Business Cycles and Barrier Options

I was at an NBER conference in early 2008 when we really didn’t know if we were in a recession, and Markus Brunnermeier explained to a group of esteemed economists that while the housing collapse was real, it represented only a couple hundred billion dollars, and by then the stock market seemed to have lost three times that, which seemed an overreaction, a sign of excessive volatility due to behavioral biases. This was not a contrary stance, rather, the conventional expert opinion. This turned out to be the tip of the iceberg, as the fundamental anomaly just continued. From a destruction in value of a couple trillion dollars in home values ultimately, the global economy lost around 60-80 trillion in value. No one knows how such small losses amplify in size and scope to create economy-wide downturns, because we have no good theory for it.

Banking expert Gary Gorton noted the strange metastasis of economic downturns:

But, when the crisis came, there was no distinction between pre‐ and post‐2006 vintages. Everything went down in value, including bonds linked to the earlier subprime vintages! Moreover, bonds completely unrelated to subprime risk, like triple‐A bonds linked to credit card receivables, auto loans – everything went down in value! [Hedge fund maven John] Paulson was right in targeting subprime, and he got the timing right. But, like everyone else, he got the magnitude of the crisis wrong. The tidal wave was much, much bigger than anyone expected.

That is, in the crisis everything lost more value than anticipated, the amplification or accelerator mechanism was underappreciated. Savvy investors may have predicted the housing debacle, but no one thought this would generalize this to autos, commercial real estate, everything, even though these market prices fell as well. This error was not because they were stupid, but rather we do not have any good model for how this works.

Here is my theory on business cycles. First, the impulse of the downturn I presented in my post on Batesian Mimicry. One could also count explicit tight interest rates as a cause, in that both would adversely affect banks. Here's my new idea, how a small loss transmogrifies into an economy-wide collapse:

Merton first created an option model to describe the value of a stock, which is really a call option on the assets of a firm. A firm’s debt is its 'strike price.' That is, owners of stock get all the upside, but if the firm loses all its value, the owners lose only their equity, the rest of the loss is born by debtowners. The average stock is levered 50%, so in general, stocks are options on the value of the firm. When I was at Moody's we were active in modeling public firm default rates using the Merton approach, where using the value of the stock (aka the 'call option'), the value of the debt (the strike price), and the volatility of the stock, you can back out an estimate the probability of default.

Interestingly, recovery values on defaulted debt tend to be well below the amount of total debt, about 50% on average. That is, if lenders could seize assets immediately, once the asset value of the firm hit the value of the debt (99% of par), the lenders would take over with minimal loss of principal. In practice debt holders are able to sieze the firm only after the firm’s value is well below its strike price.

This implies there is an 'absorbing barrier'. The absorbing barrier on companies is that firm value where debt owners force the firm into bankruptcy. A company can live forever, but at some point debtholders stop the clock, declare 'game over', and cut their losses. Thus stocks are not just call options, but barrier call options (specifically, down-and-out calls). Good models of down-and-out-options weren’t available prior to the late 1990’s (see Haug and Zheng).

Vega is the change in option value given a change in volatility. Positive vega means the option value increases with an increase in volatility, and regular puts and calls always have positive vega: more volatility increases their value. For a regular option vega is always positive, peaking at the strike price (when it is at-the-money). To make this clear, consider the bank owners (ie, equity owners), are managing the option value, and so the vega corresponds to its directive to take more risk.

Now, when banks are suffering due to some exogenous shock created by Batesian mimicry, the depositors become worried. Bank liabilities are generally shorter than their assets, where depositors have an option to call them back at any time. A bank run is statistically unlikely in normal times, but if people think the bank may be insolvent (ie, assets less than liabilities), they will rush to take out their deposits prior to anyone else, creating a self-fulfilling prophesy, so that the effective absorbing after a big decline in some parochial sector leads investors to wonder if their bank was overexposed to this sector. Quarterly balance sheets do not indicate the region, industry, and seniority, and underwriting behind, various assets, so when investors see a conspicuous asset decline they are rationally wary, as invariably some lenders will have been too concentrated in the affected sector. Thus, depositors become skittish, raising the barrier of a firm, because if depositors so much as smell a risk, they will create a run, killing the firm (eg, Bear Stearns).

The vega becomes negative when the barrier rises because now if a bank loses value, its option premium, its equity value, is extinguished. In a standard option, volatility is unambiguously a good thing, but with the barrier threatening its existence, the derivative switches sign at some point, changing the game entirely. Here, the value of the option becomes zero forever at 90, so the vega is zero there and below. Another way vega can switch signs is if the barrier is a certain level, and the asset value falls below a certain level, vega becomes negative. See below for how the vega changes as the asset value (ie, L+A) falls, for a special barrier value.

This vega switching is the unappreciated key to the transmission mechanism. To repeat: barrier call options, where there is a down-and-out option, switch to negative vega as the barrier rises, or for specific barrier levels when the asset value falls. This is unlike regular call options where the vega is always positive.

It also creates a positive feedback loop, because if banks are in this negative vega regime, they are not incented to buy any risky asset such as a failing bank. This means banks aren't able to buy other banks, effectively raising their absorbing barriers because no one is there to salvage their (non-barrier) option value. Regulators pile on, becoming more insistent on enforcing regulatory standards in order to safeguard banks, again creating a more tangible barrier above the strike (debt) price.

In a negative vega regime, banks add value by reducing risk, not increasing it. They all flee to safe assets, trying to replace risky assets with less risky ones, and avoiding the absorbing barrier. In bad times, banks have negative vega, they don't want more risky assets, and a failing bank adds a lot of risk (especially legal, as Bank of America is finding with their purchase of CountryWide).

A shock to banks causes creates a negative vega, which causes them to cut risk by cutting new lending and instead buy Treasuries (which causes interest rates to fall). This negative vega creation could be due to barriers increasing due to potential bank runs, or from vega becoming negative as the asset value falls (which holds for certain barrier levels). That may seem like a lot of steps, but consider the Krebs cycle has 8 steps, and it's ubiquitous and natural.

The implication is that the key to recoveries is pushing banks back into their positive vega position, so they again have an incentive to make risky loans. Currently, there are several outstanding class-action suits, and a suit by the Department of Justice, that could wipe the banks out. Many liberal economists are indignant that government money was used to rescue the banking sector and suggest that banks be forced to write down all their underwater mortgages as a payback to the public. Thus, even though profitability is rather high, bank asset values are still very low because they discount this possibility, and so depositors are wary, keeping banks in the negative vega region.

In contrast, the tech bubble of 2001 had a fairly limited effect on banks because most of the value destruction was in the equity, private capital. Thus banks were quickly back in the positive vega zone and the recession was pretty small. In contrast, bank stocks today are still well below prior highs. Below is a graph of the drawdown from the prior peak for the bank stock index, as generated via Ken French's data. The past peak is a high-water mark, so it tops out at zero, but in recessions falls (IndexValue/Max(prior Index values)-1). The current drawdown is comparable to that in the Great Depression, and notice it is still at historic lows (data is through October 2011).

This is why need strong banks, 'rich banks', as my old mentor Hyman Minsky used to say. Without them, financing collapses, and the economy stagnates. Only banks, with their many professionals evaluating idiosyncratic criteria with the sole objective of making money, can create the investment needed for economic growth. One can generalize ‘banks’ to any lender, which faces similar incentives and constraints. The best thing to do would be to stop threatening bank solvency with unlimited liability. All this focus on government stimulus and zero interest rates while simultaneously trying to punish banks for the past recession is guaranteed to not help because we need banks back in positive vega mode.