Re-Blog: Tales of Tails
Note: The following blog post originally appeared on June 27th, 2010 and is part of a continuing year-end 'best of' series, calling up old posts that some readers may have not seen before. I have removed some of the references to then-current market movements and otherwise cut the article down to the interesting bits. You can read the original post here.
...I also raised my eyebrows at an article in the UK Telegraph which declares that the Fed is considering a "fresh monetary blitz" since the recovery is faltering. I am always happy to be skeptical when an article doesn't name names, but this seems to me to be fairly likely to be true:
"Key members of the five-man Board are quietly mulling a fresh burst of asset purchases, if necessary by pushing the Fed's balance sheet from $2.4 trillion (£1.6 trillion) to uncharted levels of $5 trillion."
The strategy makes sense, if you believe that the long-term effects of dramatic monetary policy movements can be evaluated over a period of a couple of quarters. I would not be surprised at all to discover that the thinking at 20th Street and Constitution Avenue is something along the lines of "hey, we did it once and didn't cause inflation, so why not take out the paddles again? CLEAR! ZAP." I've written before of the odd set of speeches we saw earlier this year describing a wondrous alchemy that the Fed seemed to believe they could accomplish: buy assets rapidly to save the economy by keeping rates low and adding liquidity. Sell the assets without completely reversing the effect by doing so slowly. Clearly, if there is real belief that the Board can pump and dump without the "dump" causing any problems, then for God's sake why not pump?
Obviously, that's a bunch of hooey, but I remain wary that there may be those who believe it.
The market on Friday was led (and maybe even supported) by financial stocks, because the market finally learned the form of the financial reform bill. It is bad, and will cause severe damage to bank earnings. It isn't as bad as some people feared, but it is about as bad as was ever likely to become law. Prop trading at banks is still banned, and banks will have two years to push trading of commodities, non-investment grade bonds, and CDS that are not cleared through an exchange to separately-capitalized subsidiaries. Most derivatives will have to be cleared and traded on exchanges, which means less customization (bad for dealers, and bad for clients too). This law will be bad for turnover, bad for margins, and will cause leverage ratios to decline (probably the only reasonable part of the prescription, from my view). The Dupont model tells me those three things imply much lower ROE.
So why did bank stocks rally? This is worth a deep reflection because it explains something about markets.
Bank stocks rallied because as bad as the legislation is, the fact that we now know the form of the legislation removes the most onerous tail risks.
Bob Merton, many years ago, observed that the equity of a company can be thought of as a call option on the value of a firm: the value can only go to zero, if the firm is insolvent, but can be worth a great deal. So what do we know about options? One of the things we know is that a great deal of the value of an option comes from the expected value of unlikely, extreme outcomes. If you remove the chance at the home run, an option gets much cheaper.
This is one big reason that bear markets often end with a sharp rally off the lows (although please note that it does not follow that every sharp rally implies an end to the bear market!) - once the disaster case, the chance of an outright crash or broad economic or financial calamity, recedes in probability, the value of equities rise appreciably. A company which avoids bankruptcy by a hair will see its stock rise dramatically when the chance of losing everything goes away. Observe the behavior of many of the financials during the crisis. When TARP and other bank-supportive mechanisms began to have traction the sector leaped, not because earnings were about to be multiplied 10 times but because the fear of zeros greatly receded.
(Aside #1: Most analysts, of course, look at equity values as related linearly to earnings, and in normal circumstances they are. ...a PE of 25x is rich, 15x is cheap, for example. But this is likely because behavioral biases prevent analysts from considering the value of the disaster which they think is very unlikely. In any case, a 15x multiple might be quite expensive indeed compared to a 25x multiple, if the former company is about to receive a legal judgement that could potentially destroy the firm. Indeed, one real problem with conventional investment analysis is that the 15x multiple stock might be cheap, or the multiple may in fact be a sign that tail risks are higher for this equity than for the 25x one. Buying enormous dividend yields is often unproductive because the high yield implies a market belief, often correct, that the dividend is not likely to be paid or paid in that amount.)
(Aside #2: Because so much of the value in an option comes from the tail, evaluating options using simple Black-Scholes when the underlying risk isn't lognormal can be extremely dangerous, especially with exotic options that have path-dependent valuations and with options on underlying instruments that are known to have a high likelihood of non-linear performance - near-bankrupt equities, for example. Black-Scholes implied vols are nearly useless in such a case).
So, owning a stock or stocks generally when the tail risks are about to recede is a good recipe for making sparkling returns. But we have another name for this sort of investing strategy: "catching a knife." You can own an AIG-like bounce, but also get run over by Lehman. On the flip side, because as an equity investor you own these negative tail events naturally, you can add a lot of value by avoiding the blow-up.
Rising volatility, then, tells you two things: first, it tells you that the market's sense of the risk of a possible calamity is growing; second, it tells you that once these fears recede you might earn a solid return. You already knew this; it's why the VIX is considered a contrary indicator by some.
Does it make sense to be investing more, then, when a blowup might happen, or investing less? As it turns out, the answer to this question is not entirely clear but thanks to the Kelly Criterion we can make some observations. The Kelly Criterion describes the optimal bet size, as a proportion of the bankroll, for a series of uncorrelated bets with a given edge and payoff. The simple observation (which becomes a lot less simple after they start involving the math) is that you want to bet more of your payroll if you are (a) getting good odds and (b) are very confident of the outcome. That is, your bet size should increase if you are getting good odds, and have a good edge. Kelly worked out the math to determine what the optimal bet size should be under certain conditions.
The relevance here is as follows: when a crisis hits, two things are happening to you as an equity investor. First, you are becoming more confident that the market will reward you for buying when everyone else is selling, because (as noted above) unless the world actually does end you are likely to be getting a good price. Second, though, you need to recognize that the increasing chance of debacle implies a worse payoff. In April of 2008, the chances of losing everything the next day were pretty slim. In mid-September 2008, the chances were appreciable that a bunch of your portfolio might be in trouble. So your edge (confidence in winning, if the bet was repeated a bunch of times) was growing, but your odds (payoff if you win, relative to your loss if you don't) were worsening.
The schematic below shouldn't be taken literally, but is meant to illustrate the basic relationships.
When potential payoffs worsen, you need a lot more confidence to bet big.
These lines are the pure results from the Kelly formula for the indicated inputs. Perhaps an investor might consider his/her "bankroll" in this case to be the maximum portfolio concentration in equities. Obviously, if you are extremely confident that you are going to win, then no matter what the payoff you should be making a pretty reasonable bet; therefore, the lines converge on the right. But as we move left, we get a sense of the tradeoff between the edge and the odds. When volatility is rising, the investor is moving to the left, implying a lower confidence of a payoff; if the market is trading to lower prices, it improves your odds but you can see that you would need vastly better odds to counteract the effect of increased uncertainty. I would suggest that in the range of normal investor confidence, rising volatility implies that you should tend to be taking chips off the table, even though it means you may miss a minor pop if the world doesn't end.
We are not currently in a crisis quite like what we saw in 2008. But the elevated levels of implied volatility suggest that crisis is not so far off as we would like to see it. I think this means that we should be avoiding the possibility of the long negative tail, and taking chips off the table.
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