s expected returns. Along with being the term used for expected returns, beta is also associated with the level of risk.

Alpha is commonly considered the active return on an investment, working as a gauge to determine how a fund is performing against the average. In some cases, the alpha can be construed as the value a portfolio manager can bring to a fund. A smart manager will be capable of exceeding the expected returns, bringing a positive alpha. A manager who is not as successful and does not perform as expected will yield a negative alpha. However, a positive alpha can also be due to luck with the markets. There is no way to determine which is the case.

Calculating the alpha for a fund can be tricky and involves a number of factors. The formula for alpha is:

Alpha = r – R_{f} – beta * (R_{m} – R_{f})

r = the security’s or portfolio’s return

R_{f} = the risk-free rate of return

beta = systemic risk of a portfolio

R_{m} = the market return

The final result is a number, either negative or positive, depending on the performance of the fund. The higher your beta, the more difficult it is for your alpha to be a positive number.

With everything else being equal, the market likely would be more efficient if all companies followed the unwritten rules – or if they were required to reward their shareholders by systematically increasing the stock price via, say, buybacks with a formulaic relation between the required buybacks and earnings (among other details). As it stands, the supply and demand is driven by what appears to be a rather random perception/interpretation of the earnings announcements (among other information) by market participants. This leads to volatility and mispricings at various time horizons. These mispricings are then arbitraged away by what can be generically termed as “mean-reversion” (or “contrarian”) strategies. For a given “mean-reversion” time horizon there might also exist opportunities to profit via what can be generically termed as “momentum” strategies on accordingly shorter (and, in some cases, longer) time horizons.

One important ingredient that is implicitly assumed in the above discussion is market impact and executions. Even if every company under the Sun followed the unwritten rules, due to a large number of market players and virtual impossibility to predict supply and demand imbalances or their precise timings, mispricings and inefficiencies are inevitable. Longer horizon strategies thereby create arbitrage opportunities on somewhat shorter horizons; strategies on such scales create arbitrage opportunities on yet shorter time scales; and so on – all the way down to HFT (high frequency trading) strategies. While on the longest horizon time scales the strategies are mostly long (mutual and pension funds, holding companies, etc.), on shorter horizons strategies can be dollar neutral, hence seemingly creating profit “out of thin air” – which does not take into account substantial monetary and human capital involved.