Citi Picked the Wrong Week to Quit Hedging Swiss Francs
Oh Citi this is just too wonderful:
Citigroup Inc.’s loss on a surge in the Swiss franc this month was exacerbated by the bank’s decision to let protections against currency swings lapse a week earlier, according to people with knowledge of the situation.
The bank didn’t renew derivatives trades that would have blunted the impact from Switzerland’s surprise move to let the franc rise, said the people, who asked not to be identified discussing the strategy. The company’s losses exceeded $200 million in the hours after the announcement, before traders pared the deficit to closer to $150 million, the people said.
Citigroup was exposed after selling options on the Swiss franc to customers and failing to renew offsetting hedges, according to one of the people. The options gave buyers the right to collect from a strengthening franc and from higher volatility.
A good rule of trading -- up there with "If it don't go up, don't buy it" -- is that you shouldn't let your hedges lapse just before the thing they're hedging against happens. Also how much would you pay for an alert service that pinged you whenever Citi decided to change its hedging strategy from "hedged" to "unhedged"? And what would you do with that information?
One thing to keep in mind is that everything -- at least, every bank market-making desk like Citi's foreign-exchange flow options desk -- exists on some sort of continuum between "hedged" and "unhedged." Citi wasn't perfectly hedged before its hedges expired. You can tell because they expired, before its sold options did. Citi had, at the very least, a time mismatch. If the franc moved up before its hedges expired, and it wanted to remain hedged, it would need to go buy new hedges at a higher price. If the franc moved lower, it would need to go buy new hedges at a lower price. So it still had economic exposure to Swiss franc movements. Just as a second-order thing.
But even that is way too simplistic. Citi had probably sold lots of options, with lots of different maturities and strikes. That's its business! And it had probably bought lots of options, with lots of different maturities and strikes. (That's also its business.)
And then some of the options it had bought went away, and it had to think, hmm, should we go buy more? How do you make that decision? One thing you could do is try to make sure that every option you've sold is precisely offset by an option that you've bought, but that is not only difficult, it is also in some deep way wrong. The job of a derivatives desk is not just to find buyers and sellers of the same exact derivative, keep them from finding out about each other, and pocket the spread between them. (That's the job of stock traders. ) The job of a derivatives desk is to take on the risk of a mismatch between buyers and sellers. One company wants to buy a two-month option struck at 1.15, and another wants to sell a one-month option struck at 1.10? Great, Citi will do both of those trades, and they'll sort of offset. Not quite, but sort of. And then it will do a bunch more trades, with the goal of getting them to mostly offset in the aggregate. It won't be a one-to-one correspondence, but the whole social function of a derivatives desk is to find things that sort of offset, and to have a mathematical model that gives a useful meaning to the phrase "sort of offset."
Sadly, it turns out that the model gives a lot of different meanings to that phrase, because options are not linear, and they offset each other differently in different places. For instance. If the franc weakens by 1 percent, Option A will gain $100, and Option B will lose $100. So they sort of offset. So you buy them both. But wait: If the franc strengthens by 5 percent, Option A will lose $1,000, while Option B will gain only $400, so they don't offset there. But Option C will gain $600 if the franc strengthens by 5 percent, so you buy that too. Now you're back to even. But hang on. If the franc doesn't move at all, Option A will lose $10 and Option B will gain $10 and Option C will lose $200. So now you've got an unpleasant lump at that place. So you add Option D and ....
You're doing a whole lot of cooking, is the point, adding options here and there to balance each other out and get the exact flavors of risk that you want. While also responding to client demands to give them the exact flavors of risk that they want -- which can throw your whole carefully calibrated system off again.
So what happens on Jan. 8, give or take, when Citi's bought options rolled off? Well, Citi thinks about how much risk it has, in the aggregate, in its book of options. And the answer is -- well, I mean, in some sense, it's a lot. Someone could have said, like, "Hey, if the Swiss National Bank lifts the cap on the franc and it goes from 1.20 to 0.85 per euro before partially recovering, then we'll lose, like, $150 or $200 million!" But that would be a bizarre thing to say on Jan. 8, though of course it happened a week later. There are all sorts of weird possibilities, and you can't just treat them all as equally likely. You have to assign some probability to them and have some framework to deal with them.
And the market sort of does that. On Jan. 8, the market assigned a volatility to the euro/franc currency cross -- it was around 4 or 5 percent -- and Citi could use that to compute the expected risk of its options. Or a series of expected risks. For example, it could say, "If the franc strengthens by 1 percent, then we'll lose $100,000 on this option, but if it strengthens by 20 percent, we'll lose $150 million."
If it focused more on the first part than the second, it could hedge that exposure by buying $10 million worth of francs, which will gain $100,000 if the franc strengthens by 1 percent, but only $2 million if the franc strengthens by 20 percent. Hedging the option with just a pile of francs -- focusing only on the risk of a small move, not a big one -- would be dumb, because your risk in a pegged currency like the Swiss franc comes not from small regular-way moves (which had pretty much vanished due to the cap), but rather from the giant shock of the SNB one day lifting the cap. On the other hand, constructing your life around an imminent 20-percent move would also be dumb, and cause you to lose money, if the 20-percent move never materialized. So if you thought that that move would not materialize, you might choose not to pay to renew your hedges.
And here's the thing: The market was telling Citi that that 20-percent move was not going to materialize. That 5 percent market-implied volatility translates to a 95 percent chance that the franc wouldn't move by 10 percent over the next year, never mind twice that much in one day.
I don't know what Citi's FX derivatives book looked like, or what its risk managers were thinking when those hedges rolled off. (Citi says: "Expiration of hedges related to the franc did not drive the shortfalls in our trading activity, all of which was executed under our existing rigorous risk management limits and supervision.")
But probably they were thinking: We have a big mishmash of trades. We asked the computer what our risks look like. It told us. Yesterday our risks looked like so. Today, they look a little bit better if the franc weakens or stays flat, and a little bit worse if the franc strengthens a bit, and a lot worse if the franc shoots up in a basically unprecedented way over the next week. Yeah, we're cool with that.
This is always and everywhere a problem! It's impossible to resist the temptation to make fun of Citi, but it's important to resist the temptation to say, "Well obviously they should have been hedged." They were hedged! Sort of! You can only ever be sort-of-hedged. The question is whether you're the right sort of sort-of-hedged. After the fact, sure, the answer seems to have been Nope. But that just means that the unlikely events that Citi was preparing for were not the unlikely events that actually happened. It's hard to blame Citi too much for that, and it's important not to write that off as a fluke. Most of the time, the unlikely events that you prepare for are not the unlikely events that happen.
In the same vein, consider the plight of oil producers, or airlines, or Swiss exporters. "They should hedge their oil/fuel/currency exposure," you say. But those exposures, for a public company, are eternal. If an airline hedges its next year of fuel consumption, and fuel prices go up over that year, then, great, it's hedged! Except at the end of the year, it needs to buy more hedges -- and, because fuel prices are higher, those hedges are more expensive than they were at the beginning of the year. So maybe it should have hedged the next two years. But you can repeat the argument. Maybe it should have hedged the next 30 years of fuel costs? But who'll be around in 30 years?
I kid, come on, time mismatch is a mismatch. Even if it's a millisecond.
"They expired about a week before the Swiss central bank’s decision," which was Jan. 15.
I am using dollars in the text since that is the currency in which the profits and loss are expressed, but it seems likely that the trades here were EUR/CHF, given the low expected volatility of that pair, so that "taking the hedge off" might make sense.
Looking at Bloomberg OV, it seems like the delta of a one-month, 1.10 strike EURCHF call as of Jan. 8 would be pretty close to zero. A week later that call had a 90 percent delta, and its value had increased a thousandfold. So a $200 million loss could come from an option worth less than a million dollars.
Less money, of course. Less than $150 million or whatever. It costs less to buy insurance on low-probability events than you lose when those low-probability events occur. But in expectation you should lose more doing that.
Imagine that this footnote contains a long disquisition on the Volcker Rule, market-making risk limits and "risk-mitigating hedging activities." Think how boring that would be!
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