(a) Tests for stationarity and distribution of the returns

As regressions were to be performed later, the data was first tested for stationarity. Results of the test for the presence of a unit root are summarised in Table 1 (details Appendix A). The null hypothesis of a unit root being present in the return series was rejected at the 1% level.

Table 1. Tests for the presence of a unit root (details presented in Appendix A).

Strategy   t-Statistic Probability
Convertible Arbitrage   −7.9293 <0.01
Short Bias   −10.9196 <0.01
Emerging Markets   −9.596 <0.01
Equity Market Neutral   −17.7315 <0.01
Event Driven   −7.6882 <0.01
Fixed Income Arbitrage   −10.4436 <0.01
Global Macro   −10.4389 <0.01
Long/Short Equity   −9.5381 <0.01
Managed Futures   −11.5436 <0.01
Multi Strategy   −7.5482 <0.01
Test critical values 1% level −4.9491 1%
  5% level −4.4436 5%
  10% level −4.1936 10%


Table 2 below summarises the descriptive statistics on the various hedge fund strategies (10) and the benchmark of S and P 500.

Table 2. Descriptive statistics for all 10 strategies and S&P 500 6/2007–1/2017.

Strategy Mean Median Maximum Minimum Std Dev Skewness Kurtosis Jarque Bera Prob
Convertible Arbitrage 0.0031 0.0031 0.0581 −0.1259 0.0024 −2.4518 16.297 970.817 0
Short bias −0.0079 −0.0139 0.1031 −0.1128 0.0447 0.4462 2.929 3.873 0.1442
Emerging Markets 0.0031 0.0042 0.0696 −0.1363 0.0275 −1.4139 8.6909 190.185 0
Equity Markets Neutral −0.0017 0.0029 0.0366 −0.4045 0.0402 −8.1180 88.923 37,184.51 0
Event Driven 0.0026 0.0049 0.0422 −0.0575 0.019 −0.8694 3.9609 19.075 0
Fixed Income Arbitrage 0.0029 0.0049 0.0433 −0.1404 0.0196 −4.2558 29.0433 3628.401 0
Global Macro 0.0044 0.0054 0.0444 −0.0663 0.0161 −0.8460 6.3701 68.731 0
Long Short Equity 0.003 0.0039 0.0523 −0.0781 0.0225 −0.7765 4.5441 23.183 0
Managed Futures 0.0023 0.0023 0.075 −0.0581 0.0318 0.0789 2.0548 4.439 0.1087
Multi Strategy 0.0039 0.006 0.0428 −0.0735 0.0163 −1.8300 9.9337 297.117 0
SP500 0.0034 0.0095 0.1023 −0.1856 0.0453 −0.8928 5.0006 34.755 0

The mean return, standard deviation, median, minimum return and maximum return of each of the ten strategies, is stated in the table above, and can be contrasted with that of the benchmark SP 500 over the whole data period (June 2007–January 2017). The null hypothesis of normality of returns distribution was rejected at the 5% level, for all but two of the strategies (Short Bias and Managed Futures). There was evidence of negative skewness and leptokurtosis (kurtosis > 3), for nine of the eleven series tested.

(b) To visualise the performance of the different strategies in the period of the study (June 2007–January 2017), the value of all series on the various strategies, indexed at 100 at the beginning of the series, is plotted below in Figure 1:


Figure 1. Relative series performance over the whole period: June 2007–January 2017.

Visual inspection of the performance of the various strategies over the period of 2007–2017, shows that there was a downturn in 2008 and that there were clearly two different periods to analyse – a period of downturn from the middle of 2007, up till the end of the first quarter of 2009, and then on an upturn, up till the first month of 2017. Therefore, it was decided to study the entire period of June 2007 to January 2017, in two split periods (a) crisis period – June 2007–March 2009 (b) after crisis – April 2009–January 2017, and also the whole period.

The gross performance of the various strategies in each period, i.e., a value of $100 invested in a particular strategy, at the beginning of the period (whole period, during crisis and after crisis) are summarised in Table 3 below:

Table 3. Performance of strategies and (S&P 500) in the whole period, during crisis and after crisis.

Period Whole Period During Crisis After Crisis
Strategy/Rank * Value Rank Value Rank Value Rank
Risk free rate 104.7 3 104.16 9 100.52 2
Convertible Arbitrage 138.88 10 73.92 4 187.87 10
Short Bias 35.42 1 127.46 12 27.79 1
Emerging Markets 136.56 8 77.94 5 175.21 8
Equity Market Neutral 72.45 2 60.17 2 120.41 4
Event Driven 132.08 6 84.5 8 156.31 6
Fixed Income Arbitrage 136.44 7 73.71 3 185.11 9
Global Macro 164.47 12 107.66 10 152.77 5
Long/Short Equity 137.35 9 83.77 7 163.97 7
Managed Futures 123.1 4 116.89 11 105.31 3
Multi-Strategy 154.84 11 80.72 6 191.82 11
SPX 131.86 5 49.42 1 266.85 12


Table 3 shows that:

(i) Over the entire period, seven strategies performed better than the S and P 500: The Global Macro, Multi Strategy, Emerging Markets, Long/Short Equity, Event Driven, Convertible Arbitrage, and the Fixed Income Arbitrage; with Short Bias and Equity Market Neutral and Managed Futures doing much worse than the benchmark S and P 500.

(ii) In the crisis period (June 2007–March 2009), the S and P 500 was the worst performer, with an investment of $100 falling down to $49.42; while all the other strategies did better; the best performers being Managed Futures, Global Macro and Short Bias, with values above investment in the risk-free rate.

(iii) After the crisis: April 2009–January 2017; the worst performer was Short Bias while the S and P 500 was the best performer with the value of an investment of $100 at the beginning of the after-crisis period rising to $266.85; the next best being Multi Strategy, Convertible Arbitrage and Fixed Income Arbitrage.

To get a detailed overview of the strategies' performance, in the various periods, Table 4 contains the mean return and standard deviation in each period.

Table 4. Mean and standard deviation of the strategies in the whole period, during the crisis and after.

Period Whole Period During Crisis After Crisis
Strategy Mean Rank+ Stdev Rank+ Mean Rank+ Stdev Rank+ Mean Rank+ Stdev Rank+
Convertible Arbitrage 0.31% 8 2.36% 6 −1.27% 4 4.21% 7 0.68% 9 1.48% 5
Short Bias −0.79% 1 4.47% 10 1.24% 11 5.23% 9 −1.27% 1 4.16% 11
Emerging Markets 0.31% 7 2.75% 7 −1.04% 5 4.26% 8 0.62% 7 2.18% 8
Equity Market Neutral −0.17% 2 4.02% 9 −1.78% 2 8.77% 11 0.21% 3 1.35% 4
Event Driven 0.26% 4 1.90% 3 −0.74% 8 2.18% 1 0.49% 5 1.76% 6
Fixed Income Arbitrage 0.29% 5 1.96% 4 −1.30% 3 3.78% 6 0.66% 8 0.87% 1
Global Macro 0.44% 11 1.61% 1 0.37% 9 2.79% 3 0.46% 4 1.20% 3
Long/Short Equity 0.30% 6 2.25% 5 −0.76% 7 3.04% 4 0.55% 6 1.96% 7
Managed Futures 0.23% 3 3.18% 8 0.77% 10 3.41% 5 0.10% 2 3.13% 9
Multi-Strategy 0.39% 10 1.63% 2 −0.93% 6 2.68% 2 0.70% 10 1.07% 2
SP500 0.34% 9 4.53% 11 −2.96% 1 6.16% 10 1.12% 11 3.68% 10


Table 4 shows that over the whole period, the highest mean return was achieved by Global Macro (0.44%) and Multi Strategy (0.39%), with the S and P 500's return being the third highest (0.34%). The lowest mean return was generated by the Short Bias strategy (−0.79%). The benchmark and Short Bias strategies exhibited a much higher standard deviation, compared to the other strategies in the sample. The table above gives further insights into the return risk profile of the strategies, during and after the crisis. Again, during the crisis, the benchmark S and P 500 had the lowest mean return and next highest standard deviation, with Short Bias having the highest mean return and third highest standard deviation. In the after-crisis period, Short Bias had the lowest return and highest standard deviation, while the benchmark S and P 500 had the highest return and next highest standard deviation.

Ackermann et al. (1999) found that hedge funds were riskier than the market indices. These results could not be confirmed by the findings of this study. Over the ten-year period of 2007–2017, the benchmark (and inversely, the Short Bias strategy) had the highest standard deviation and therefore, the highest risk. This was consistent with a study by Liang and Kat (2001) who found higher volatility in the market benchmark (S and P 500). He attributed the lower risk of hedge funds to the cross-style diversification. A major area of interest was the correlation of hedge fund strategies with the benchmark S and P 500.

Table 5 sets out the correlation of returns between the various strategies, in the whole period and during and after the crisis.

Table 5. Correlations of returns of various strategies with S&P 500 returns in the whole period and during and after crisis.

Strategy/Period Whole Period During Crisis After Crisis
Convertible Arbitrage 0.56 0.55 0.54
Short Bias −0.77 −0.64 −0.85
Emerging Markets 0.71 0.71 0.73
Equity Market Neutral 0.34 0.3 0.58
Event Driven 0.71 0.65 0.76
Fixed Income Arbitrage 0.56 0.66 0.41
Global Macro 0.3 0.29 0.35
Long/Short Equity 0.8 0.73 0.87
Managed Futures −0.01 −0.17 0.12
Multi-Strategy 0.66 0.6 0.71

Three strategies showed a positive correlation above 0.7, over the whole period. During the crisis, two strategies showed a high correlation (>0.7) with the S and P 500 (Emerging Markets and Long/Short Equity). After the crisis, Emerging Markets, Event Driven and Long Short Equity, showed a high positive correlation with the benchmark, while Short Bias showed a high negative correlation. The lowest positive correlations, over the whole period and the benchmark, were Global Macro and Equity Market Neutral; while Short Bias and Managed Futures showed a negative correlation.

Although Fung and Hsieh (1997) or Schneeweis and Spurgin (1997) found that hedge funds exhibit a low correlation to the benchmark, the findings of this study were different. A test for difference of means in the correlation values, during and after the crisis showed that there was no significant difference (Appendix B). This meant that some strategies had increased their correlation with the S and P 500 after the crisis, whilst others had decreased, but overall, there was no significant difference. In sum, the results implied that some alternative investments provide diversification and can improve risk-adjusted returns, as stated in the literature.