Who is the Father of Low Volatility Investing?

Any good idea is found independently, and there are always early works that seem to unambiguously imply the ultimate result even if they never really focused on it. So it is with low volatility investing.

Bob Haugen has been touting unconventional investment tactics for decades, starting with The Incredible January Effect published in 1987. Alas, the January effect was one of those anomalies centered on low-priced, small-sized, firms, that usually don't scale well. Do you remember the 'low price' effect? It was popular in the 1980s, along with the size effect, as small size and low priced stocks were highly correlated and both seemed correlated with very high returns. The low price funds are now something anyone associated with them at the time conveniently forgets, because trading them is very costly, like trading options instead of stocks.

Anyway, I saw him being interviewed at a Dutch conference, with the talk 'The Low Volatility Anomaly' on the screen, where he was arguing investors should move their equity exposures to low volatility oriented equity funds. At one point the interviewer asks if 'will you be known as one of the big heroes of the twenty first century?' In sum, I would say he was the first to publish on this, but he didn't know what he found, so the importance of his early work only appears with hindsight, or to those who took his facts and ignored his interpretation and emphasis.

Haugen did publish a very prescient piece in 1975, Risk and the Rate of Return on Financial Assets, that clearly empirically addressed the basis of the CAPM, and found beta was not related to returns as expected. He even states 'we find little support for the notion that risk premiums have, in fact, manifested themselves in realized rates of return.' Right on! Unfortunately, I think the issues then were on methodologies for simultaneously estimating betas and expected returns, so this was not very highly cited, and Haugen, like the rest of the profession, turned to highlighting factors that seemed to explain expected returns irrespective of risk (eg, calendar effects, value). The testing of the CAPM was left to the econometricians, with work by people like Gibbons, Shanken, and Ross.

In 1996, Haugen again argued that low-risk stocks tend to outperform high-risk stocks. But the emphasis on this paper was this was a consequence of market inefficiency. He created a model with many factors, grouped into 1) risk (eg, beta, volatility, 2) liquidity (eg, volume, price), 3) value (eg, P/E), 4) growth potential (eg,ROA), 5) past returns (eg,past 6-month return), and lastly 6) sector variables. Each class had ten or so highly correlated metrics within them. A more recent paper he did (again, with co-author Nardin Baker), basically applied the same idea. He noted the highest returning portfolio constructed via this backfitting were of lower volatility and beta than the lower returning portfolios, but that was incidental.

The emphasis was clearly on a model that predicted returns, and even now he touts 70 factors, many of which are highly correlated. The factor risk premia are calculated on a rolling basis, so signs on these factors bounce around. It's a classic kitchen sink regression. I don't see the emphasis as being 'low volatility', rather, that is a characteristic of his 'highest expected return' portfolios, which is his focus. For example, his 1996 Journal of Portfolio Management article on this riff was titled 'The Effects of Intrigue, Liquidity, Imprecision, and Bias on the Cross-Section of Expected Returns.' Lately he discusses three types of volatility--event-driven, error-driven, and price-driven--which he tries to separate and use differently. I think he's slicing this too thin, as you get pretty similar results using total or idiosyncratic volatility. That's a lot going on, but clearly volatility and risk are not emphasized as prime movers, he just found that risk was inversely correlated with these more interesting factors.

I do think he's a bit disingenuous with his performance. His page showing the cumulative returns for his various models shows a rather incredible upward growth since 1999. However, I remember some using his factors in the latter half of 2003, and the model generated a significant draw down, well-outside the scope of his backtests. Interestingly, there's no evidence of that in his charts. I presume that was an earlier version that got dropped down the memory hole.

In sum, I think he didn't prioritize volatility until the low-volatility movement get really going to get credit for 'low volatility' investing per se. While I wrote my dissertation on this back in 1994, but it went over like the Hindenburg with academia, and I never got refereed publication on the volatility result, so I wouldn't say I'm a founding father (I didn't have an equilibrium story then, and this was before Freakonomics and the popularity of behavioral finance, so back then it just didn't make sense). I would say that the two main academic pieces I relied upon for my finding then were Bruce Lehman's 1990 Residual Risk Revisited, and Ed Miller's 1977 Risk, Uncertainty, and Divergence of Opinion. Both focused on volatility, and implicitly noted that there appeared an attractive investment strategy implied by the poor average returns to highly volatile stocks. Indeed, in 2001, Miller mentions this strategy in the Journal of Portfolio Management. It seems, one needs a theory to see something, and because Miller had this theory (winner's curse) he had thought relevant to equities, he saw the investing implication before others. That is, one could deduce it as a corollary of Fama and French's 1992 finding that beta was uncorrelated with average returns, but as Fama and French merely extended the standard model to other risks, they missed the low-volatility/beta bandwagon. For example, Haugen's big theory had been that markets are inefficient, and so I think he wasn't focused on volatility for the reason that this insight is incomplete: inefficient in what way?

By the mid aughts, several academics had discovered this in various guises. There's Analytic Investor's Clarke, de Silva, and Thorley (2006) and Robeco's Blitz and van Vliet (2007), which focused on low volatility portfolios. Then there's Ang, Hodrick, Xing and Zhang (2006) highlighting the poor cross-sectional returns to higher volatility stocks, and that really was seminal for academics. Firms like Analytic Investors, Robeco, Arcadian, and Unigestion all started low volatility funds around this time, so they had all seen this years earlier. Indeed, many of these guys read Haugen and Baker (1991), which documented this first, but again, Haugen inferred something different from this and went on a return-factor hunt. While all this was becoming common knowledge, I was fighting a lawsuit by a former employer trying to stop me from using volatility as an investment factor, and I remember thinking how crazy it was that I had to fight to use something I had been touting since 1993 that then had a pretty large publication thread.

Quantitative Easing Tough on Pensions

From the WSJ:

While quantitative easing boosts the value of pension assets, it lowers investment returns and increases estimates of future liabilities. Because typical defined-benefit plans are only 70% funded and face liabilities several years longer than their assets, that leads to wider deficits...But many trustees say the best response would be for the BOE to stop buying long-dated gilts and buy bank bonds instead. Not only would this ease bank funding difficulties, and thereby improve the supply of business loans, it would allow gilt yields to rise.

With interest rates at historic lows, pension funds are in a tough spot. If interest rates rise, they will suffer capital losses and actually be in a tougher spot. I'd say this is good reason to avoid bonds that are attached to entities with large, unfunded pensions (eg, states, munis).

When the government tries to improve prices, it creates winners and losers.

IMF Chief Economists Blames Problems on Investors

Olivier Blanchard is a very well-respected academic economist, and currently also Chief Economist at the International Monetary Fund. He sees today's current big problems primarily due to investors.

• Self-fulfilling outcomes of pessimism or optimism, with major macroeconomic implications.
• Incomplete or partial policy measures can make things worse.
• Financial investors are schizophrenic about fiscal consolidation and growth.
• Perception molds reality.

So, the unsustainability of Euro member fiscal policy is supposedly irrelevant, compared to the insane, self-fullfilling prophesies of investors. As John Cochrane noted, the Euro leaders keep looking for the Big Announcement that will soothe markets into rolling over another few hundred billion euros of debt. Alas, the problem is reality, not psychology.

Regulators Don't Help

One of the reasons why I'm a libertarian comes from my experience with financial regulators. They are totally out of their depth, not understanding where risk really lies because the essential information simply can't be grasped by flying in and looking and talking to people for 2 weeks. I have never worked in a financial firm where I felt I understood what was really going on for at least a couple years. They fill out reports conceived by someone ten years ago that would have caught last decade's big error, and come back next year. The good ones, and there are many, realize the futility, but it's a paycheck.

Anyway, now here's the European regulators repeating the mortgage fiasco. Remember pre 2007 regulators encouraged mortgage lending without qualification. Now, the issue is Greek debt. John Cochrane nail it:

Indebted governments have been pressuring banks to buy more debt, not less. As banks have been increasing capital, they have loaded up even more on “risk-free” sovereign debt, which they can use as collateral for ECB loans. The big ECB “liquidity operation” that took place yesterday will give banks hundreds of billions of euros to increase their sovereign bets...So much for the faith that regulation will keep banks safe....They keep looking for the Big Announcement that will soothe markets into rolling over another few hundred billion euros of debt. Alas, the problem is reality, not psychology

Banks Lend, Charge, Too Much

The suit against BAC/Countrywide was based on disparate impact, basically looking at averages for Blacks and Latinos vs. EveryoneElse. Presumably they controlled for some kind of credit metric too, but as Thomas Sowell has noted many times, it is common to run a regression looking for discrimination with an incomplete proxy for education like whether they had a degree, then put in a dummy variable for race, and find discrimination by looking at the loading on the race dummy, even though given the lower socio-economic status of minorities the variable omits a lot of other important variables (eg, what kind of school? what kind of degree?).

The key point is as follows:

In 2007, for example, Countrywide employees charged Hispanic applicants in Los Angeles an average of $545 more in fees for a $200,000 loan than they charged non-Hispanic white applicants with similar credit histories. Independent brokers processing applications for a Countrywide loan charged Hispanics $1,195 more, the department said.

So, they were charging the victims too much. But another narrative of the 2008 crisis is that they foisted loans upon people who couldn't afford to pay them back. Isn't price the key way a supplier rations goods to consumers? As Jesse Van Tol of the National Community Reinvestment Coalition (NCRC) argues: "the major contributing factor to the foreclosures crisis was reckless and irresponsible lending.” By this, I presume he thinks banks lent too much. In 1994 Obama was party to a class-action lawsuit alleging banks rejected too many minorities.

Back in the bubble, I'm sure a lot of borrowers were less worried about closing costs because many builders, non-profits, and even our government's own HUD would bundle those into a loan. The borrower then has a costless call option: if prices rose--as they had for the past 10 years--they would win big, if prices fell they could walk away and leave the bank with the property. Mortgages are non-recourse, banks can't take anything more than your mortgage back. Thus, I don't see the overpaying minorities as victims here so much as greedy dupes who were part of the mortgage fiasco.

So, banks lent too much at too high a price, when not lending enough. These are simply inconsistent allegations, highlighting the no-win situation for bank lenders. With such rules, no wonder political insiders like Peter Orszag, Henry Cisneros, and Bob Rubin are essential banking executive talent.

True Value Weak Guide

I remember seeing an update of investment bank analysts, and they separated their ability into two groups: those good at predicting earnings, and those good at predicting stock prices. There wasn't much overlap. So I found a spreadsheet from a colleague's thesis that looked at the Pound/dollar exchange rate from 1973-2005, and noted while there was a pretty boring pattern in purchasing power parity ratio, but the market's value of the pound against the dollar fluttered around it quite a bit. It seems that if for some reason you were the only person in the world who knew the inflation rates in these two countries, your investment strategy would only be marginally attractive.

Keynesians Believe in Markets Too

Paul Krugman argues that the fact that interest rates are currently low in the US proves his standard Keynesian diagnosis is correct. Here he is in the NYTimes arguing again why the fiscal and monetary stimulus dials should be turned to 11:

Early on in this crisis I and quite a few other economists — but not enough! — declared that we had entered a classic liquidity trap ... even large government borrowing won’t drive up interest rates, and you can print as much money as you like without causing inflation...[non-Keynesians] declared that soaring inflation was just around the corner, and that interest rates would spike...

So how’s it going? Interest rates have, of course, remained very low. As I post this, the real interest rate on 10-year bonds is actually negative.

He sounds like a caricature of an efficient markets theorist. Well, Markit's A-tranche for the all their vintage mortgages traded above 99 cents on the dollar at the end of 2006. By the end of 2007 they were around 45 cents, and today they all trade around 7 cents.

I remember GM being a zombie for years and their stock defied my expectations for a decade, but eventually equity owners were zeroed out and they went bankrupt. You can go a long time with negative profits if people are willing to give you credit. Yet as any small business lender knows, the only thing that stops these institutions is a lack of cash. Currently, US debt is so liquid, and has such a strong history, it remains a top credit. Yet it's good to remember that when I was in charge of economic risk capital allocations back in the 1990s for bank, mortgages had the lowest economic risk rating for any non-sovereign debt. Now it is on par with credit cards (ie, the worst credits).

I don't think this is going to end well for US debtholders, but time will tell. I don't expect Krugman to ever say he was wrong regardless given he called for a housing bubble in 2002 to stimulate the economy, and later explained that was an economic analysis, not a policy statement, as if that makes a difference.

Willpower for the 99%

The 99% is a story that fits many journalist's favorite narratives about the major problem today: inequality. This seems like altruism, but focusing on the top 1% is also consistent with envy. Many think the top 1% are responsible for the poverty of the 99%, especially the truly poor, those in the bottom quartile. Yet the poor are pretty far removed from anything the top 1% can do. Graduate from high school, get married before you have children, work at any kind of job, even one that starts out paying the minimum wage. Fewer than 10 percent of families that follow his blueprint live in poverty, while 79 percent of those who don't follow the three-step plan end up poor. There is no redistribution scheme imaginable close to this in reducing poverty.

A good Christmas gift for the poor would be Roy Baumeister and John Tierney's Willpower, a great little book with timeless advice. It notes that Willpower has an effect on life outcomes as great as IQ, and more importantly, is much more amenable to nurture as opposed to nature. Perseverence, discipline, patience, all take practice, and make you a happier, healthier, and more productive person. The basic premise comes from the Stanford marshmallow experiment, where a group of four-year-old children were given one marshmallow, but promised two on condition that he or she wait twenty minutes, before eating the first marshmallow. Some children were able to wait the twenty minutes, and some were unable to wait. The children able to delay gratification were tested in later adolescence and found to be psychologically better adjusted, more dependable persons, and had higher SAT scores. Given hardly anything is predictive at that age, this is quite remarkable.

Baumeister has spent much of his career as a psychologists studying and designing tests on willpower. He notes it is a finite resource, and so quitting smoking is much harder when you are also studying (the rigorous study of common sense!). But willpower is like a muscle in that it weakens while you use it, but also strengthens the more you use it, so practicing it daily by doing things like standing up straight and not swearing transfers to other areas. Making decisions is exhausting, it depletes one's willpower, so its useful to design simple rules for much of your daily toil. Being low on energy from lack of sleep or nutrition also hurts your willpower. Basically, practice daily acts of self-control to become more productive.

This reminded me of a Eric Kandel's work on brain memories. He won a Nobel prize by looking at snails and finding that long-term memory, unlike short-term memory, involved the synthesis of new proteins. You get long-term memories through repetition in the same way you build muscle through exercise, so if you practice something daily and it becomes a habit--the muscle memory of a golf swing, the neural memory of saying 'please' and 'thank you'--you actually have altered your brain. Your habits are not just abstract character, but have a biological substrate. This surely encourages cryogenics fans who want to freeze their dead heads in vats of liquid nitrogen so that they can be re-animated in the future.

Life is a journey from ignorance and instinct to higher virtues, including the prudence needed in a complex world. Such prudence comes mainly from acting with thoughtful resoluteness towards the many petty people and temptations around us. Willpower is a great book that reaffirms the power within us to become better people.

The 1 Percent

From Sports Illustrated, discussing the kick return phenom Patrick Peterson, who ran back a 99-yard kick to beat the Rams in overtime:

Peterson, 21, had also ignored instructions. In his case it was an order to not field the ball inside his own 10-yard line. He apologized to Spencer several days later. The two had a long talk, and Spencer informed Peterson that average players need rules. Special players need guidelines. Peterson now has guidelines.

Physical vs. Emotional Trauma

The issue seems to be we remember the emotionally traumatic events more than the physical. From When hurt will not heal, by Chen et al:

The present study examined an important distinction between social and physical pain: Individuals can relive and reexperience social pain more easily and more intensely than physical pain. Studies 1 and 2 showed that people reported higher levels of pain after reliving a past socially painful event than after reliving a past physically painful event. Studies 3 and 4 found, in addition, that people performed worse on cognitively demanding tasks after they relived social rather than physical pain.

Aaron Brown's New Risk Book

I got a copy of Aaron Brown's latest book Red-Blooded Risk, which is kind of like My Life as a Quant by Derman, in that's it's a very personal account of how finance works. I think it's very useful for 50-somethings to write retrospectives like this, because otherwise it's written by people too far removed or too naive. For example Michael Lewis's Liar's Poker is now a classic, but he was a mere bond salesman for 3 years; while his anecdotes were interesting and well-told, his big take-aways on how finance fits with the modern society and the economy were as naive as your typical 25-year old bond salesman.

Brown makes several important points. For example,he notes that the 99% value-at-risk might capture more relevant data, but it needs so much data one should look at 95% value-at-risks. While you can derive this from statistics, it is a practitioner point that clearly is better appreciated from experience. He clearly comes across as someone who understands both the math and how it is applied.

The book tries to deal with how to manage risk, mainly from the point of view of a hedge fund, or something where one is looking at a bunch of strategies. That is, in my experience as a risk manager at KeyCorp, most of our risk there was incidental as a market maker with customer flow, and such risks were rather trivial once one had 'rogue trader' risks under control. His view is more like if you are looking at a book with pairs traders, a momentum trade on government debt, and other such strategies.

Brown mentions early on that he is thinking about risk differently than the standard model, where risk is a cost, and return a benefit. He never really boils it down to something concrete, but rather over the course of the book tries to argue about his view of risk that is qualitatively different. It's kind of like trying to present the meaning of life, not with an aphorism, but rather a bunch of examples. On one hand, this can get you closer to the truth, on the other hand readers can come away confused.

As any professional realizes, however, the gestalt nature of 'risk' limned in this book is the way risk feels to most people--something important and hard to pin down, like meaning and justice--and so Brown's experience is illuminating and should save people a lot of time rediscovering these insights themselves (better to learn via a book than trial-and-error). I'm very sympathetic to the idea that standard risk models are misleading.

Brown's book is very opinionated and has the feel of a smart guy looking at lots of real situations. I think for big ideas, such as risk, meaning, and justice, it's good to have strong beliefs weakly held. That is, you only learn in these ambiguous domains by taking stands, trying to defend them, learning from the process and adjusting your prior prejudices.

It's a cliche to say risk management is the combination of art and science. You need to know something about history, statistics, and programming to be useful as a risk manager. You also need common sense, and that is best informed by experience, which is greatly abetted by reading insider memoirs like this.

Private Sector Incentives

A Northwestern grad student (just like I used to be) blogs on academic papers over at A Fine Theorem, and I was struck by this snippet:

The benefit of capitalism can’t have much to do with profit incentives per se, since (almost) every employee of a modern firm is a not an owner, and hence is incentivized to work hard only by her labor contract. A government agency could conceivably use precisely the same set of contracts and get precisely the same outcome as the private firm (the principle-agent problem is identical in the two cases).

This is wrong. I've worked in small and large firms, and in either case, being part of any initiative that makes money increases your pay and stature rather clearly. Now, the bigger the firm, the more people involved in any initiative, and the more people will exaggerate their involvement with successful projects and downplay their involvement in losers. But the bottom line is the bottom line, and the best way to get your boss to appreciate you more is to help him make more money for the firm. The scope of your command is rarely specified in detail, though increases in scope are the most obvious ways of increasing your power when the 'contract' comes up for renegotiation: work is a repeated game. The government principle has a very different objective function than the private firm principle, the former with a diverse set of stakeholders to satisfy, often with vague and inconsistent objectives, the latter to simply make more profits.

It's true that some people, especially those in over their heads, who are overpaid, dislike productive and smart direct reports because they sense their boss will recognize an attractive replacement. Yet even here the incentive clearly exists for this bad boss to be replaced by his boss, because his boss is not optimizing this position in that case (and watching the bad bosses employees leave when they recognize this is a really good signal that their boss is not a good one). It's also true that salaried employees like cashiers and secretaries may not be proactive about increasing their stature within the firm and simply follow orders, but their bosses recognize this and so are less likely to increase their responsibility.Every ambitious worker tries to make more with less all the time, because they can quantify this, which is the best way to go into an annual performance review. Just because you do not have shares in the firm does not mean you aren't highly incented to make money for shareholders, because the shareholder desire for more profits truly trickles down.

If this kid doesn't appreciate this, he's missing a big part of what makes private organizations work as they do. The nice thing is that it isn't a really fragile result like some of these theoretical models based on the types of agents and some envelope theorem. Common sense tells you the more you appear to be creating profits, the better your future will be in the firm and the industry, and the best way to appear to create profits is to actually do so. Economics, as Tom Sargent notes, is 'organized common sense.' Unfortunately, while you can formalize and thus teach models, you can't formalize and teach common sense, which is why game theory is so ambiguous on these important matters.

Investing Rule

I was on the Chicago Tribune website, and the top banner ad contained the following picture links to a site promoting penny stocks. The link went to a site with those annoying pop-up ads that are difficult to destroy. I think a good investing rule, or at least guideline, is to not buy stocks promoted at websites with half-naked women. Another might be to avoid investments that present +1000% returns as examples (see here or here), which are often common on these sites. As mentioned, average penny stock returns are pretty dismal, the ultimate lottery stocks.

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.