Saturday, January 31, 2009

The Nature of Risk - Alpha

Risk seems to encompass:
i) volatility (how much the price of an asset fluctuates);
ii) holding power (whether an investor can hold on to an asset for a certain period of time);
iii) the probability of the permanent loss of capital (what happens at the end, the final payout).

If an investor is patient, smart, and attentive, volatility works in her favor. She understands value, so can quickly buy when prices are depressed and sell when prices are elevated. Yet this depends on holding power, which can be contractual or psychological. Since no one can time the exact bottom, an investor needs to buy and hold on, either till the price swings back up temporarily (volatility) or till the end when the price converges to the final value. If an investor takes outside debt or equity and these providers pull out before the upswing or value convergence, she does not have contractual holding power. If she can't stomach the risk mentally, she does not have psychological/emotional holding power. All three are linked: vol, duration/holding power, and final payout probabilities all matter in defining risk. I'm not sure if there is a single equation or metric that can capture it all (VAR, cVAR, drawdowns, etc.).

As Vega notes, models and risk managers failed horribly, for many reasons. The most honest explanation I've seen of this failure came from an anonymous article by a risk manager at a big investment bank, here: Confessions of a Risk Manager. As the risk manager notes, multiple assumptions about risk were wrong. Flawed models failed. And incentives were skewed, allowing traders to take on much risk and get the upside, but neither trader nor risk manager bore a share of the downside (heads I win $10 million, tails the bank loses $10 billion).

The saddest part of this are the reports of the major bank heads, who had no clue about the risk being taken in their firms. This happened even at the best firms, and continues today. For example, the CFO of Goldman Sachs, Jeff Viniar, commented in late 2007 regarding one fund that: “We were seeing things that were 25-standard deviation moves, several days in a row. There have been issues in some of the other quantitative spaces. But nothing like what we saw last week.” This statement shows that at least one bank head doesn't understand risk, since a 25-standard deviation event is only supposed to occur once a few million years (i.e. never). I talked to one banker today, who mentioned that the largest investment banks in the US and Europe (including his own - one of the world's largest) are fully insolvent. They haven't taken anywhere near the amount of losses on their assets to reflect reality. They can't, because that would show their insolvency. So if they can't acknowledge reality, how can they acknowledge risk and uncertainty?

To end, Frank Knight's distinction in Risk, Uncertainty, and Profits is important:
Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated. . . The essential fact is that "risk" means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomenon depending on which of the two is really present and operating. There are other ambiguities in the term "risk" as well, which will be pointed out; but this is the most important. It will appear that a measurable uncertainty, or "risk" proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all. We shall accordingly restrict the term "uncertainty" to cases of the non-quantitative type. (emphasis added, I.I.26)

Basically, the difference between risk and uncertainty is:
i) risk = a measurable, finite set of outcomes, with probability and magnitude known;
ii) uncertainty = an unmeasurable set of outcomes, where either one or both, probability and magnitude are not known, or the set isn't finite; hence anything not "risk."
Unfortunately, the line between the two isn't often clear.

The Nature of Risk - Ari Paul

What is risk? Is it the volatility of returns? The threat of a permanent loss of capital? Is risk the chance of a significant drawdown, and if so, what defines "significant"? In the past year, Volkswagen briefly became the biggest company in the world and much of Wall Street ceased to exist. According to sophisticated quantitative models, we witnessed once a millennium, 5 standard deviation moves and even the statistical equivalent of pigs flying and hell freezing over.

Where did the models and risk managers go wrong? The simplest explanation is that they were the unlucky victims of a rare "black swan" event, but there was no black swan. The collapse wasn't started by a natural disaster or terrorist attack. A speculative bubble and credit pyramid were built up over the last 7 years and are now being unwound. Like with most bubbles, traders and analysts examined data from the last few years and extrapolated the safe returns forward. It's like looking at last year's weather and concluding you won't need an umbrella this afternoon…even after it starts raining.
Let's take a closer look at the common risk metrics through the lens of two simple games. In the first game, we flip a twelve sided die. If it lands on an even number you get $3, if it lands on odd you owe me $1. In the second game we flip that same die; if it lands on a 12 you get $12, otherwise no money changes hands. Which game is riskier and which game would you rather play? Your expectation in both games is the same: you'll average a $1 profit for every roll. By most common investment metrics, the second game is riskier; it has more volatility and a lower sharpe ratio. Yet common sense tells us that the first game must be riskier because we are exposed to unlimited losses and a high likelihood of being down after a few rolls. In the second game we can sleep easily at night and just keep playing until we win. We can construct similar games to expose the faults of VAR and the Capital Asset Pricing Model as well.

As this example suggests, risk metrics can be irrational under the best of circumstances, and they can be downright devastating when correlations and volatility change as they have in the past year. What's the alternative? If not with complex metrics, how can we manage risk? I'll leave that for my next post.

Sunday, January 25, 2009

First Post - Why We Blog - Alpha

So why keep a blog about how to think about investing, markets, economics, macro forces, industries, securities, etc.?

Three reasons:

Write well to think well. The first reason for an investor to write well is that it forces you to think well, that is: be concise (have economy in thought); simplify (avoid too much complexity and the bounds of rationality); embrace multiplicity (know all the variations of the future and speculate on how you could be wrong); and take strong positions/forecasts within one's circle of competence (otherwise not write or invest in something outside one’s circle).

Stay disciplined and informed. What hurts great investors isn’t failure, but success. After years and the first hundred million of carry, most talented investors lose their drive and hence their edge. They don’t stay disciplined; they don’t do the necessary daily work; they spend money lavishly in their personal lives and lose respect for frugality and their investors’ capital.

Communicate ideas clearly (or just have fun). With enough labor, I hope to someday write as well as Keynes, Orwell, Vidal, and Hemingway. That would make me happy – to develop a style and write something which is read decades from now. Also, as an investor I want to inform my limited partners about how to think. While the first and main thing limited partners care about is performance, they also care about information, that is, they want to be informed. They want to understand how you’re taking risk on their behalf, with their hard-earned money. They want to understand if you’re speculating or investing. They want to know you’re still passionate about protecting and compounding capital. Ultimately writers don’t write for others, they write for themselves. We write because we like writing. We have something to say.

For context, consider George Orwell's Why I Write.