Understanding the data associated with the study is always crucial for the success in the analysis and interpretation of results later. Thus, it is appropriate to look at the general direction of the indexes that have been chosen for the study, the comparison between the logarithmic returns of the different asset classes as well as some descriptive statistics related to the data. Figure 7 shows the progression of the indexes between the end of May 2011 and the end of May 2021.
Figure 7: Index comparison of the asset classes between 05/2011-05/2021
Just based on the eye test the assets can be classified in three groups: high returns, medium returns, and low returns. Equity and real estate indexes have risen the most in value, with the base index being 100 and both going clearly above 200. These are then followed by private equity and hedge funds, which have had medium returns and their indexes have ended somewhere between 150-200. Unsurprisingly, bonds and ILS have had the lowest returns, with ILS having the lowest index gains of all the asset groups within the comparison.
In figure 8, the arithmetic returns of all asset classes are compared during the timeframe.
Some asset classes like real estate are quite volatile, while little variation can be seen in the returns of assets like the bonds or ILS. Two more significant drops can be noticed regarding the ILS index, which will be elaborated on later.
Figure 8: Time-series comparison of the arithmetic returns of each asset class
To gain a better understanding of the data used for the study, a look at the descriptive statistics for each asset class is required. The descriptive statistics of ILS will mainly be
considered, with some comparison to equity and the two bond indexes selected. Figure 9 shows some of the key statistical characteristics of each asset class. As mentioned previously, 120 observations were gathered in total within a 10-year time frame from the end of May 2011 to the end of May 2021.
Figure 9: Descriptive statistics of the monthly arithmetic returns of each asset class
Mean represents the total average monthly logarithmic returns of each asset class.
Unsurprisingly, equity, which in this case is represented by MSCI World Investable Market Index, has the highest average monthly return of 0.90 % per month across the time-series, or a yearly return of roughly 10.82%. ILS has the lowest returns, with the average return of only 0.22% per month, or 2.59% per year, losing out to both bond indexes quite significantly. Standard deviation is the typical measurement of risk in finance, and ILS displays low risk characteristics, with a standard deviation of around 0.983 % per month and 11.80% annually. In comparison, equity, has the standard deviation of around 4.01% per month and 48.12% annually, posing clearly higher risk, as is typical among assets with higher returns. Comparing ILS to the bond indexes we can see that S&P International Corporate Bond Index has had higher returns with roughly 0.29% returns monthly and 3.49% annually, while having a 2.5% and 30.37% standard deviation respectively. Interestingly, the S&P U.S. Aggregate Bond Index has had a 0.26% monthly return while only having the standard deviation of 0.80%, with annual values of 3.08% and 9.56%. Thus, if only looking at returns and standard deviation and with the consideration that bonds and ILS are interchangeable, with no regard for correlation and covariance, the aggregate bond index seems to have higher returns for less risk, and objectively seems like the better investment.
What particularly stands out about the ILS index is its high negative skewness and excess kurtosis. Simply by looking at the numbers, ILS returns are clearly not normally distributed, which is further demonstrated in figure 10, where the distribution of ILS returns are compared to a normal return distribution. The negative skew can be seen with the returns being concentrated on the left side of the distribution. What this means, in essence, is that the investor can expect small gains more frequently and a lesser number of large losses. Understandably, the ILS asset class is distinguishable with the potential of major losses within small time periods. The returns of ILS are seemingly leptokurtotic, with long and skinny tails. Although realistically the tail is only long into one direction, as ILS do not exhibit abnormally large returns, but they do exhibit abnormally large losses.
You can particularly notice the excess kurtosis characteristic of the ILS returns with the left side of the distribution spiking at roughly -9% and -4% returns. The highest negative spike of -8.61 % can be explained with the impacts of hurricanes and earthquakes during the month of September in 2017. Artemis (2017) reported that 33 of the 34 constituent funds within the Eurekahedge ILS Advisers Index reported negative returns, with multiple earthquakes in Mexico, as well as hurricanes Irma and Maria causing major losses within the ILS sector. Similarly, in prior to November 2018, hurricane Michael caused great losses that plagued the industry for a long period of time, with Artemis (2019) reporting losses of around USD 7.44 billion, with over 10000 more open claims left over a year later.
Figure 10: The arithmetic return distribution of the returns of ILS compared to a normal distribution
Naturally, with return characteristics like this, the risk associated with ILS products may be higher than one would assume purely based on risk and return characteristics. For the investor this is valuable information, because being prepared for major losses is crucial for the risk management of any portfolio containing assets that have a propensity for high, unpredictable volatility.
Other noteworthy characteristics for ILS in the descriptive statistics are minimum, maximum, median and madn (median absolute deviation). The minimum can be considered the worst monthly loss in the time-series, which we established to be around -8.61 %. The maximum on the other hand is the highest recorded gain for the index during the timeframe, which is a more modest 1.42 %. The median return for the whole time- series for ILS specifically is 0.32 % with the median absolute deviation of 0.33 %. Finally, an asymptotic and a normality test were conducted, both of which had significant results for all assets except the aggregate bond index. Thus, it seems that the arithmetic returns for most of the assets selected for the study are not normally distributed, as is typical with financial instruments.
Figure 11: A correlation matrix between the selected assets
Finally, we will have a look at the correlation matrix between the selected assets to illustrate the correlations between them. This should not be confused with the variance- covariance matrix described earlier, as it is a separate entity. From the correlation matrix it can be noted that ILS seemingly has a very low correlation with all the assets selected, with correlation values being in the singles or low 10s, percentage wise. Compare this to, for example, equity, and you can see that the linear relationship between equity returns and other asset returns seem to be a lot higher in comparison. None of the other assets displayed similarly low correlation to all assets, although U.S. bonds had negative correlations to both equity and private equity. From this, we can deduce that ILS returns have a seemingly low correlation to the returns of other assets, perhaps suggesting that they indeed do offer diversification benefits as the returns of ILS products are not as strongly linked to market movements as the returns of other asset classes.