Fractional reserve bullion banking and gold bank runs - the model says we are hedged

In yesterday's post I discussed the various types of gold assets that sit on a BBs gold balance sheet. Often goldbugs refer to these generically as “paper gold”, but I think this hides the great differences in riskiness between the various types of paper gold assets and is so overused that people fail to appreciate the real risks involved. So what are these risks?

For some paper gold instruments it is quite easy to estimate the size of the exposure, for other more complex derivatives, a BB would rely on something like Black Scholes model and it is here that a lot of risk is introduced. Consider these limitations of Black Scholes from the Wikipedia link:

• the underestimation of extreme moves, yielding tail risk, which can be hedged with out-of-the-money options;
• the assumption of instant, cost-less trading, yielding liquidity risk, which is difficult to hedge;
• the assumption of a stationary process, yielding volatility risk, which can be hedged with volatility hedging;
• the assumption of continuous time and continuous trading, yielding gap risk, which can be hedged with Gamma hedging.

The article I think naively says some of these risks can be hedged, with other derivatives! But then how are these valued, using similar formulas? Ultimately, there is often just another counterparty on the other side and we get back to these assets being either an outright promise (unsecured) or a promise covered by collateral or margin. But that collateral itself needs to be valued, by those same formulas in many cases. And how to determine the amount of margin? By those same formulas.

It is the false assumption underlying much of the formulas used by the BBs to work out how to “hedge” themselves that I think is the problem, as this article The mathematical equation that caused the banks to crash explains.

In it Professor Ian Stewart notes that even though the Black-Scholes equation was based on false assumptions “the model performed very well, so as time passed and confidence grew, many bankers and traders forgot the model had limitations.” Are the people within BB are considering tail, liquidity, volatility and gap risks? And if they are, are they looking at it from the same viewpoint that gold investors do, which is one that looks over a long timeframe and is more adverse to extreme events? Doubtful.

By way of example, some years ago the Perth Mint was looking at Treasury software packages. I remember the salesperson saying that the software had all the complex “formulas” inside it and worked them all out for you. I asked where it got the key inputs from, like volatility. The answer was from one year’s worth of data of the underlying asset! That didn’t seem to me to capture events like the 1980 $850 boom and bust.

I can’t say I’m totally confident that BB are taking into account the new branch of mathematics called complexity science, which Professor Stewart explains “models the market as a collection of individuals interacting according to specified rules” which reveal that “virtually every financial crisis in the last century has been pushed over the edge by [traders] the herd instinct. It makes everything go belly-up at the same time.” Therefore the gold assets of a BB are, to my mind, barely robust in the face of extreme events.

At this point it is worth discussing the liability, or sources of funding, side of a BB’s balance sheet. It is obvious that people buying and leaving gold with a BB, as unallocated, is a big source of funding. But BBs can also acquire funding via derivatives, or to be more accurate, net off their assets with opposite ones of a similar type. For example, long futures against short futures, or options against options.

However, these would rarely line up in terms of maturity, so on top of the misestimation of the value of these paper golds, outright counterparty exposures, inadequacy/variability of the collateral/margin calculation, you have maturity transformation – a deliberate mismatching of maturities of these products to their sources of funding, which assumes that if needed, new sources of funding can be found or existing ones rolled over.

Considering all this complexity and room for error one would conclude that we have a highly unstable system, one that Nassim Taleb would call fragile and sensitive to stress, randomness and disorder.

However, the fact is that the bullion banking system has not failed. For example, in 1998 open interest vs stocks exceeded 40:1 (when from 1975 to today it has never been over 15:1), yet there was no failure. What about LTCM, or AIG (40:1 gold leverage as per Jeff Christian). Shouldn't that have been enough to blow up the system? So how do we explain this apparent robustness?

Hmm, but wasn’t it in 1999 that “We looked into the abyss if the gold price rose further”. So tomorrow we look at the interaction of BBs with each other via their clearing firm and whether bullion banking is thus a freebanking system, and the role of central bankers.