# The Market Completionist

Thoughts on finance, economics, and beyond

### The CAPM and Facebook: When Up Is Down

March 04, 2014 — Evan Jenkins

One of my favorite topics in finance (one that I will delve into deeply in future posts) is understanding cross-sectional stock market returns. A thankfully now-common piece of investment wisdom is to not invest in individual stocks but rather to invest in the market as a whole, that is, in a fund like the Vanguard Total Index that owns shares in all stocks weighted by market value. But is this actually the optimal way to invest? Do some stocks perform better than other stocks, and do some stocks tend to move together, an important consideration for hedging risk?

The rich theory of cross-sectional pricing that has been developed over the past half-century is all too often swept under the rug when it comes to the popular financial media. It really boils my blood when I hear things like what I heard on a prominent national radio show this evening: Facebook (NASDAQ:FB) was up 2% today on news that it was considering buying a drone manufacturer. Now, it’s certainly possible for news to move a stock’s price. But even the most basic asset-pricing theory will put the kibosh on that particular interpretation.

One of the first successful models of stock market returns was the capital asset pricing model (CAPM), developed independently by a number of researchers in the 1960s. I plan on talking much more about the CAPM and its successors in future posts, but today I’m just going to explain just enough about it so that you can start yelling at the radio too.

The idea of the CAPM is that the only predictable thing about the excess return $R^{ei} = R^i - R^f$ (the return minus the return on the risk-free asset) of stock $i$ is its covariance with the excess return $R^{em}$ of the market portfolio (think the S&P 500 or the Vanguard Total Index). In other words, if we run a time-series regression of $R^{ei}$ against $R^{em}$ to get $R_t^{ei} = \alpha_i + \beta_i R_t^{em} + \epsilon_t^i,$ we should have $\alpha_i = 0$, so that the only difference between our stock’s return and a constant multiple of the market return is some unpredictable random factor $\epsilon_t^i$.

According to NASDAQ, the coefficient $\beta_i$ for Facebook is 1.78. In other words, for every 1% the market goes up (or down), we should expect Facebook to go up (or down) 1.78%. (I’m ignoring the risk-free rate here because these days it’s pretty much zero.) So how did Facebook do here? Well, the S&P 500 went up 1.53% today, which means that Facebook should have gone up $1.53 \times 1.78 = 2.7\%$. But it only went up a little over 2%! Even though Facebook’s stock went up (and, in fact, it went up more than the market as a whole), it underperformed by about 0.7%! The effect of the drone news, which should live in $\epsilon_t^i = -0.7%$, was negative!

Now, the CAPM isn’t perfect, but I doubt the various corrections to it would be enough to account for this huge underperformance. Any sensible investor, insofar as they care about Facebook rumors, should see the drone news as likely having had a negative impact on Facebook’s valuation. (A more nuanced analysis would look only at the return since the news broke, but I can’t be bothered if the guy on the radio can’t.)

Anybody who has ever listened to financial radio or watched financial television knows that this isn’t an isolated event. Individual stock movements are retroactively fit to the day’s news in isolation without any regard to the intricate relationship among different assets. I’m not saying that there’s no value to analyzing the impact of the day’s news on asset prices, but why do it in such a ham-fisted manner the you’re likely as not to get the sign of the effect wrong? Are the purported financial professionals simply incompetent, or do they not bother doing an actual analysis because they think it will bore or confuse their audience? In either case, isn’t it irresponsible to portray this stuff as financial news?

I hope you’ll agree that this isn’t just one blogger’s smugness getting the best of him. I believe in financial markets as a means for people to improve their lives. But when the people who are held up as experts say things, knowingly or not, that are so completely wrong, it should not come as a surprise that few people have a good grasp of basic financial concepts. It’s obvious to most people, I hope, that Jim Cramer is peddling fluffy infotainment, but the problem goes much deeper. Virtually all financial media is aimed at the lowest common denominator. But if you don’t invite your audience to stretch their thinking, they’re going to remain uninformed, and they’ll quite likely suffer because of it.

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