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I recently heard that Deutsche Bank had $72trillion of "derivatives exposure", which is many times greater then the entire German GDP.

Now as I understand it, derivatives are essentially just bets on the movement of assorted prices... so I am assuming that "derivatives exposure" means the total amount you would have to pay out if you lost every single one of your bets. The likelyhood of this scenario may of course be vanishingly small, but presumably with $72trillion of exposure, you wouldn't need much of a losing streak in order to leave you bankrupt.

So some people are saying - "ooh this looks scary, it could lead to disaster"... but my reaction is "ooh this is scary... but why on earth hasn't it led to disaster already?".

Now I know there were multiple disasters around 2007/8 already and derivatives may have played a significant role in that... but I'm referring to, lets say, the past five years. How could Deutsche Bank have gotten to $72trillion of exposure without blowing up again? What kind of bets have they been doing such that they haven't had enormous losses?

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up vote 10 down vote accepted

While gross notional exposures are huge, net exposures at the banks are much smaller, on the order of 0.1 percent of gross exposures. Since most financial risk (but perhaps not operational risk) is proportional to net exposures this is a more sensible measure of total derivative risk at the banks. Since net exposures at the 6 banks with the largest derivative exposures circa 2014 were on the order of \$300 billion while their total assets were more than \$10 trillion, we may not have seen a disaster because the actual risk is appropriate to the scale of their broader operations.

Here is an example of how this works. At time 0 a bank does derivative trade with notional of 100 with A and collects the offer (or ask) price. That is, the bank sells the derivative to someone who wants to buy it. At time 1 a bank does derivative trade with B with notional of 100 and collects the bid price. That is, they buy the derivative from someone who wants to sell it. Total (gross) derivative exposure is 200, two derivative contracts each with an exposure of 100. However, net exposure is zero, and the bank keeps the spread as profit for its trouble. There is likely some remaining risk in the form of operations and credit risk, but this is what the spread and initial and variation margin are for.

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I'm not sure what you mean by "net exposures" - do you mean that the bank may simultaneously hold bets that X will happen and bets that X won't happen, so that either way the bank neither wins nor loses? – Mick Feb 12 at 16:06
    
That's correct. At time 0 a bank does derivative trade with notional of 100 with A and collects the offer (ask) price. At time 1 a bank does derivative trade with B with notional of 100 and collects the bid price. Total (gross) derivative exposure is 200, net exposure is zero, and the bank keeps the spread as profit for its trouble. – BKay Feb 12 at 16:14
    
Okay @EnergyNumbers. I can do that. – BKay Feb 14 at 13:33

As well as most of the positions being hedged, Big banks have large desks of mathematicians modelling these things. The sensitivity to first, second and cross derivatives of possible market moves are monitored, and the Value at Risk (a measure of Risk) is reported to markets and to regulators. Banks must hold capital (ie. allocated equity) against this risk. Value at Risk is measured according to historical simulation (both recent periods and last 'stressed' period) and/or fat-tailed correlated Monte Carlo simulation. If risk is increasing, banks will act to close out or hedge their positions. The major risk remains 'herd behaviour' - banks run to other banks to insure positions. However, this is somewhat limited with derivatives as much of the exposure is to other banks - if one financial institution is long another will be short. That's not to say there is no problem, just to say that the problem is different than that which one might expect from gross figures.

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It comes down to net exposure (and hedging as much as you can). Simple example: hold 1 bond maturing in 3 years. Sell 1 future that delivers that 1 bond in 3 years. If you can't perfectly hedge (which does happen), you either have risk (the unhedged amount or security) or you over-hedge (because you have to hold something to offset your risk).

Assuming not all things blow up together or blow together in harmony - your net exposure remains very small.

In the above example, you make money on the bond coupon, and make money on selling the future. You are also guaranteed to dispose of the bond. You'll lose money if the bond defaults (early) as you still need to deliver it (or an equivalent) at the end of the period.

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