The Alpha and the Beta of Investing
August 5, 2014
by Adam Jared Apt
Stone House Capital Partners returned 4.1% for September, bringing its year-to-date return to 72% net. The S&P 500 is up 14.3% for the first nine months of the year. Q3 2021 hedge fund letters, conferences and more Stone House follows a value-based, long-long term and concentrated investment approach focusing on companies rather than the market Read More
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This article is intended for the educated layman. It was written as part of a continuing series of articles on a variety of investment topics. To view all the articles in this series, click on “More by the same author” in the left margin.
See how the Fates their gifts allot,
For A is happy — B is not.
Yet B is worthy, I dare say,
Of more prosperity than A!
The Oxford philosopher J. A. Smith reportedly told his students, “Nothing that you will learn in the course of your studies will be of the slightest possible use to you in after life—save only this—if you work hard and diligently, you should be able to detect when a man is talking rot, and that, in my view, is the main, if not the sole, purpose of education.”
Although the main purpose of my essays has really been to convey the currently agreed best useful thinking about investing, still, if you have read them diligently and come away with just the ability to identify investment nonsense, they have succeeded.
This essay reverses my priorities. My main purpose here is, indeed, to help you detect when someone is talking rot. Nevertheless, in the end, there will be two distinct practical lessons worth remembering and applying. One concerns the relationship between risk and return, and it will behoove you to keep this lesson in mind whenever you’re inclined to throw caution to the wind in pursuit of better stock returns. The other concerns what counts as skill in selecting stocks, a matter to which I’ll return in the last essay in this series, when we look at boasts and brags about investment performance. This lesson is of such importance as to justify the entire essay.
There was a time when the rhetoric of economics mattered nearly as much as its logic. To read Adam Smith is to savor the elegant, fluent, and bracing clarity of eighteenth-century prose. John Maynard Keynes, who was a successful investment manager and wrote about the stock market in his General Theory (1936),1 was also a skillful stylist. Like most texts of any importance, early economic writings cannot be read as if they have only one obvious, indisputable and unmediated meaning. But the study of economics wasn’t limited to its adepts; its texts didn’t require a knowledge of higher mathematics and statistics, the prose was not narcotically hazy, and the vocabulary was not esoteric.2
For all that economics has lost with the introduction over the last century of the mathematics and models that require formal education, it has stood to gain in precision and power. Now, alas, few of us can read original economics texts that matter and advance the field, especially texts in the technical sub-discipline of financial economics, and the public must rely on interpreters and popularizers, many of whom are not economists and are ill qualified for the role that they have recklessly assumed.
In no area of modern financial theory are the fruits of ignorant popularization more rotten than in the matter of the words alpha and beta.
For those of us who are curious about financial theory and who happily labor in the fields of investing, these words are common currency. It is nearly impossible to discuss investments without them. The cluster of ideas that they represent to us is the point of departure for nearly all deeper analyses of the behavior of stock prices and returns. But for those members of the public who want to understand how to manage their personal finances, or to understand what an investment manager does, they really aren’t very important at all. Still, if you ever proceed beyond my essays in your reading about investing, you are certain to encounter this professional jargon, and you stand in danger of falling victim to someone who is talking rot.
Rather than keep you in suspense, or more likely a confused stupor, while I lead you by the hand through a technical explanation to the real meanings of these terms, I will begin with their conventional definitions.
Defining alpha and beta
Beta is a measure of the sensitivity of a stock or a portfolio of stocks to the stock market as a whole. It is the multiple of the stock market’s return that tends to produce the corresponding return of the stock or portfolio. For example, if a stock has a beta of 1, then the stock will have a tendency to go up and down by the same return as the market. If it has a beta of 2, then it will have a tendency to go up by twice the market’s return when the market goes up, and down twice as much as the market when the market goes down. If it has a beta of 0.5, then it will have a tendency to go up by half the market’s return when the market goes up, and down half as much as the market when the market goes down. It’s important to note the word “tendency;” there is no implication of a rigid relationship, and beta in no way tells you if the tendency is strong or weak. One of the vulgar errors propagated by popularizers is that a stock’s beta will always tell you its return, given the market’s return. A related error is the notion that a stock with a beta of, say, 2 has twice the risk of the market.
Some think of beta as akin to the correlation between the returns of a stock or of a portfolio of stocks and the returns of the market. Both beta and correlation are measures of how two things are paired. But they’re not quite the same. Correlation is really the measure of the strength, that is to say, the consistency, of the tendency measured by beta. A stock’s returns could have a high correlation with the market’s returns, yet still have a low beta.
Alpha is the extra return of a stock or a portfolio of stocks beyond the return produced by the stock market. Alpha can be positive, negative, or zero. If an investment manager has the ability to pick stocks that beat the market, the portfolios that he manages have a positive alpha. When speaking among themselves, investment managers often say that a manager generates a positive alpha, when the layman would instead say that he has skill in picking stocks. One manager will ask another, about a third, “What was his portfolio’s alpha?” (It can be rude for one manager to ask another directly for his alpha; it comes off sounding a little like, “Yeah, says who?”)
You now know just enough to be confused and bamboozled by the next shyster or ignoramus who abuses these terms.
For one thing, even honest and knowledgeable investment professionals, when using “alpha” and “beta,” often exercise Humpty Dumpty’s prerogative: “When I use a word…it means just what I choose it to mean—neither more nor less.” Two alternative meanings of “beta,” quite common among professionals and dependent upon context, are, first, “the stock market’s risk,” and second, “the stock market’s return.” It’s a convenient shorthand. Anyone not acculturated into the finance community may be perplexed at finding that the same word can stand for both “return” and “risk,” but the former meaning is usually more like “return with its attendant risk.” The meaning that I absolutely refuse to countenance is the identification of beta with volatility. This is simply a mistake. Beta is not volatility; it doesn’t even tell you much about what a stock’s volatility is. If you want to be pretentious and to refer to volatility by a Greek letter, say “sigma.” (Sigma, or more correctly, ?, is the symbol for the statistical concept of standard deviation, which is what I have in mind when I refer to the “volatility” of returns.) I think I know how this mistake comes about. Because beta can be interpreted as a kind of investment risk, there arises the false syllogism, “Beta is risk; risk is volatility; therefore, beta is volatility.” But beta is only a kind of risk, a contributor to overall investment risk. And besides, as I wrote long ago3, even the usual statistical sense of “volatility” underestimates the real total risk of investments. An alternative name for beta is market risk, because it stands for the portion of a stock’s total risk that arises from going along with the market, even though it’s not expressed as a percentage or fraction of the total risk.
In order really to understand alpha and beta, you have to know whence the words came. So I’m going to pursue a sort of etymology by way of mathematics, Ursprache durch Technik. The math I’ll use, though, is only of the simple, middle-school sort.
Why would anyone want to relate the return of a stock, or of a portfolio, to the return of the stock market as a whole? Well, there’s a certain amount of intuitive sense to it. We know that stocks exhibit herd behavior; if they didn’t, then the market, which is the herd comprising all stocks, wouldn’t go up and down. So there’s a relationship, even if not a strictly deterministic one, between the change in price of a stock and the change in price of the market. And the herd behavior itself makes sense, because the market, as a whole, seems to be sensitive to broad influences, like changes in the country’s economic outlook, which very much includes the outlook for corporate profits, or perhaps the group psychology of the people who are trading stocks. (The more years one spends managing investments, the more cynical one becomes about the rationality behind the market’s behavior, but nonetheless, there has to be something moving the market.) Moreover, it also makes sense that stocks will vary in their sensitivity to changes in the stock market, or whatever is moving the market. The more stolid companies, like electric utilities, have tended to produce reliable profits quarter after quarter, year after year. Nervous, excitable companies, like the producers of high-tech consumer products, tend to be very sensitive to the least change in the outlook for the economy. But again, beware of confusing beta with volatility. A stock’s returns could be very volatile, while at the same time being only moderately sensitive to changes in the stock market as a whole.
It’s also intuitively reasonable to expect a high degree of symmetry in a stock’s behavior. Could a stock tend to go up more than the market when the market rises, but down less when the market falls? Quite possibly, though likely not for very long. Contrariwise, a stock that goes up less than the market when the market rises but down more than the market when the market falls will soon be pushing up financial daisies.
The simplest relationship that we can posit between the return of a stock or a portfolio and the return of the market is a linear one; that’s another way of saying that the return of any given stock or any given portfolio tends to be a constant proportion of the return of the market, whatever the market’s return may be.4
To visualize such a relationship, let’s plot a graph of the returns of a (hypothetical) stock against the returns of the stock market, where each point represents one month’s return on the stock and the same month’s return on the stock market. We’ll get a graph that looks something like this:
In other words, let’s say the stock market, over a given month, had a return of 4.5%, and the return of the stock was 7.3%. This would correspond to the highlighted point in the graph.
What we have is a scatterplot, not the graph of a line. But you can see that a line might “fit” the scatter and represent the relationship that we perceive in the graph of the two sets of returns. That relationship is the tendency of which I spoke earlier.
- There is an unpublished paper by David Chambers, Elroy Dimson, and Justin Foo, “Keynes the Stock Market Investor: A Quantitative Analysis,” September 2013.
- Much of the General Theory requires a grounding in the writings of Keynes’s predecessors, but not the section in which he writes about the stock market.
- See Peabody River Asset Management Newsletter, issue 3, January 2009, essay, “How to Think about Investment Risk.”
- Note that I am talking not about prices but about returns, by which I mean total returns, not price returns.
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