# Alpha and Beta

You can often hear an investment professional say, “That’s a high-Beta stock.”  Less frequently, you may see the claim, normally in writing, that someone “is searching for alpha.”   Here’s what they’re talking about:

How It Started

After World War II, as the first commercial mainframe computers were developed, an economist named Harry Markowitz proposed using this new computational power to calculate the risk/reward characteristics of portfolios of stocks.  With this information in hand, you would be able to determine the best portfolio for you to own, i.e., the highest-return portfolio for a given level of risk.

Markowitz used a statistical concept, variance–a measure of how far away from a trend line a stock’s price might temporarily drift–as his definition of the riskiness of a stock (this is a terrible definition of risk, in my view, although it’s, even today, the academic standard).  From this definition, it follows mathematically that the riskiness of a portfolio is the riskiness of the individual stocks in it plus a factor (covariance) of their tendency to move together in herds.

The general idea was that you could quantify, and therefore compare, the riskiness of different portfolios that offered the same return, as well as the returns of portfolios that had the same risk.  So you can “optimize,”  that is, eliminate unnecessary risk by picking the best portfolio–highest return for a given level of risk, or  lowest risk for a given level of return.

There’s a practical problem, though.  If the universe has only two or three stocks in it, calculating this information is straightforward.  If the universe is the S&P 500, however, figuring out all the interrelationships among all the stocks becomes a real pain in the neck.

(There’s a much bigger problem, though.  The virtues of short-term price volatility as a measure of risk is that the data are easily available for many stocks and that variance is part of an established mathematical framework.  So it has been widely adopted by academics and consultants.  Unfortunately, it’s otherwise not very informative, I think.  It’s like saying that the risk in an airplane flight should be measured by the amount of air turbulence en route.  By this measure, the plane that recently took a smooth ride into the Hudson River would be classified as a safe flight.)

The Simplified Theory, Alpha and Beta

William Sharpe tackled the complexity problem in the early Sixties by suggesting that the returns on a given stock be compared with the returns on an index, like the S&P 500, rather than with the returns on all the other stocks in the universe.  The regression calculation for the stock would take the form:

stock return = α + β (index return) +ε,

where α is a constant and ε is a random error that can be disregarded.

(This isn’t the final Sharpe equation that goes into his Capital Asset Pricing Model–more in a subsequent post–but it’s good enough for now.)

β

β is pretty straightforward.  A stock with a β of 1 moves with the market; a β of 1.4 means the stock moves in the same direction as the market but moves 1.4x as much; a β of .8 means a move in the same direction as the market but with only 80% of the magnitude.  A stock with a β of 1.4 would be a very aggressive stock, one with .8 is a defensive name.

You can easily calculate the β of a portfolio.  It’s the weighted average of the betas of the portfolio’s constituent stocks.

β is a commonly-used tool.  Value Line, among others, lists calculations in its publications, so they’re easy to find.  Remember, though, that betas are shorthand statements of historical relationships.  In rapidly changing industries, say, newspapers, they won’t tell you much.  Also, given what I’ve written so far, what do you think a β of zero, or near zero, means?  In the early days, true believers in the CAPM theory took a zero β to mean the stock was riskless.  That isn’t what it means, though.  If β measures how closely a stock follows the index, a zero just means the index doesn’t explain anything about how that stock’s price moves.

α

From the equation above, you can see that α is the portion of a stock, or portfolio, return that is not explained by the return on the market and the β of the stock or portfolio.  α can be positive or negative.  “Looking for (positive) α” means looking for stocks, or creating a portfolio, that will do better than its β characteristics say it should.  AAPL, for example, has a β of 1.15, according to the latest Value Line report.  Anything over 1.15x the market return during, say, the past three years, would be positive α.

Adherents to the CAPM believe positive α is like UFO sightings–in fact, worse than UFO sightings, because positive α is in principle impossible to achieve.

True, CAPM has crazy “simplifying” assumptions, which are on the order of:  let’s say we all come from the planet Krypton, and all have exactly the same strength, skill and desire to beat the opponent.  So the CAPM conclusion, that predicting the winner of an arm-wrestling match with Superman is impossible, is a little less than startling.  And although it’s still taught to MBAs, nobody much believes in it anymore.  Still, CAPM would be a lot easier to make fun of if we could produce more people with credible claims to have achieved positive α over long periods of time.  On the other hand, if you could do this, why in the world would you ever tell someone else?

### 5 responses

1. Great background on the formation of volatility as the predominant measure of risk. “Traditional Risk”, measured by volatility, should be considered the 4th or 5th most import risk factor. Potential loss (including probability of that loss) as measured by fundamental research should be the largest factor in measuring overall portfolio risk. Liquidity, Leverage, and Sector Exposure are all more important than volatility in determining position size. These measure Fundamental Risk (https://www.alphatheory.com/pdf/AlphaTheoryDifferentiationfromPortfolioOptimization.pdf). Because these factors do not conform well to statistical analysis and determining potential downside through fundamental analysis is hard work, they are not the first things that come to an investors mind when evaluating risk. They should be and it is important for an investor to create a discipline to ensure that these factors always influence portfolio position sizing (www.alphatheory.com/demo).

• dduane says:

Thanks. It’s funny that, as you say, people tend to mistake calculating a precise result for having revelvant information. By the way, as I was reading your comment, I thought about having seen the volatility framework applied to smaller markets outside the US, with very peculiar results. In New Zealand during the Eighties, for example, that market was dominated by several large forest products companies. So the high-beta sectors were things like consumer staples and the stocks with a beta around 1, construction materials.

• The investing world is misguided in their use of volatility and I think most know that, but can’t get away from their “precise results.”

Here’s another thought. What about mistaking a “precise result” like Beta as a equally important for all stocks? The Beta of a stock is only as good as its R2 or Correlation. What if you started making sure you only used the Beta when it actually matter. Check this out: http://blog.alphatheory.com/2009/04/better-beta-not-all-beta-is-created-equal.html. It is a way to calculate Beta and only use it if it matters.

• Joe says:

Linear regression is abused by economists. Extreme simplifications like the one you posted are really frustrating to the point that the whole theory becomes silly. For the academics, alpha is the bastard brother of beta and it is almost always assumed to be zero for practical purposes: If the market index rises by r% then the stock price is expected to rise by (β x r)%. Where did alpha go?. I don’t know. Let me know if you find it
Joe

• dduane says:

Thanks for your comment. Sorry it has taken me so long to reply.

You’re right about a number of things. You can find individual portfolio managers, like Warren Buffett or Peter Lynch, who appear to be able to produce alpha. But there aren’t many. And the market sstudies them intensely, divines their secrets and eventually, as a result, even the greats return to earth.

The Value Line ranking system produced alpha for maybe twenty years before being extensively copied. Tellingly, in debates with academics, the professors’ arguments were often of the form that theory “proved” that what Value Line was doing was impossible–therefore, the firm mustbe incurring an as yet unidentified form of risk.

There are also many bells and whistles–like upside beta and downside beta–that sellers of statistical information provide in an attempt to differentiate their services and to charge more money for them. None of these “improvements” seem to me to add to what is, as you point out, a pretty silly theory.