by Vineer Bhansali, PIMCO
- While tail risk hedging is a new and critically important area of modern portfolio management practice, the relative newness of the area means standard frameworks for benchmarking such portfolios have not developed.
- In fact, we’ve found that once the framework for proper tail hedge construction is defined based on key guidelines (including exposures, attachment, cost, and basis risk), the task of creating a proper index becomes relatively straightforward.
- To compensate for insufficient real-time performance measurement, we believe that tail hedges need to be evaluated on the basis of scenario analysis.
This article was originally published in the May/June 2012 edition of the Journal of Indexes, www.indexuniverse.com.
No topic has gathered more interest since the financial crisis of 2008 than the topic broadly called “tail risk management.” The term and its practice have been open to much interpretation; this phenomenon of initial confusion is not particularly different from the growing pains experienced by many other market sectors. Mutual funds, hedge funds, even ETFs at the very beginning of their life cycle operated without much uniformity or proper reference indexes. As the market for tail-hedging solutions evolves, it will become critical that the end-user at least have a framework within which to evaluate the potential and realized costs and benefits of particular practices. We believe that to add value over time, tail risk management has to be active rather than purely passive; thus, a proper benchmarking framework is not simply a luxury but a necessity. The purpose of this article is to start to lay out exactly such a framework, which we have evolved over almost a decade of implementation.
Defining a hedge mandate
As discussed in much detail elsewhere1, a small set of inputs or guidelines is the natural starting point for defining a tail hedge mandate. In our view, the minimal set consists of the following:
1. Exposures
2. Attachment
3. Cost
4. Basis risk
The first step is quantifying exposures. Our analysis of the long-term history of many different types of assets shows that a small set of risk factors drives the returns of these assets. The two major secular exposures are the equity beta and the interest rate or duration exposure. In addition, over cyclical periods, factors like liquidity, currency exposure, momentum and monetary policy also play important and significant roles. In our practice, we first try to quantify the exposures of each underlying portfolio to these key factors, both for normal and stressed periods. Interestingly, both our research and the work of others show that even very diversified portfolios exhibit similar exposures to the key risk factors, with equity beta as the dominant risk exposure.
The second step is to define what we have called the “attachment” level (taking a term from the reinsurance industry). The closer the attachment level is to the current value of the portfolio, the higher one should expect the cost of the tail risk program. Generally, we believe that broadly diversified portfolios should have an attachment level anywhere from 10% to 15% below the current portfolio value.
This brings us to the important question of cost. We generally do not believe that tail hedging can be done efficiently in a perfectly costless manner over short-term horizons. Yes, there are structures (especially exotics) that purport to reduce the cost, or in many cases even eliminate the cost, but usually they consist of embedded sales of options that one would frequently rather not sell. Instead of this hidden discount, we believe that an explicit cost target is essential both to thinking of tail risk management as an asset allocation decision and as a commitment that one can continue to support in periods where fat tail events do not occur. Because of the natural difficulty in forecasting the time and form of the next tail event, we believe that tail hedging is an “always on” part of any risky investment portfolio. Our empirical and theoretical research validates the belief that over longer periods (three to five years), tail hedging is generally self-financing when one accounts for both the ability to tilt portfolios more aggressively and following a systematic approach to rebalancing in the presence of such hedges.
Finally, one has some freedom to replace what might be expensive direct hedges with relatively cheaper indirect hedges, taking advantage of the tendency for correlations to increase, especially when extreme events happen. This cheapening comes with a trade-off, that the indirect hedges will not perform as well as the direct hedges conditional on the extreme event happening. To quantify this basis risk, we specify a level of confidence within which the likely outcomes of the actual portfolio are likely to fall relative to the direct hedge through simulations. The performance of a particular hedge program should be quantified in terms of the trade-off between basis risk and cost savings relative to a low- or no-basis-risk benchmark.
Creating a proper index
Once the framework for proper tail hedge construction is defined, the task of creating a proper index becomes relatively straightforward. If the benchmark is equity beta, we can use the most liquid traded market sectors that carry the key risk factor exposures to start with a shortlist of potential benchmark constituents. For instance, it would make sense to use S&P 500 Index options close to the maturity of the hedge mandate as a reference instrument, since by definition this index has an equity beta of 1 to itself (one can choose another equity index for this reference, e.g., the MSCI World, if that is the index of reference for the underlying portfolio). If the reference portfolio is a blend of equity beta and fixed income – for instance, something like the MSCI World Index combined with the Barclays Aggregate Bond Index – then the tail hedge will be a blend of the best equity beta and duration hedges for this combination. The best reference market instruments will therefore be options on the equity and bond indexes. But since options on bond indexes are not very liquid, it makes sense to select options on tradable markets such as Treasury futures for index construction. Also, note that tail options on a portfolio are not the same as the sum of options on the individual constituents, so adjustments for the correlations of the underlying constituents need to be made.
Once the proper sectors are identified, the next step is to set a “strike” for the portfolio of reference market options. As an example, if the attachment level for an overall 60% equity, 40% bond portfolio is set at 85% (i.e., 15% out of the money for the whole portfolio), then assuming that the bond part remains static, the reference equity option strike is 15%/0.60 = 25%. So the natural strike of the reference equity option is 25% out of the money. One can proceed in a similar manner for the other underlying risks as a crude starting point.
The advantage of constructing the basket of reference securities in such a way is that they can be monitored in real time. Options-based tail hedges have various “Greeks,” such as time-decay, gamma, vega, theta, etc., which are very dynamic and have to be actively monitored and traded. The value added by an investment manager is proportional to how the actual portfolio of hedges behaves over time relative to the theoretical benchmark. It also solves the problem of behavioral aversion to cost. Once the actual hedge cost and time decay is put relative to the cost of a theoretical hedge, it is much easier to commit to the cost as a long-term asset allocation decision and to compare this cost versus the implied cost of de-risking or buying government bonds. The important point is that all types of tail hedging cost something, and this includes de-risking and moving to cash. The process of going through the relative value comparison of different types of hedges allows the investor to anchor the tail-hedging analysis to something realistic.
We should emphasize that the use of market-traded options is a simplification that works only if the underlying hedge objective is rather plain vanilla. If the objective is more complex, e.g., “hedge so that at no point in time the portfolio suffers a loss more than x percent,” the reference index security would have to be more of an exotic option such as a knock-in option. While these options are traded heavily in the over-the-counter markets, their prices are not as easily available as vanilla index options. More complex replicating option portfolios can be constructed to index these payoffs. Complexity vs. transparency is an important trade-off when it comes to tail hedging. We generally err toward simple portfolios and hence simple benchmarks to measure them against.
Measuring performance
For traditional indexes, the task of performance measurement is relatively straightforward. One can look at the returns of the actual portfolio versus the index and discern whether the decisions of the manager are adding or subtracting value. For tail risk hedging, the problem is only simple if all the hedges are relatively plain vanilla and the underlying instruments are liquid and replicate the portfolio without any basis risk. The moment the hedges become complicated, performance measurement takes a new twist. The reason simply is that the current price of the hedge does not reflect the potential it has for a large tail payoff, and since tail events are rare events, observation of a few nontail periods is not sufficient to identify the prospects of the tail hedge. Naively, a tail hedge could look like it is performing better than a reference index of securities by losing time value slower than the reference hedges, but this is most likely to offer less potential of payoff if there is a jump event in the market (if the option hedges have less time decay, they probably, though not necessarily, have less gamma as well). To compensate for this shortcoming of real-time performance measurement, we believe that tail hedges need to be evaluated on the basis of scenario analysis. By identifying scenarios of concern and shocking the underlying market factors at different horizons, one can evaluate the potential of these hedges to pay off in the situations that matter. Robust technology and sensible stress-testing systems are thus of paramount importance for this exercise.
Conclusions
While tail risk hedging is a new and critically important area of modern portfolio management practice, the relative newness of the area means standard frameworks for benchmarking such portfolios have not developed. In this article, we sketched the rudiments of benchmark construction that we have used. While much work remains to be done, we believe that standardization and benchmarking in this area will result in the same value added to investors as it has done in the areas of traditional equity and bond portfolio management. Most importantly, it will give end-users a means via which they can quantify the “distance” of a bespoke tail hedge portfolio versus an easily measurable index to evaluate the cost versus benefit trade-offs.
1. See, for example, V. Bhansali, “Tail Risk Management,” Journal of Portfolio Management, Winter 2008.
The products and services provided by PIMCO Canada Corp. may only be available in certain provinces or territories of Canada and only through dealers authorized for that purpose.
Past performance is not a guarantee or a reliable indicator of future results. All investments contain risk and may lose value. Tail risk hedging may involve entering into financial derivatives that are expected to increase in value during the occurrence of tail events. Investing in a tail event instrument could lose all or a portion of its value even in a period of severe market stress. A tail event is unpredictable; therefore, investments in instruments tied to the occurrence of a tail event are speculative. Derivatives may involve certain costs and risks such as liquidity, interest rate, market, credit, management and the risk that a position could not be closed when most advantageous. Investing in derivatives could lose more than the amount invested.
There is no guarantee that these investment strategies will work under all market conditions or are suitable for all investors and each investor should evaluate their ability to invest long-term, especially during periods of downturn in the market.
This material contains the opinions of the author but not necessarily those of PIMCO and such opinions are subject to change without notice. This material has been distributed for informational purposes only and should not be considered as investment advice or a recommendation of any particular security, strategy or investment product. Information contained herein has been obtained from sources believed to be reliable, but not guaranteed. No part of this material may be reproduced in any form, or referred to in any other publication, without express written permission.
© 2012, PIMCO.
