Alpha, Beta Sigma: Understanding the Greeks
I got my college education on the other side of the Atlantic, at a place where the frat-boy equivalents preferred to vomit in their tailcoats and where, rather than Greek letters, social clubs often bore the names of the homosexual lovers of medieval kings.
It’s the other Greeks I’ll talk about. The ones used in finance, which are as much misunderstood as the idea that hummus is a Greek dish (it’s not!). The list is pretty long, thanks to the creative use of an alphabet of twenty-four letters. But here I’ll refrain from getting deep into the exotic maze of greek squiggles and contain myself to three of them—the sigma, the beta and the alpha. What are they?
The sigma, ***σ:***Say you think of yourself as a pretty mellow and jovial guy on average, yet, with frequent bouts of Dalai-Lama bliss to “American Psycho” lunacy, or anything in between. Abstracting from the fact that you might want to see a shrink, an economist’s diagnosis of your condition would probably sound something like “a jolly fellow more or less, whose mood exhibits a high standard deviation.” That so-called “standard deviation” is the sigma. It is a measure of how erratic, how dispersed your moods can be, “above” and “below” your average jovial self.
Now say that in the course of your college life you came across a few other “high-sigma” soulmates and you decided to form a fraternity—call it Phi Tau Delta (ΦΤΔ), the Greek initials of the expression “Beware of the Greeks!”. Now, not only are your “brothers” as temperamental as yourself, but your moods tend to vary together; similar things excite you at similar times. We’ll call that a high covariance. No Greek letter here, although a variant concept—correlation—has been assigned by the pros the letter ρ (rho).
Both the standard deviation and the covariance are important for understanding risk, especially when it comes to investing in a portfolio of different securities. To understand this better, let’s go back to our frat-boy example.
Avoiding idiosyncrasies: Suppose I am a bar owner and one of my “regulars” is a ΦΤΔ member. A loyal client, an ardent g&t consumer, yet potentially a nasty business given his sporadic destructive splurges, especially manifested when his baseball team loses. However, I could still do just fine, if my clientele is fairly large and diverse and perhaps less passionate about sports or less keen on participating in havoc. In that case, at worst, I might get a couple of broken chairs, some spilled-over g&t’s and a few spells of foul language before our ΦΤΔ friend is kicked out of the door by those who want to keep on with their happy-hour cocktails in peace.
In other words, by having a large and diversified clientele with variable tastes for anarchy and/or baseball, I managed to minimize the “idiosyncratic risk” to my business from our friend’s eccentricity. In a similar way, if I own a stock that is volatile because of certain idiosyncratic features of the corresponding company—say it’s a mining company in Chile whose workers invariably go on strike—I can diversify away that risk by buying the stocks of many other companies which have neither labor issues nor an exposure to Chilean politics. This idiosyncratic risk is effectively what is encapsulated by the standard deviation.
Risky business: Imagine on the other hand a scenario where the entire ΦΤΔ membership are regulars at my bar, while the rest of my clientele are also pretty passionate sports fans, as well as supporting the same team as ΦΤΔ. Now that’s a risky business. Sure those ΦΤΔ guys drink a lot, which can’t be bad for revenue; and sure, there is something to be said about the entertainment value of a bunch of loud drunkards trying to quote Hamlet while throwing chairs at each other. But hey, these are my chairs that they are throwing, these are myglasses that are broken on the floor… and that is my autographed Yankees shirt they’re about to take down from the wall to wipe off their mess!! Worse, while they’re at it, everyone else is drawn in, though perhaps less “passionately” than the frat-boys, and the entire place gets smashed.
Put it plainly, the fact that my entire clientele tends to drink, get loud and destroy together in response to the same stimuli, makes my business very risky because I have no way to diversify away that risk. I can’t find different clients. That non-diversifiable risk is called the “systematic risk.”
The beta, ***β:***This is where the beta comes in. Beta is a measure of the systematic risk of, say, a single stock or a portfolio of stocks. It measures the risk that stems from the portfolio’s covariance with the stock market as a whole—the risk that you cannot diversify away by adding more and more securities. The higher the covariance, the higher the beta, the higher the systematic risk. And the higher the risk you’re taking, the more you want to get paid.
So let’s go back to the frat-boy example. In our second scenario earlier, our ΦΤΔ boys are “high beta.” Their mood tends to swing in the same direction as the mood of my other patrons, but more: Under the “right” prodding, they will drink more, shout more and destroy more. This makes them a rather risky addition to my clientele—I mean, I’d much rather have a fraternity that promotes spiritual development by discussing yoga breathing exercises (over alcohol of course) while everyone else roars as the Yankees are getting smacked by the Indians.
But choice I have not. And given the risk I’m taking here, I expect to get paid for it. That is, I will tend to require higher compensation from the frat boys than the rest of my patrons in the form of, say, regularly higher tips for the potential physical and reputational damage that they may cause on my establishment. Similarly for stocks. If a stock has a high beta (that is a beta larger than 1, which is the beta of the market as a whole), I will expect proportionately higher returns from that stock than the returns of the market index (say the S&P 500).
The alpha,α: So what about that alpha? Alpha is a measure of how well a portfolio of stocks has performed after adjusting for the risks involved. Effectively, what you want to know is how well your portfolio did compared to other portfolios with similar risk characteristics. One way to adjust for these risks is to look at portfolios with similar beta as yours. While simplistic, this approach can be a first step in understanding whether your investment manager has given you great returns because of his/her superior acumen rather than because of riskier choices (which would lead to a higher beta).
Going back to that bar of mine, if I tell you that my profit for the year was 30 percent higher than the other bars in my neighborhood, you might want to congratulate me at first. But on second thought, just when you’re about to give me a check for that loan I asked you for, you may want to ask me a few questions. Am I really a genius or could I be relying for my revenues on those rowdy ΦΤΔ characters who, at any time, could ransack the place? What matters for judging an investment manager’s ability is not the higher returns stemming from higher systematic risk (higher beta) but those due to superior stock picking (that will yield a higher alpha).
So there you go. Your first step in understanding the Greeks (although, as I hinted earlier, what is referred to as “the Greeks” in finance are greek letters used in the context of pricing options—such as the γ (gamma), the δ (delta), the θ (theta) and the ν (called “vega” by the traders, even though the actual Greek letter is called “ni”). Still.. even with this limited knowledge, you will at least know how big a tip to give me when you come to watch the playoffs at my bar!