Definitions in finance and is alternative beta cheap alpha?

There is significant disagreement in finance on the very definition of terms more so than in other sciences. This is different than saying there is disagreement on theories to explain some phenomena. This is also more fundamental than the finance problem that many theories prove not to be true empirically and thus cause disagreement through anomalies. This disagreement on definitions is one reason why finance will not or should not be considered physics. 

For example, what is the definition of alpha? If there is not agreement on the market portfolio or the benchmark, then it is not easy to measure or define alpha. I focus on alpha definition because it should be so simple to define and is fundamental to making good investment decisions.

Simple concept:

• Alpha is excess return not associated with systematic risk.
• Managers who have skill will generate alpha or returns above systematic risk.
• Investor should seek and pay for skill managers who generate alpha.

To find alpha, investors need to define beta since alpha is only measured after accounting for beta. Yet, if you ask for a manager's beta, there is no single measure or definition. There has to be agreement on the timeframe for measurement, the sample period, the benchmark or a set of benchmarks to be used, and on looking at a market portfolio or a set of risk premia. If you went to three analysts and asked them to measure the alpha of a hedge fund manager, my guess is that you will get at least five different measures. 

A way out of this problem is to switch from trying to measure the elusive alpha to measuring different forms of risk premia which may be better defined. Alternative risk premia and their betas focus on the core issue of measuring specific risk and the excess return for taking on those risks. This is not so much buying skill, but rather isolating risk premia for which investors should receive a return.

Measuring risk premia changes the investment game from looking for skill to looking for risks taken. Since many hedge fund managers generate return through taking on specific risk premia as well as trying to generate alpha and show skill, perhaps it is better to find the alternative beta they are generating and determining whether that is what you want to hold. 

If risk premia can be isolated more easily than skill it can serve as a substitute measure for what is desired, uncorrelated returns to market betas. Buy different risk premia and not look for skill. These risk premia should be obtained more cheaply than alpha and the pricing can be more transparent. Buying portfolios of alternative beta may be a form of cheap alpha.