Diversication Benets of Cat Bonds: An In-Depth Examination Abstract We investigate whether the inclusion of Cat Bonds in portfolios composed of tradi- tional assets and common factors is benecial to investors. Various mean-variance span- ning tests show that under dierent market conditions, the addition of Cat Bonds gives rise to previously unattainable portfolios. By way of the Engle (2002) Dynamic Condi- tional Correlation (DCC) model, we nd that including Cat bonds increases signicantly the time-varying Sharpe ratio and the Choueifaty and Coignard (2008) diversication ratio. Cat Bonds provide needed diversication during critical times particularly during episodes of crisis and of high volatility. Under the second-order stochastic dominance ef- ciency (SDE) tests, the null hypothesis that portfolios without Cat Bonds are ecient cannot be rejected. Out-of-sample analyses indicate that the performance of portfolios with Cat Bonds included varies depending on the performance measure employed, the portfolio optimization technique used and the assets or factors considered. Keywords: Catastrophe Bonds, Asset Allocation, Factor Investing, Diversication, Stochas- tic Dominance Eciency, Mean-Variance Spanning, Portfolio Optimization, Time Vary- ing, Regime Switching, Dynamic Correlation. 1 Introduction With average annual temperatures rising and frequencies of natural disasters increasing in all parts of the world, dire environmental impacts, vital socio-political and important economic problems associated to global warming are growingly alarming. In its 2007 report (Bernstein et al., 2008), the Intergovernmental Panel on Climate Change (IPCC) describes the eects of global warming that are already being felt and the IPCC expects these eects to grow in magnitude and costs in the future.1 Catastrophic risks associated with these environmental phenomenon are of great importance for nancial institutions, markets, all quarters and constituencies as well as governments whose stakes are greatly aected by natural disasters. It ensues that increases in the frequency and severity of natural catastrophes in recent years have propelled the use of alternative risk-transfer instruments for managing catastrophic risks. To cover against disaster risk and transfer some of the risks they do not want to retain, insurance and reinsurance companies typically use reinsurance or retrocession (reinsurance for reinsurers). However, for catastrophic natural disasters, the margins charged by rein- surers are often prohibitive. Therefore, insurance-linked securities (ILS) have been launched to cover these types of losses at relatively lower costs. Among this alternative risk transfer instrument, the most important asset class is catastrophe bonds (Cat Bonds hereafter), see Cummins (2008), Bouriaux and MacMinn (2009), Cummins (2012), Barrieu and Albertini (2010), Smack (2016). The size of the outstanding catastrophe bond and insurance-linked securities markets at the end of 2018 is $37.8 billion.2 Naturally, Cat Bonds returns incorpo- rate risk premiums rewarding investors who are willing to assume a hardly diversiable and hedgeable risk. In fact, among ILS, Cat Bonds are the only nancial instrument securitized and traded in secondary markets. As a complement to reinsurance, Cat Bonds have been used to transfer the risk attached to the highest layers of reinsurance. While both reinsurance and Cat Bonds oer companies a means to transfer disaster risk, only Cat Bonds use the capital markets for this purpose, see e.g., Canter et al. (1996), Krutov (2010), Kish (2016). There are two main benets from using Cat Bonds: 1- Their presumed zero or very low correlation with other nancial assets allows for additional diversication to a portfolio e.g., Litzenberger et al. (1996), Hoyt and McCullough (1999), Kish (2016), Sterge and van der Stichele (2016) and 2- Their historical risk-adjusted returns are attractive to investors, see e.g., Schöchlin (2002), Kusche (2013) among others. In fact, Cat Bonds are considered as a high-yielding xed income asset class with returns independent from macroeconomic risks and cycles. In addition, Cat Bonds show a high level of intra-class diversication provided by their correlation to dierent and independent risk factors arising in dierent parts of the planet (i.e., tsunami, hurricanes, oods, etc.). Therefore, Cat Bonds, exhibiting a low 1In 2018, the IPCC sounds an alarm on "the impacts of global warming of 1.5 degrees Celsius above pre-industrial levels and related global greenhouse gas emission pathways, in the context of strengthening the global response to the threat of climate change, sustainable development, and eorts to eradicate poverty", Special Report on Global Warming of 1.5oC at https://www.ipcc.ch/. 2See Q4 2018 Catastrophe Bond & ILS Market Report at http://www.artemis.bm and Insurance- Linked Securities market update, Swiss Re, August 2018 at https://www.swissre.com. 1 correlation to other traditional asset classes (e.g., equities, bonds and commodities) oer institutional investors a great portfolio diversication with an appealing risk-return prole. Institutional investors (mainly pension funds and hedge funds) looking for a steady, relatively high-yield and exotic asset class in the current low-interest rate environment are said to be lining up capital to support the increased appetite in the insurance-linked securities market for Cat Bonds (see for instance, Sterge and van der Stichele (2016), Kish (2016) and Carhart et al. (2014)). The purpose of this paper is to examine in-depth whether the addition of Cat Bonds to an investor portfolio does eectively provide him the benets of diversication. We conduct an analysis of the time varying performance associated with the inclusion of Cat Bonds under dierent nancial market conditions. We consider two dierent benchmark universes. The rst is formed from traditional asset classes and the second one from common factors. Well- known factors in the literature which were constructed as the underlying drivers of risk and return across assets and asset classes, can be macro oriented (e.g., economic growth, ination) or style oriented (e.g., value, momentum, quality). Further, factors are not directly investable, but factor exposures are an oshoot of investing in assets. With relatively more stable returns than those from asset class returns over time, depending on the market environment some factors perform better than others, see for instance, Cerniglia and Fabozzi (2018), Dimson et al. (2017), Naik et al. (2016), Ang (2014). The asset classes are U.S. equities, global equities ex-U.S., emerging markets equities, real- estate, U.S. treasury bonds, U.S. corporate bonds, U.S. high-yield bonds and commodities. The factors consist of equity market, value, size, momentum, volatility, mortgage, default, term, high-yield and commodity curves. To represent Cat Bonds, we use ve dierent Swiss Reinsurance indexes.3 Standing out from previous studies, we conduct our study using the following four dierent approaches. First, we perform a battery of mean-variance spanning tests. These are based on the methodology developed in Kan and Zhou (2012). Furthermore, to split the sample into two economic regimes, we use three approaches 1- the separation called by the NBER data, 2- the turbulence index à la Kritzman and Li (2010), and 3- a Markov-Switching model applied to the US stock market index and the US bond market index à la Hardy (2001). We conduct our tests using the full sample as well as the regime-based periods. We nd that the addition of Cat Bonds leads to portfolios previously unattainable regardless of the regimes. Second, by way of the Engle (2002) dynamic conditional correlation model (DCC), we study the time-varying eects of including Cat Bonds. We start by estimating the correlations between Cat Bonds and other assets. We then use these correlations to obtain the maximum 3Weekly prices from January 4, 2002 to June 30, 2017 are used. Albeit the Swiss Re indexes are not investable, Jaeger et al. (2011) present a methodology that would allow the construction of a Cat Bonds index that would be investible. Their procedure is implementable and enables investors to have exposure to Cat Bonds returns. In fact, the index created presents descriptive statistics similar to the Swiss Re indexes and exhibit a very high correlation with these. The growing popularity of Cat Bonds might lead to a launch of Cat Bonds Exchange Traded Funds (ETFs). This would facilitate the investors' access to the Cat Bonds market. 2 Sharpe ratio and maximum diversication à la Choueifaty and Coignard (2008) portfolios with and without Cat Bonds. This gives rise to time varying increases in the Sharpe ratio as well as of increases in the diversication ratio. Our results in terms of the Sharpe ratio and the maximum diversication ratio reveal that the benets of adding Cat Bonds not only vary considerably over time but also increase signicantly. Third, under a stochastic dominance eciency test à la Scaillet and Topaloglou (2010), to determine whether a portfolio of traditional assets stochastically dominates a portfolio created from the same universe with Cat Bonds added, we employ a two-step method as in Daskalaki et al. (2017).4 We perform the tests on the full sample under the dierent market conditions mentioned above. We nd that the null hypothesis that portfolios that do not include Cat Bonds are ecient under the second-order stochastic dominance criterion cannot be rejected. This means that adding Cat Bonds might not achieve diversication when we consider higher moments of the return distribution. Finally, by means of a rolling window method, we analyze the out-of-sample performance of the portfolios of maximum Sharpe ratio, of maximum diversication and those constructed from the second-order dominance criterion. To take into account the fact that the returns do not follow a normal distribution and the amount of trading needed to re-balance the portfolios, (i.e., portfolio turnover), we use the conditional Sharpe ratio (CSR) à la Maillard (2018) and the Omega ratio à la Keating and Shadwick (2002) as metrics of performance.