Descriptive statistics

Hedge fund data is gathered from Lipper TASS Hedge fund database, which divides the data in an “active”–category¹² and a “Graveyard”-category¹³. The “Active”- category consist of 1610 individual hedge funds and the period between January 2004 and September 2012 is chosen. This period is chosen so that one can analyse pre-crisis and post-crisis differences. Finally, the thesis focuses on only hedge funds following the managed futures strategy.

Other data restrictions include companies, which do not report net of fee returns, that report in other currencies than US dollar, that report less frequently than monthly, or that have fewer than 24 observations. This leads to a total sample size of 189 hedge funds.

12Includes only of active hedge funds

13Includes only closed hedge funds

To analyze the effect of these restrictions and to test data sufficiency, the next section analyzes the time series length for individual hedge funds.

Time series length for individual hedge funds 6.2.1.

The life cycle of a hedge fund is shorter than for traditional mutual funds. Further, previous studies have shown (Baquero, Horst, & Verbeek, 2005) that there exists a problem with the time series length. The required length for the time series is 24-months.

Table 6 present the median, average, minimum and maximum monthly observations for individual hedge funds. It can be concluded that no problem with short time series exists in the data.

Table 6 Time series length for individual hedge funds

Managed

Median 101

Averagee 94

Minimum 24

Maximum 129

All funds 189

Above 36 observations 182 Above 54 observations 157 Above 72 observations 143 Above 90 observations 127

Table 6 presents descriptive statistics for number of observations and number of individual. The table above presents number of observations and the table below presents the number of funds.

Descriptive statistic for individual hedge funds 6.2.2.

Table 7 presents monthly descriptive statistics for individual hedge funds. Descriptive statistic for individual hedge funds

Table 7 Descriptive statistics on individual hedge funds.

Table 7 present descriptive statistics for the individual managed futures hedge funds returns between January 2004 and September 2012. Normality % indicates the proportion of hedge funds that have normal distribution according to the Jarque-Bera test. Autocorrelation % indicates the proportion of hedge funds that exhibit statistic significant AR (1) coefficient. The significance level is 5%.

The returns for individual hedge funds tend to be positive as the average and median values are all positive. The financial crisis can be seen in the extreme values as the investments fail, resulting in low returns.

Hedge funds do not usually follow normal distribution (Agarwal & Naik, Risk and Portfolio Decisions Involving Hedge Funds, 2004). The managed futures strategy seems to differ from the overall hedge funds as 48 % of individual hedge funds have returns that follow the normal distribution on a 5 % significance level. This is a surprising finding, as one could expect a non-normal distribution due to tail-events during the financial crisis.

Autocorrelation is not an issue for the individual hedge funds, but should be pointed out that 21% of them show signs of autocorrelation on a 5 % significance level. Managed futures invest mostly in derivatives products with high volatility and therefore the autocorrelation is excepted to be lower for this category compared to other hedge fund categories. This must be taken into consideration when making concluding remarks of the results.

Descriptive statistic for variables returns 6.2.3.

Table 8 presents monthly descriptive statistics for the factors; average return, median return, minimum return, maximum return and standard deviation. Also the kurtosis, skewness, kurtosis, normality and autocorrelation are presented. The data is graphically represented in figure 5.

The average annualized return for the S&P 500 is 7.1 % between January 2002 and September 2012. The financial downturn in late 2008 is seen in the low returns of -38.4% for the S&P 500. Also, the data shows the USD devaluation during last decade, as the average return for USD is – 3.1. %. The hypothesis that small companies earn premium returns compared to larger companies is also suggested by the data, as the SMB annual return is 3.7%.

One can also observe a high kurtosis in credit spread due the Lehman Brothers bankruptcy. In October 2008, the return for BAA companies was -14.3%, while the return for AA companies was “only” – 5.1 %. Further, the commodity price index have explicit three large bull-markets and these are both observable from figure 5.

Many of the variables follow normal distribution. The Bond, SP500, Credit and Mortage variables all follow normal distribution on a 5 % significance level. Commodity follows normal distribution on a 10 % significance level. The USD and SMB variables are non-normal. On the other hand, neither autocorrelation nor multicollinarity (Appendix 4) exists in the variables. Heteroskedasticity exists in Bond and SP500 with a 5 % significance level and in Mortage with a 10 % significance level. The OLS regression uses heteroscedasticicty consistent standard errors to improve the OLS estimates. Overall, the descriptive statistics for the variables are as expected.

Table 8 Descriptive statistics for factor returns

USD BOND SP500 CREDIT MORTAGE COMMODITY SMB

Average return (%) -0.260 0.039 0.462 -0.086 0.213 0.731 0.335

p.a. -3.101 0.482 7.161 -0.889 2.539 7.203 3.946

Median (%) -0.234 0.186 1.370 -0.174 0.135 1.989 0.050

p.a. -6.261 -0.636 11.760 -0.691 3.696 12.550 3.695

Max (%) 7.385 5.090 12.816 9.190 4.330 17.183 5.840

p.a. 10.140 10.315 28.426 14.481 13.283 27.493 22.082

Min (%) -6.089 -5.136 -23.745 -4.373 -4.136 -21.539 -5.150

p.a. -14.971 -3.695 -38.462 -14.677 -3.701 -44.507 -0.445

Standard dev. (%) 2.510 1.304 4.715 1.389 1.164 6.881 2.435

p.a 7.225 3.985 18.540 6.673 4.370 20.012 8.107

Skewness 0.240 -0.289 -1.254 2.095 0.407 -0.639 0.184

Kurtosis 0.499 3.395 4.481 15.354 2.888 0.642 -0.489

Normality 4.888 23.356** 18.068** 41.358** 27.076** 6.423* 3.179

AR(1) 0.416 0.969 0.854 0.847 0.767 0.254 0.384

Heteros. 1.103 2.772** 2.732** 0.952 3.469* 1.355 3.106

Observations 129 129 129 129 129 129 129

Table 8 present descriptive statistics for (1) USD: the U.S. Dollar index return; (2) BOND: the return on the Barclays intermediate corporate Bond (AA) index; (3) SP500: The SP500 total return, (4) CREDIT: The spread between Barclays intermediate corporate Bond (BAA) index and the Barclays U.S. 5 year treasury index; (5) MORTAGE: The spread between GNME mortage index and the Barclays U.S. 5 year treasury index; (6) COMMODITY; the return of SP GCSI Commodity index; and (7) SMB; The spread between small and large company spreads (Fama-French factor) during the time period between January 2002 and September 2012. AR (1) proxies autocorrelation for the individual variables and Hetero. indicates heteroskedasticity. *, **, ** indicates significances at the 10%, 5 % and 1% levels.

Figure 5 Graphical representation of variable returns

500 1000 1500 2000 2500 3000 3500 4000

2002m1 2002m6 2002m11 2003m4 2003m9 2004m2 2004m7 2004m12 2005m5 2005m10 2006m3 2006m8 2007m1 2007m6 2007m11 2008m4 2008m9 2009m2 2009m7 2009m12 2010m5 2010m10 2011m3 2011m8 2012m1 2012m6

USD Bond SP500 Credit

Mortage SMB Commodity

7 RESULTS

This section presents the results. The section follows the same structure as the methodology section. First, it discusses the classification of hedge funds. This is followed by the results from hedge fund risk-exposure analysis. Thereafter the results from building the replicators are given. The section ends with analysis of replicators’

performance and analysis of replicators’ replication quality.

7.1. Classification of hedge funds

The hedge funds are classified in two categorizes based on their six month average Sharpe ration. As mentioned in the method section, the All sample includes all hedge funds and the HP sample includes 50% of sample hedge funds with highest Sharpe-ration. Table 9 presents the number of observations, the returns and the Sharpe rations for both categories.

Four monthly observations are required per period, and some funds do not meet the restriction. These funds monthly returns are deleted and Appendix 3 elaborates on this.

The risk-adjusted returns for the HP sample are tremendously higher than those for All sample. This is expected as the portfolios are sorted by their respective risk-adjusted performance. However, it is interesting to notice that the difference is so large. The average difference between the All sample and the HP sample is 3.04 Sharpe ration.

Also, the standard deviation for the All category is lower on average. The average standard deviation for the whole time period for HP is 9.69% as it is 11.63% for the All category. Hence, the HP sample hedge funds have been able to create higher return with lower risk. As a result, the average Sharpe rations is 2.72 and -0.13, respectively.

This is in line with the findings that hedge fund returns show short-term performance persistence.

It is also worth mentioning, that the initial analysis indicates that Sharpe ration for All sample is relatively low. In more than 50% of time periods, the funds in the All sample generate negative risk-adjusted returns. This is in line with the criticism towards hedge funds capability to create abnormal returns. On the other side, the All sample performs well compared to other assets during the market downturn in 2008. This indicates that the hedge funds offer hedging-like properties and good diversification benefits during downturn.

Table 9 Hedge fund classification in HP sample and All sample

All HP

Return Sharpe Return Sharpe

Observations Average Median SD Median SD Observations Average Median SD Median SD 1.1.2002-31.6.2002 67 0.051 0.059 0.090 -0.915 -0.978 34 0.120 0.113 0.047 1.979 1.011 1.7.2002-31.12.2002 68 0.132 0.116 0.128 1.221 1.139 34 0.223 0.187 0.107 2.997 40.956 1.1.2003-31.6.2003 78 0.100 0.087 0.102 0.147 0.072 39 0.174 0.144 0.085 3.205 15.826 1.7.2003-31.12.2003 84 0.094 0.059 0.231 0.276 0.048 42 0.199 0.119 0.281 3.314 19.565 1.1.2004-31.6.2004 91 -0.018 -0.019 0.077 -1.905 -1.982 46 0.041 0.026 0.051 0.630 3.224 1.7.2004-31.12.2004 103 0.081 0.061 0.090 0.916 0.753 52 0.146 0.129 0.078 4.332 48.914 1.1.2005-31.6.2005 112 0.006 0.011 0.091 -1.424 -1.479 56 0.078 0.067 0.052 2.117 16.554 1.7.2005-31.12.2005 122 0.063 0.040 0.101 -0.044 -0.096 61 0.128 0.100 0.100 3.612 20.190 1.1.2006-31.6.2006 128 0.064 0.053 0.095 -0.491 -0.551 64 0.129 0.107 0.082 2.662 2.110 1.7.2006-31.12.2006 134 0.042 0.035 0.115 -0.756 -0.830 67 0.114 0.078 0.116 3.658 3.171 1.1.2007-31.6.2007 139 0.059 0.063 0.079 -0.123 -0.264 70 0.113 0.101 0.045 3.413 14.428 1.7.2007-31.12.2007 142 0.077 0.056 0.140 0.662 0.552 71 0.179 0.133 0.117 3.699 13.668 1.1.2008-31.6.2008 148 0.164 0.141 0.161 2.336 2.289 74 0.280 0.223 0.147 5.038 13.213 1.7.2008-31.12.2008 157 0.056 0.058 0.191 -0.273 -0.357 79 0.192 0.165 0.114 2.864 17.214 1.1.2009-31.6.2009 165 -0.035 -0.036 0.115 -2.417 -2.484 83 0.048 0.027 0.081 1.165 10.510 1.7.2009-31.12.2009 173 0.009 0.010 0.101 -0.746 -0.840 87 0.079 0.057 0.070 2.647 13.353 1.1.2010-31.6.2010 181 0.008 0.017 0.085 -0.890 -0.961 91 0.070 0.051 0.054 1.952 12.619 1.7.2010-31.12.2010 188 0.133 0.100 0.162 2.148 2.074 94 0.233 0.172 0.172 5.146 23.340 1.1.2011-31.6.2011 189 -0.029 -0.031 0.084 0.039 0.039 94 0.027 0.015 0.058 0.204 11.460 1.7.2011-31.12.2011 189 -0.013 -0.008 0.118 0.041 0.041 94 0.059 0.036 0.110 1.343 14.291 1.1.2012-31.9.2012 189 0.009 0.008 0.087 -0.612 -0.719 94 0.070 0.045 0.069 1.327 19.394 Table 9 presents the number of observations, the average return, the median return, the standard deviation and the Sharpe rations for individual hedge funds. The sorting is done every six month and therefore the sample is divided into 21 six month time periods. Hedge funds are sorted according to their Sharpe ration. HP sample includes the top 50% hedge funds based on that periods Sharpe rations and All sample includes all hedge funds in sample.