Wednesday, January 13, 2010

Attempting to prevent financial disasters is too costly

What does it mean to prevent financial meltdowns?  Suppose you could buy an insurance policy against a financial catastrophe.

Let's keep this very simple, for a concrete example.  Suppose you want to buy a binary security linked to GDP for one year.  Such a security pays the holder $1 if U.S. GDP drops by 10% or more in a calendar year, zero otherwise.  That's what we'll define as a financial meltdown.  The price of this security is the insurance premium for one year of financial disaster protection.

Suppose a household needs $1 million of this security to hedge their exposure to the risk.  This $1 million payoff presumably must cover (the net present value of) losses to financial assets, employment income, real estate, etc. if such an event occurs.

In addition, the buyer of the insurance must be confident that the provider of this protection will be able to pay off the $1 million if the event happens.  That's a serious concern.
  The buyer must be convinced that the seller is hedged well enough, and has enough capital to pay off this security and every other security they've sold under close, but not quite as bad scenarios.  In the extreme, to be certain the $1 million will be available, it must be held in trust, fully backed by riskless securities.  Securities that will remain riskless in a 10% down GDP catastrophe.

In late 2007 and early 2008, securities like these could not be purchased.  Not even ones that allowed the buyer to take the credit risk of the counterparty.  I know because I tried.  However, I tried in substantially larger size, and this is where the problem with insuring against disasters becomes interesting.

Suppose I ask Goldman Sachs to provide me $100 million of this protection.  Suppose we even agree this is a 1 in 200 year event, and I'm willing to pay them $5 million, which is 10 times their expected loss, (a very good price based on premium to expected loss.)  However, Goldman has to figure out how to make sure they can make good on this transaction.  In the event GDP is down 10%, they're deep in their own catastrophe.  Either they have to say we'll reneg on our promise to Marc, or they have to allocate a huge amount of capital to this risk.  To be certain, they need $95 million, (because I've paid them $5 million.)  If it doesn't happen, they make a return slightly above 5% on their capital.  Not very good for Goldman.  So, they can't do the trade.  Even if they wanted to make 15% on the trade (before tax!) they'd have to charge me close to 15%, which starts to approach their expected return on capital.

That's for a "tiny" trade.  When it gets large, it gets interesting.  My pricing in the previous paragraph assumes the trade is small relative to the whole book of Goldman risk.  This makes no sense, as 10% down GDP is correlated with everything, but bear with me.  Make it a big risk.  I'm Swiss Re, not a small asset management firm.  I need $20 billion of this protection.  Even if I'm willing to pay 15% ($3 billion cash!) Goldman won't do it at that price.  At that price, it becomes undiversified risk.  Because it's a bigger risk relative to their book, they have to charge even more.

Remember, this binary security is not normally distributed in its payoffs.  It skews the distributions of Goldman's outcomes.  When it is small, it doesn't matter.  Remember college statistics?  A large collection of binary outcomes converges to a normal distribution.  But, if you don't have enough, or some are too large, you need to build in cushion because the distribution of possible outcomes isn't normal.

The problem just gets worse as the size of the trade increases.  So, I'm Congress.  I want to buy protection against a 10% GDP drop.  I need, say, $1.4 trillion of exposure.  This would "cost" a very large amount.  In fact, this simply means (to make sure there's no credit risk) Congress needs a trust fund (that politicians can't touch!) with 10% of GDP sitting in it.  Earning nothing but T-Bill returns.

So, what does this mean for regulatory reform?  Regulatory costs certainly can be no less costly than the actual cash cost of the protection.  Regulatory reform will be costly to implement, probably not particularly efficient, etc.  Therefore, to protect against a 10% drop in US GDP with regulations will "cost" at least 10% of GDP.  I'd imagine we'd all prefer that 10% or more as a productive part of the economy.

1 comment:

  1. There's a few points I'd want to say are complicating here and most of them are related to the protection provider:

    (a) I've made this argument in the past about deposit insurance, but what the argument shows is that it's a losing proposition for any private party to try to write crash insurance -- it's why only the government can be the FDIC.

    (b) I'm not sure I grant that regulatory costs must be as expensive as the cost of protection. It's not obvious to me that we're not in a situation more analogous to Chubb masterpiece policies here -- cheaper to reinforce your windows than charge a higher premium for the risk. If what we're talking about is securing pool enclosures I'm disinclined to dismiss regulation so easily.

    (not to say I'm broadly in favor, necessarily -- just that regulations need to be judged good or bad in terms of what they actually are)

    (c) "T-bill returns" is a bit the giveaway, though, isn't it? If we thought there was a compelling governmental reason to offer crash insurance we'd be like Citizens in Florida and price in a way we thought was actuarially fair (though ideally with some margin for safety). Congress certainly doesn't need to collateralize an obligation like this as they can just print more money. In fact, since the bog-standard monetarist response to financial crisis would be to print more money it might make sense to do this automatically -- the fed could sell these binary puts with the expectation that they'd be paid with printed money if they ever required payment. Increasing the money supply by 10% of GDP would be a big deal but justified in the situation and at a 5% premium there probably wouldn't be buyers in that size. I could imagine 1% of GDP pretty easily but that's a totally reasonable number.

    In other news, hi! Dennis from QVT here -- how's the world?