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The unfolding mayhem in the financial markets triggered by Switzerland's decision to unpeg its currency from the euro last week offers a valuable lesson about the frailty of highly leveraged financial firms and the danger of overrelying on simplified risk models.

The "Swiss Miss"
For three and a half years, the Swiss National Bank intervened in currency markets to stop the Swiss franc from rising above an exchange rate of 1.2 francs to the euro. It did so to ensure that exporters of watches and other goods and services wouldn't be at a disadvantage to their competitors in neighboring European countries.

But this policy came to an end last Thursday, when the Swiss National Bank announced that it will no longer support the cap. In short order, the exchange rate of the franc proceeded to rise by almost 20% versus the euro.

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To most people, a 20% increase in the value of an asset may not seem like an existential event. Individual stocks rise and fall by that degree all the time.

But in the currency markets, a move like this is huge. So big that a number of foreign-exchange brokers were forced into insolvency. The largest in the United States would have failed on Friday, for example, but for a last-minute $300 million rescue package from the investment bank Jefferies Group.

And it's not just foreign-exchange brokers that took a hit. According to multiple media sources, Deutsche Bank and Citigroup suffered somewhere along the lines of $150 million in losses each, while Barclays racked up "tens of millions of dollars in losses."

So here's the question: Why are financial firms so vulnerable to sudden fluctuations in currency values? Isn't this what foreign-exchange traders and risk managers on Wall Street get paid so much to navigate?

While the answer to the second question is obviously "yes," understanding why financial firms get caught off guard so frequently (and fatally) is a bit more involved.

The role of extreme leverage
In the first case, because currencies are presumed to fluctuate less than, say, stocks do, currency traders rely on leverage to magnify the effect of otherwise small changes.

"Currencies don't move that much," observed the CEO of FXCM (NYSE:FXCM), the foreign-exchange broker that collapsed into the arms of Jefferies Group. "So if you had no leverage, nobody would trade."

At FXCM, customers were allowed 50-to-1 leverage by default. This means that a person had to put up only 2% of the value of a trade to execute it; FXCM would finance the rest.

So let's say you make a $1 million bet that the Swiss franc won't appreciate against the euro. At 50-to-1 leverage, that will cost you $20,000. If the franc depreciates by 1%, you'll earn $10,000, or 50% on your investment. Not bad! However, if the franc instead appreciates by, I don't know, say, 20%, then you're not only out your $20,000 investment, but you'll also have to cover the $180,000 loss incurred on your behalf by FXCM.

This is what led to FXCM's current predicament. According to a press release the firm issued on Thursday:

[Because of] unprecedented volatility in EUR/CHF pair after the Swiss National Bank announcement this morning, clients experienced significant losses [and] generated negative equity balances owed to FXCM of approximately $225 million.

As result of these debit balances, the company may be in breach of regulatory capital requirements.

What went wrong here? Are firms like this -- and remember that FXCM is the largest, and thus presumably one of the most sophisticated,foreign-exchange brokers in the United States -- so inept that they can operate only if currency fluctuations conform strictly to historical patterns?

Overreliance on simplified risk models
The problem is that financial firms compound their vulnerability to shocks in currency values by overrelying on simplified risk models known as value-at-risk, or VaR, models.

Invented by statisticians at JPMorgan Chase in the 1990s, VaR models are designed to measure a firm's risk exposure from one day to the next. They do so by projecting past market volatility into the future, and they have become ubiquitous because they reduce the concept of risk down to a single number that anyone can understand, irrespective of statistical acumen.

Let's assume, for example, that a firm's VaR number is 50. This means that, based on the historical volatility of the firm's outstanding positions, 95% of the time the firm stands to lose a maximum of $50 million over the following trading day.

Of course, one issue with models like this is that they don't capture tail risk. We saw this during the financial crisis, when VaR models failed to alert risk managers to the possibility that housing prices could fall on a nationwide, as opposed to a regional, basis. That hadn't happened in the recent past and thus wasn't reflected in the historical data.

As Bethany McLean and Joe Nocera wrote in All the Devils Are Here: The Hidden Story of the Financial Crisis:

The fact that VaR told you how much your firm might lose 95% of the time didn't say a thing about what might happen the other 5% of the time. Maybe you would lose a little more than the VaR number -- no big deal. Or maybe you'd get caught in a black swan and lose billions.

It was an identical oversight, in turn, that struck when the Swiss National Bank abandoned the franc's three-and-a-half-year-old peg to the euro. As The Financial Times' Tracy Alloway noted: "The move from the SNB constitutes a classic VaR shock following a period in which banks have seen their VaR estimates slip further and further lower following an historic period of low volatility."

The point here is that Wall Street banks, and all other types of highly leveraged financial firms, know much less about risk than they have led us -- or, for that matter, themselves -- to believe. In the face of extreme leverage, one must always assume that unexpected events are the rule, not the exception. The consequences of assuming otherwise, as FXCM discovered last week, can be fatal.

John Maxfield has no position in any stocks mentioned. The Motley Fool owns shares of Apple, Bank of America, Citigroup, Deutsche Bank AG (USA), and JPMorgan Chase and owns shares of Apple and Bank of America. Try any of our Foolish newsletter services free for 30 days. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.