# Unlocking the full potential of ILS

Until recently the performance of insurance-linked investments was not readily available as a composite but had to be collected from the data of individual managers in that space. The only proxies available were the Swiss Re Cat Bond Indices. Those indices however, as their name says, reﬂ ect only the performance of the traded cat bonds, which are just one part of the underlying investment universe of those funds.

In order to raise the visibility of this very attractive asset class, ILS Advisers, an independent ﬁ rm of advisers, and swissQuant Group, an independent provider of quantitative decision tools and analysis, approached Eurekahedge in 2011 with the idea of launching a new index that reﬂ ects the performance of the entire insurance-linked investment space, rather than only a part of it.

Early on it became clear that the index should compare apples with apples and therefore it was decided to include only managers whose focus was on non-life risks and who do not allocate more than 30 percent to life risk. In terms of the underlying investment vehicles it was decided to leave this criterion open. It was especially clear that limiting it to cat bonds would be too narrow and not do justice to the investment opportunities available in the space.

Furthermore, we wanted to make sure that we did not include duplicate funds; for example, if there were two funds from the same manager with the same strategy, differentiating only in the reference currency, then just one would be included. If on the other hand two funds with different strategies are available from the same manager, both funds are included.

Another important decision was the start date. In the institutional world, where everybody is looking for long track records, one would like to go back as far as possible. However, based on our research, it became clear that before 2005 there were not enough funds available to create a representative index.

The result of all the work is, in our view, very convincing. Since its inception in December 2005 through August 2012, the Eurekahedge ILS Advisers Index has returned more than 7 percent per annum, with a volatility of 2.5 percent and a Sharpe Ratio of more than 2.

**Making the index investable**

Given the attractive features of the Eurekahedge ILS Advisers Index it was not long before the question of how to make it possible to invest in the index arose. While it is possible to physically replicate the existing pure cat bond indices it is more difﬁ cult once private transactions are added to the investment universe. Most institutional investors, however, can access private transactions only through the specialised funds. As a result, the only feasible way to go is to track the index by investing in the constituent funds of the Eurekahedge ILS Advisers Index.

**The need for tracking**

An index is, by deﬁ nition, constructed using a strictly deﬁned constituent universe and transparent formulae and rules for calculating the weight for each constituent. It may, however, not always be the case that all the constituents of the index are investable at all times, for example when a fund closes for new investors but remains in the index.

An investable index fund on the other hand requires this by deﬁnition. In this case the need arises for a robust index tracking solution that invests in a subset of the index universe (the investable funds) whose deviation from the index itself is limited.

Standard approaches to index tracking would however not work, due to the unique risk and return characteristics of ILS products. The securities typically provide stable premium income in good times, resulting in a smooth upward-sloping line on the performance chart. However, from time to time, large and unexpected losses are caused by triggered insurance events, which distort the otherwise stable performance. This behaviour leads to a heavy-tailed and skewed return distribution, which deviates strongly from the normal (Gaussian) bellshaped distribution of returns commonly used among practitioners.

Conventional index tracking solutions assume normality and use standard deviation to measure and control the tracking error. This renders them improper for the purpose of tracking an ILS index. Making these assumptions for ILS will gravely underestimate the tail risk, due to their signiﬁ cantly non-normal behaviour.

**The swissQuant Group approach**

For an ILS index tracker to be successful, two requirements have to be met. First, the appropriate model for the returns has to be used—one which is able to correctly capture the heavy tails, skewness and other non-normal properties of ILS. Second, a measure of risk which is more appropriate and suitable for the job than standard deviation, has to be selected. The swissQuant tracking solution meets both requirements.

In order to capture the stable but occasionally loss-stricken performance of ILS, jump diffusion-like models are used. These incorporate a stable, low-volatility drift component as well as downward jumps from a heavy-tailed loss distribution, such as the Pareto or Gamma distributions—a suitable match for ILS.

To measure and control the true risk embedded in ILS, a risk measure called CVaR—conditional value-at-risk (also known as expected shortfall, or tail risk)—is used. CVaR as a risk measure has many advantages compared to the more commonly known value-at-risk (VaR) and, even more, compared to standard deviation. The CVaR, as opposed to the VaR, not only tells you what loss level won’t be exceeded more than 5 percent of the time, but also what you can expect the size of the loss to be when it does occur. Compared to standard deviation, CVaR has the advantage of being a downside risk measure, enabling you to limit the risk of loss while maintaining upside potential. Furthermore, CVaR is model-free, in the sense that no assumption of normality of returns is necessary.

**An independent gauge**

With the Eurekahedge ILS Advisers Index, investors and other market participants have the possibility to gauge the risk and performance of the ILS market as a whole and not only parts of it. The investable index fund additionally enables investors to invest directly in an index that is representative of the entire ILS space in a simple and cost-efﬁcient manner. Due to the signiﬁcantly non-normal behaviour of ILS, they cannot be tracked using standard approaches that assume normality and use standard deviation as a risk measure.

The swissQuant Group approach uses realistic models from insurance mathematics to closely replicate the true, skewed and heavy-tailed ILS return distributions. The use of CVaR as a risk measure makes it possible to limit downside risk, keep upside potential and remain free of distributional assumptions.

We hope that heightened visibility and simpliﬁed accessibility through a passive approach will lead to many more institutional investors investing in this unique asset class.

Stefan Kräuchi is a partner at ILS Advisers. He can be contacted at: sk@ilsadvisers.com

Aljosa Bilic is a quantitative analyst at swissQuant Group. She can be contacted at: bilic@swissquant.ch