In his 2003 memoir, former Treasury Secretary Robert Rubin wrote:

There is one type of financial risk, the risk of remote contingencies -- which, if they occur, can be devastating -- that market participants of all kinds almost always systematically underestimate. The list of firms and individuals who have gone broke by failing to focus on remote risks is a long one.

This is smart, but depressingly ironic. While writing the book, Rubin was chairman of the executive committee at Citigroup (NYSE: C). Five years later, while still under Rubin's watch, the bank added its name to the list of firms who went broke (or close to it) by failing to focus on remote risks. 

I remembered this story this weekend when reading a blog post from economist Noah Smith, one of the sharper commentators out there. Smith was discussing hedge fund returns (or lack thereof), and wrote:

To evaluate hedge funds -- or any investment -- you need to look not only at the return, but at the risk. If hedge funds have higher return-to-risk ratios (such as Sharpe ratios) than a passive stock-bond portfolio, then they are a better investment. Why? Because in that case you can borrow money and invest it in hedge funds, and your leverage will increase the returns (and the risk) of the hedge fund investment. 

Pardon me, but I disagree. 

The problem here is the definition of "risk." As defined in finance textbooks, including the Sharpe ratio Smith mentions, risk is volatility.

But volatility is a strange way to think about risk. Time and time again, investments utterly implode after periods of silky-smooth calmness.

Take Rubin's Citigroup. Before it blew up, it has a long record of stable, consistent profits:

Source: S&P Capital IQ.

Or consider AIG (NYSE: AIG). Before it blew its top in 2008, the insurer enjoyed two decades of smooth, predictable, volatility-free profits:

Source: S&P Capital IQ.

In each case, equating volatility with risk would have sweet-talked you into a dangerous sense of complacency. The narrative, which is common among large companies, probably went like this: AIG earns stable profits year after year. That makes it a safe, low-risk investment. Maybe even safe enough to leverage up on. 

And then ... boom! Investors lost almost everything overnight.

To be fair, Smith was talking about hedge fund returns, not corporate profits. But there's a classic example of hedge fund investors getting duped to death by focusing on volatility as a measure of risk.

The hedge fund Long Term Capital Management is now infamous for being the largest hedge fund failure of all time. In 1998, during a period when seemingly no investor could lose money, the geniuses at LTCM -- including two Nobel laureates -- lost everything. They literally went bankrupt during a period when Barbra Streisand was a successful day trader.

But before LTCM's blowup, the fund was known for one thing: low volatility. A 1996 article in Institutional Investor describes it like this: "Before August, when returns dipped 0.24 percent, LTCM had not had a down month since February 1995, and only six down months in total."

And the fund's Sharpe ratio was an amazing 4.35, meaning it was earning big returns with low volatility. "If a fund manager can sustain a Sharpe ratio of 1, he is doing well," the magazine wrote. "But a Sharpe ratio of more than 4 is off the charts."

The article closes by asking, "how long can they produce those kinds of returns before suffering some spectacular crash?"

We now know the answer: about a year. 

LTCM was a glaring reminder that past volatility is a terrible measure of future risk. Yet we still obsess over volatility, convinced that it tells us how safe an investment is.

Nassim Taleb describes using volatility as a measure of risk as the "turkey problem." He writes in his book Antifragile:

A turkey is fed for a thousand days by a butcher; every day confirms to its staff of analysts that butchers love turkeys "with increased statistical confidence." The butcher will keep feeding the turkey until a few days before Thanksgiving. Then comes that day when it is really not a very good idea to be a turkey.

So if volatility isn't a good measure of risk, what is?

I like the Berkshire Hathaway (NYSE: BRK-B) credo:

Warren Buffett: "Risk comes from not knowing what you're doing."

Charlie Munger: "Risk to us is 1) the risk of permanent loss of capital, or 2) the risk of inadequate return."

Buffett's definition of risk is most applicable to individual investors. If you don't know what you're doing, you are rolling the dice at best. Add in fees, and you will you almost certainly lose.

Mugner's definition is more relevant to institutional investors. For pension funds, the biggest risk is not suffering a down month or a bad quarter; it's that, over a 20- to 50-year period, they won't earn high enough returns to cover their obligations.

But for both groups, past volatility tells you very little about future risk. "Using volatility as a measure of risk is nuts," Munger says.

Check back every Tuesday and Friday for Morgan Housel's columns on finance and economics. 

Fool contributor Morgan Housel has no position in any stocks mentioned. The Motley Fool recommends American International Group and Berkshire Hathaway. The Motley Fool owns shares of American International Group, Berkshire Hathaway, and Citigroup and has the following options: Long Jan 2014 $25 Calls on American International Group. Try any of our Foolish newsletter services free for 30 days.

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