Sunday, September 30, 2012

Banks Still in Negative Vega Zone

Recent increases in the monetary base have all gone into excess reserves, and so inflation has remained low, and monetary stimulus isn't stimulating. This puzzles many people, but I have a theory for it. The idea is that while equity owners--management--are like owners of call options on the assets of a firm (aka the Merton Model), banks are like down-and-out call option owners, because if their book equity goes down too far they will be forced into a fire-sale or liquidated by regulators.

 This is a barrier option, and has the interesting property that its vega--the derivative of the value of the equity with respect to asset volatility--is negative when it gets close in value to its barrier. A standard call option loves volatility, the greater the better. This can be shown by noting that an option is worth something like max(0,x), where x is a random variable; the higher the volatility of x the more an option is worth.  With a down-and-out constraint, a loss can cause the equity to forever extinguish, and this causes the vega to actually go negative when close to the absorbing barrier.

 That is, consider the difference in vega in the graph below.

If you have negative vega, adding risk or volatility hurts your equity value, so you turtle in, and wait like the 1990 Japanese banks for inflation and retained earnings  to cure your precarious position. Banks are still in their negative vega zone currently, afraid to do anything that will either get them into legal trouble, or generate any losses that would force them into liquidation. So, they aren't lending their new cash balances but rather hoarding them as protection.

 Bank of America recently paid a $2.4B fine to settle claims it misled investors about the acquisition of troubled brokerage firm Merrill Lynch. That brings its total fines since 2010 to $29B with no end in sight (eg, the Libor fixing scandal). Banks get fined for not lending enough to minorities, and lending too much.  If the government would stop treating the banks like the Knights Templar circa 1307, the economy would recover much faster. A modern economy needs banks, ones that want to take risks and grow.


Anonymous said...

Eric, I'm a big fan of your blog, but I can't help but think your assertions about how big banks are being persecuted by governments seems misguided from a longer-term perspective.

While it's true that healthy economies require healthy banks that are incentivized to take risks, the choice by governments to paper over bad bets introduces gargantuan moral hazard. If we unshackle banks without first wiping out shareholders then banks have no incentive to NOT execute the same bad choices all over again, which means we are back in the same situation again in 10 years, but with more government debt and outstanding derivatives.

That doesn't sound like a constructive trajectory to me...

Eric Falkenstein said...

I'm all for letting banks fail, but if we decide not to wipe them out, we should then leave what's remaining free. A wounded bank industry, forever defensive, is the worst solution.

Anonymous said...

Citizen's viewpoint

Near 99% loss of confidence in the financial "industry". Banks deserve to be scared after all the criminal gambling they have done with "our" money.

Banks are NOT an industry. They don't PRODUCE anything.

One issue, to be fair, is that if enough citizens emptied their accounts then international trade - oil, shipping - would be mightily affected and those countries depending on trade for food and energy would be mighty uncomfortable for their inhabitants.

Perhaps _THIS_ is the debate we should be having.

Conscience of a Conservative said...

I would have said it simpler. Banks lend based on their balance sheet, not reserves sitting at the Fed. Looking at bank stock prices, the current price to book ratios tells you the market does not believe the accounting is honest and that they are all capital impaired, which of course they are.

Fed policy is aimed at beefing up bank earnings and helping banks repair the balance sheet over time, so the Fed pays banks interest on reserves, announces some for of QE instrument such as treasuries or mortgages that the banks can front run, buy and then sell to the Fed at a profit. Additionally the whole meat of QE is to lower risk premiums and raise the price of risk asset which of course is how the banks are reporting their earnings aided by removing previous additions to loan loss reserves.

Mercury said...

Has HFT changed the barrier options market? It seems like algos could be used to very briefly whip the underlying around to the barrier point and knock in/out certain options unless the definition of the barrier event has been adjusted accordingly.

I think the TBTF banks are more like the Knights Hospitaller in this story however. It is they who end up with hoards of unearned wealth.

You could have a lot of morbid fun with this analogy in several concurrent areas. But generally the dwindling but proud American middle class are the owners of the much coverted "fabled riches", we all know who King Phillip IV is and The part of Clement V is played by the Amercian institutions and authorities that should know better.

Anonymous said...

"Has HFT changed the barrier options market? It seems like algos could be used to very briefly whip the underlying around to the barrier point"

LOL... as if `algos' possess some sort of special magic... Buying is buying and selling is selling, whether `algo' or point/click driven.

Anonymous said...

Is this a call or a put? If it is a put we would have a RKO which following the analogy would have really horrible risks at the barrier. If it is just a KO it won't be that bad.

Barriers are also tempting targets to take out. Liquidity hole there.

Anonymous said...

opps didn't see that this is a call so it is a ko option. which makes quite a lot of sense. although i'm puzzled as to why equity owners are like owners of call options. if volatility goes up, they can make money from vega although they would lose on the delta aspect which might mean that they can make money from declining share prices... even though they own the equity

i like the ko analogy. too many things in life we only have 1 shot at.

Anonymous said...

Reserves are not "monetary stimulus". End of story. They do increase bank profits because the Fed is paying interest, but that's a side issue.

Anonymous said...

Down and out calls don't have negative vega

Unanimous said...

I'm with anonymous at 5:42 PM.

Reserves are used by banks to transfer deposits between each other and between them and the central bank, not between themselves and their customers. Many central banks don't even call them reserves any more because they are interbank transfer accounts.

Unless the population starts withdrawing trillions of dollars in physical cash (which are claims on the government, rather than claims on the banks as deposits are), there isn't really any way for banks as a whole to run down their reserves. Central bank purchases of government bonds increase bank reserves and deposits of the former owners of the bonds, so they add to the money supply (the total amount of deposits held by the non-government sector) and to bank reserves.

So given central bank policy, the reserves are as would be expected under any economic situation. Still, I think Eric's main point probably holds, because it's really an argument about risk rather than reserves.

Anonymous said...

excellent post, thought this was a very interesting theory

Anonymous said...

Q: How much intermediation does a "modern" economy need?

Thought provoking post, btw. Thanks.