The debate on the relationship between volatility, risk, and permanent impairment of capital rages on. Below are some thoughts on the subject from Cliff Asness of AQR Capital Management, extracted from an article titled “My Top 10 Peeves” published earlier this year in the Financial Analysts Journal.

“Volatility” Is for Misguided Geeks; Risk Is Really the Chance of a “Permanent Loss of Capital”

There are many who say that such “quant” measures as volatility are flawed and that the real definition of risk is the chance of losing money that you won’t get back (a permanent loss of capital). This comment bugs me.

Now, although it causes me grief, the people who say it are often quite smart and successful, and I respect many of them. Furthermore, they are not directly wrong. One fair way to think of risk is indeed the chance of a permanent loss of capital. But there are other fair methods too, and the volatility measures being impugned are often misunderstood, with those attacking them setting up an easy-to-knock-down “straw geek.”

The critics are usually envisioning an overvalued security (which, of course, they assume they know is overvalued with certainty) that possesses a low volatility. They think quants are naive for calling a security like this “low risk” because it’s likely to fall over time. And how can something that is expected to fall over time—and not bounce back—be low risk?

What we have here is a failure to communicate.A quant calling something “low risk” is very different from a quant saying, “You can’t lose much money owning this thing.” Even the simplest quant framework allows for not just volatility but also expected return. And volatility isn’t how much the security is likely to move; it’s how much it’s likely to move versus the forecast of expected return. In other words, after making a forecast, it’s a reflection of the amount you can be wrong on the upside or downside around that forecast. Assuming the quant and non-quant agree that the security is overvalued (if they don’t agree, then that is an issue separate from the definition of risk), the quant has likely assigned it a negative expected return. In other words, both the quant and the non-quant dislike this security. The quant just expresses his dislike with the words “negative expected return” and not the words “very risky.”

A clean example is how both types of analysts would respond to a rise in price unaccompanied by any change in fundamentals now or in the future. On the one hand, those who view risk as “the chance of permanent loss” think this stock just got riskier. Viewed in their framework, they are right. On the other hand, quants tend to say this stock’s long-term expected return just got lower (same future cash flows, higher price today) rather than its risk/volatility went up, and they too are right!

It is also edifying to go the other way: Think about a super-cheap security, with a low risk of permanent loss of capital to a long-term holder, that gets a lot cheaper after being purchased. I—and everyone else who has invested for a living for long enough—have experienced this fun event. If the fundamentals have not changed and you believe risk is just the chance of a permanent loss of capital, all that happened was your super-cheap security got superduper cheap, and if you just hold it long enough, you will be fine. Perhaps this is true. However, I do not think you are allowed to report “unchanged” to your clients in this situation. For one thing, even if you are right, someone else now has the opportunity to buy it at an even lower price than you did. In a very real sense, you lost money; you just expect to make it back, as can anyone who buys the same stock now without suffering your losses to date.

If you can hold the position, you may be correct (a chance that can approach a certainty in some instances if not ruined by those pesky “limits of arbitrage”). For example, when my firm lost money in 1999 by shorting tech stocks about a year too early (don’t worry; it turned out OK), we didn’t get to report to our clients,“We have not lost any of your money. It’s in a bank we call ‘short NASDAQ.’” Rather, we said something like, “Here are the losses, and here’s why it’s a great bet going forward.” This admission and reasoning is more in the spirit of “risk as volatility” than “risk as the chance of a permanent loss of capital,” and I argue it is more accurate. Putting it yet one more way, risk is the chance you are wrong. Saying that your risk control is to buy cheap stocks and hold them, as many who make the original criticism do, is another way of saying that your risk control is not being wrong. That’s nice work if you can get it. Trying not to be wrong is great and something we all strive for, but it’s not risk control. Risk control is limiting how bad it could be if you are wrong. In other words, it’s about how widely reality may differ from your forecast. That sounds a lot like the quants’ “volatility” to me.

Although I clearly favor the quant approach of considering expected return and risk separately, I still think this argument is mostly a case of smart people talking in different languages and not disagreeing as much as it sometimes seems.