Wag the Tai - The New Theory of 'Iceberg Risk'
‘Iceberg Risk’ is a new theory which attempts to improve on existing portfolio strategy. Here, Kent Osband the creator of ‘Iceberg Risk’ outlines the key benefits.
Q: What do you mean by iceberg risk?
Osband: Two things. First, situations where risks tend to clump together, i.e. where your ship does not normally hit much ice but, when it does, it turns out to be a disaster. You can also think of it as ‘when it rains, it pours.’ Second, situations where you do not really know the risks – so much that they are obscured like an iceberg underwater.
Q: What is the problem with standard portfolio theory?
Osband: Standard Markowitz/Sharpe theory presumes multivariate normality, which amounts to saying all your risks are bell-shaped. In such a happy world, knowing the overall means, volatilities, and correlations suffices to answer any possible question about risk. Unfortunately, that cannot deal with iceberg risk. Rather, it just assumes it away. No skewness, no kurtosis, etc.
Q: Why does standard theory ignore skewness and kurtosis?
Osband: Tractability. It is no big deal to estimate the skewness and kurtosis on individual assets. But in order to estimate portfolio skewness and kurtosis, which is what really matters, you need to measure the higher cross-moments too, all the co-skewnesses across assets and co-kurtoses and so on. Their numbers multiply so quickly that you can easily wind up needing millions of parameter estimates – millions of parameters that are hard to estimate reliably, much less use in spreadsheets or even understand what they really mean.
Q: Do not techniques like Value-at-Risk (VaR) address iceberg risks?
Osband: To some extent, yes. At its best, VaR tells you the risks of various big outliers, but it cannot tell you how to weigh those risks against the associated rewards. You end up having to impose some ad-hoc criterion, such as ‘maximize expected return subject to the 1%-ile risk not exceeding X.’ I say, why not the 2%-ile or the 0.5%-ile? Are you really willing to put an absolute cap on risk no matter how high the rewards are? Of course not.
Q: What do you think about a hybrid approach combining Markowitz and VaR?
Osband: That is like trying to breed a unicorn by mating a horse and a narwhal! Noble aim, but the two species are not compatible. Markowitz implies a certain set of VaR estimates based on normal distributions, so if you buy normality you do not need an extra VaR overlay. Plus, any extra information that VaR gives cannot be embedded directly back into Markowitz.
Mind you, I am not against risk managers trying to take the best from both worlds. Good judgment can cure a lot of sins. But it is misleading to claim that those judgments are rooted in science, when the core assumptions are not even internally consistent. Unfortunately, much of the risk community seems too inured to the contradictions to take notice.
Q: How does your approach solve this problem?
Osband: I model the world as a probabilistic overlay of different scenarios or regimes. A regime refers not to a particular outcome but to a general market climate, e.g. a bear market, a bull market, a choppy market. In any given regime, the risks are bell-shaped, but the specific features vary by regime. For example, in a bull market, the mean drift is up. In a bear market, it is down. In a crash regime, it is way down.
Assuming away iceberg risk within a given regime should not cause any problems. If it does, then just add an extra regime. For example, you might carve out an extra regime to handle another huge terrorist attack. The hard part is coming up with appropriate probability assessments for the different regimes. You might assess, say, a 10% probability of another crash, a 20% probability that the market flies, and a 70% probability that it trends mildly up. All your results will hinge on that.
Q: Does your theory indicate how to form those assessments?
Osband: No, at least not in its current incarnation. But let me emphasize that those assessments are what any good risk manager should be focusing on. Otherwise, you would risk missing the iceberg for the ice cubes. Plus, it is a lot easier to brainstorm with non-quants about future regime odds than about means or covariances within a regime. For the latter, I suggest relying on historical statistics. Save your noggin for the important stuff.
Q: Is there any other information the model needs?
Osband: Yes. Risk aversion. The model needs to pick a risk aversion parameter. Ideally it should pose a few ‘which portfolio do you like better’ questions. But, if needed, the model can simply infer an average risk aversion parameter from market behaviour as a whole.
Q: Can you really compress attitudes toward risk into a single parameter?
Osband: Interestingly, yes. At least you can if you assume people never knowingly take sucker bets — bets probabilistically guaranteed to lose them money — and if you cannot differentiate your clients by wealth. A couple of chapters in the book are devoted to explaining that, as well as how to estimate risk aversion.
Q: So, do you wind up with a simple formula for optimal portfolios?
Osband: Not simple, but as simple as it can be. The book summarizes the calculations in a few short cookbook recipes. If you do not like math, then have someone else do the cooking.
Q: What are some of the other benefits of this approach, and how does it compare with other measurements?
Osband: To begin with, it is intuitively appealing because the answers are expressed in terms of risk-adjusted returns. Moreover, the same techniques that handle non-normal risks also handle options and other non-linear assets. All you need are the options’ deltas and gammas at the midpoint of every regime. Last but not least, all this can be done in real-time in Excel, whereas most of the alternatives require computationally expensive Monte Carlo simulations.
Q: Is it easy to implement?
Osband: If all the data are in place and properly tagged, yes. The cookbook recipes involve a handful of formulas that take a few minutes to type in, copy and paste. Fixing stupid mistakes in the first step takes a few hours to a few days; at least that is what it took me. The only really hard part, like for any risk-analysis system, is wiring in the data.
Q: You work in a hedge fund. Do you use it there?
Osband: A simple version, yes. Three of us built it within a few weeks, and most of that work went to automating updates since our positions are changing all the time. We still have not wired in the derivatives. We are a start-up, so we all wear a few hats, and most of my time is spent working on trading models.Kent Osband is author of Iceberg Risk: An Adventure in Portfolio Theory. Former manager of a global bond fund for CI Funds of Toronto, he currently heads quantitative trading and risk management for Drawbridge Global Macro Fund in New York.
This interview first appeared in the GARP Risk Review, Issue 10, Jan/Feb 03.