In every field of human endeavor, there is some attempt at communication, and that communication relies upon definitions. When a word or phrase is used, misused, overused, by myriads of people with different working definitions, communication becomes difficult, if not impossible, without first reaching agreement on what we’re talking about. If we consider that most of the working definitions being bandied about are non-robust, it’s easy to see that communication fails and we might as well be speaking jabberwocky. Take the definition of “alpha” (please!), probably the most blathered-about , over-used, and misused word in financial discourse nowadays, for our example.

Working Definitions

While we’d probably like to think we know what each other is talking about, the truth is that we all rely on personal working definitions, and we merely hope they have enough intersection with others’ definitions so that conversation is meaningful. By “working” I am not implying that the definitions are functionally useful, I use the term “working” as in “laboring,” or “laboring under the assumption that ‘x’ means ‘blah’.”

One website I recently visited said in a sidebar conversation about manager’s macro bets that “a manager’s alpha (= daily returns – benchmark)”. The author is a financial professional, i.e., has earned a living running money and consulting with money-runners.

Wikipedia defines alpha as a “risk-adjusted measure of the so-called ‘excess return’ on an investment. It is a common measure of assessing an active manager’s performance as it is the return in excess of a benchmark index.” It goes on to say that the “alpha coefficient (α) is a parameter in the capital asset pricing model. In fact it is the intercept of the Security Characteristic Line (SCL).”

Investopedia has this to say: “The equation calculated from the regression analysis will be a simple line equation that ‘best fits’ the data. The slope of the line produced from this equation is the portfolio’s beta, and the y-intercept (the part that cannot be explained by market returns) is the alpha that was generated.”

Meanwhile other sites, such as one prominent hedge fund commentator, spend countless pages worth of electrons debating whether outperformance (measured in some unspecified way against some unspecified benchmark) can truly be called “alpha” if it is the result of applying some known factor or anomaly, i.e., should that be “beta” or better still, “exotic beta?”

Now, it is possible that the writers of Investopedia and Wikipedia could communicate both quickly and meaningfully to each other about “alpha.”

Neither, however, could have effective communication with the money-runner in the first definition, or the hedge fund commentator in the fourth definition! Additionally, the money-runner and hedge fund commentator would be incapable of meaningfully discussing “alpha” with each other!

From the “investo/wikipedia” standpoint, the first calculation, which was done simply by subtraction, would be in error, because it would confuse “alpha” with “beta,” and leverage would be confused with risk-adjusted out(under)performance.

Meanwhile, even if the hedge-fund commentator agreed with the “investo/wikipedia” sites on the formulae used, it still might not be “alpha” in the commentator’s view if it doesn’t have some magical quantity not found formulaically, and this commentator has admitted that he doesn’t know exactly how to define “alpha,” meaning that his working definition isn’t of very much help in the first place.

Finally, if you take a money-runner with a subtractive definition of “alpha” and a hedge fund commentator with a statistico-nebulous definition of “alpha” trying to meaningfully discuss performance metrics, you have a perfect recipe for miscommunication.

As an aside, I’ve previously discussed “alpha” in Alpha and Beta and the Meaninglessness of Alpha.

Robust Definitions

This is my working definition (hah!) of a “robust definition.” Robust definitions should be clear, objective, current, appropriate, and useful.

“Clear” as in clearly defined. Take the “investo/wikipedia” definitions and ask whether the regressions should be run against daily returns, annual returns, monthly returns? I can’t tell from how they’ve worded it. Anything that’s not clear in the vernacular should be clear in the discussion, i.e. footnoted or asided, such as “this manager’s alpha (annual returns run at daily intervals from April 2005 through February 2008 against the S&P 500 total return benchmark)” – you get the point?

“Objective” almost perfectly follows from be clearly defined, but it’s worth its own shout-out. I should be able to give you, Henry, Dallas, Jeff, and Barry (well, maybe not Barry, as he’ll find something negative about anything) the same data file and the same definition, and they should all come up with the same determination.

“Current” is a prerequisite for “useful,” but again, it’s worth a shout-out. Can you make this determination now, or do you have to wait? “Recession” is probably the biggest violator of this requirement, because as defined by the NBER, a recession will always be called in retrospect. Anything that requires revision long after the fact (like GDP) will, of course, fail the “currency” requirement for a robust definition.

The very fact that groups of nimrods and dipshits gather regularly to discuss, or that individual nimrods and dipshits devote time in articles to discuss, whether or not the U.S. is in a recession NOW speaks volumes about both their inability to think clearly and their inability to properly define their terms. If you can’t tell if “example a” is in “condition b,” then obviously they both lack a good defintion of “condition b,” and they also lack the logical skills to recognize their lack of definitional determination.

“Appropriate” is harder to get a handle on, but thankfully, “alpha” gives us some really big clues that its appropriateness is related to benchmarking.

Anyone who says “[w]hat looks like alpha vs. one benchmark may, of course, be beta when compared to a different benchmark” obviously doesn’t have a robust definition of alpha. Anyone who asks “can asset allocation itself generate alpha?” obviously doesn’t have a clue about selecting an appropriate benchmark, because the question of alpha generation is benchmark-specific. Using an inappropriate benchmark for the system introduces error; using an appropriate benchmark provides clarity.

The universe abounds with simple annually-rebalanced asset allocation schemes that generate regression-equation alpha vs. the S&P 500, but is the S&P 500 the appropriate benchmark for something that plays with bonds, commodities, and foreign stocks?

Hell, is the S&P 500 even an appropriate benchmark for U.S. equity investors? Not if they play in small-cap valueland, it ain’t!

I previously discussed benchmarking in some detail, and believe that absolute benchmarks are probably most appropriate for cross-comparison of diverse managers and/or systems.

“Practical” is almost (almost!) a given, if the definition is clear, objective, current, and appropriate. A practical definition should give guidance about appropriate action for bettering the situation. For example, a practical definition of “alpha” should be somewhat predictive, at least in a statistical sense, of the manager’s (or system’s) future return stream relative to benchmark. It should also be explanatory of the manager’s past results in comparison to other managers.

In other words, a practical definition should bring something to the party, other than just the occupation of several cubic feet of space, an appetite, a hollow leg, and some conversation about the weather.

Useless Definitions

Working definitions will become useless when two parties in a conversation can’t agree upon them. In a hypothetical conversation between our money-runner (who uses subtraction to define “alpha”) and our hedge fund commentator (who uses statistics but isn’t clear on benchmarking or on whether the method of generation categorizes it as “alpha” or “beta”), both of their working definitions are as useful as toilet paper, because they’re not speaking the same language. They would need to come to an agreement, even a short-term one, one a single working definition in order to have a meaningful conversation.

Any definition that fails to be robust is useless. If it’s not clear, then we can’t be sure we’re talking about the same thing. If it’s not objective, then we might be talking about the same general principle but have different conclusions about our current status. If the definition can’t be determined now, is not current, i.e. we must wait until two, three, or more months after the fact to know what it is, then it’s not worth much to us. An inappropriate definition is of no use, for example, we could agree on how to calculate “alpha” but if we agree inappropriately, such as in agreeing to use the S&P 500 as a benchmark for analyzing hedge fund managers, it wouldn’t tell us anything meaningful about two different managers’ results if one ran a stat arb fund, and the other ran a merger arb fund. Finally, even if the definition is clear, objective, current, and appropriate, if it’s not practical, it’s still useless. If we were to find that, measured by a clear, objective, current, and appropriate definition, past “alpha,” over all timeframes, was totally non-predictive of future return streams, well, then, our clear, objective, current, and appropriate definition isn’t practical, and is therefore useless.

It follows that non-agreed-upon and non-robust definitions are doubly worthless, doesn’t it?

Your Homework Assignment

Continue your current reading, watching, and browsing patterns for news and commentary about the financial markets, politics, and the economy. While doing so, ask yourself, every time a discussion ensues, about the DEFINITIONS of the words being used.

Are they agreed-upon by all parties, or do you get the sense that some panelists mean different things when they say the same word?

Is it clear what they mean?

Is it objective, i.e. if you had the data stream, and your logic were correct, would you make the same conclusion?

Are they discussing something that is knowable now, in the current time?

Is the definition in the appropriate context?

Are the definitions they use practical, i.e. do they tell you something that is of value to you?

Feel free to report your findings in the comment section below!