## Impact of Liquidity and Leverage

AIM 77.6: Assess the impact of liquidity and leverage on hedge fund performance.

### Liquidity

Positive first-order autocorrelation for a time series of monthly returns is an indication of illiquidity risk. As presented in Figure 6, all of the linear clones of hedge fund style categories have lower values for autocorrelation than the funds they replicate, with one exception. Managed Futures and the corresponding linear clone have low values for first-order autocorrelation. The low values for autocorrelation indicate that the fund and the linear clone are not subject to illiquidity risk (i.e., fund and linear clone are liquid).

Also presented in Figure 6 is the statistical significance of autocorrelation relative to the Ljung-Box Q-statistic. As with most statistics, the smaller the p-value for the statistic, the greater our confidence in the inference made by rejecting the null hypothesis. For example, we are 90% confident in rejecting a null hypothesis when the test-statistic has a p-value of 0.10, and 99% confident when we reject a null hypothesis when the test statistic has a p-value of 0.01. Smaller p-values indicate that autocorrelations are more statistically significant. All of the linear clones have larger p-values for the Ljung-Box Q-Statistic than the fund style categories that they are replicating, thereby, confirming that the clones are more liquid.

The greater liquidity of the linear clone portfolios may come at a cost. That is, many of the more liquid clone portfolios underperform the funds that they replicate. For example, the Convertible Arbitrage fund has a return of 8.41% compared to the fixed-weight linear clone return of 7.40%; however, the fund is less liquid with a first-order autocorrelation of 42.2% (Ljung-Box Q-statistic p-value of 0.110), compared to the linear clone's autocorrelation of 10.7% (Ljung-Box Q-statistic p-value of 0.556).

TASS Style Category |
Sample Size |
Expected. Return % |
Fixed-Weight Linear Clone's Returns |
Serial Correlation |
Fixed-Weight Clones Serial Correlation |
P-value Q12 Fund% |
P-value QJ2 fund fixed-u>t clone % |

Convertible Arbitrage |
82 |
8.41 |
7.40 |
42.20 |
10.70 |
11.00 |
55.60 |

Fund of Funds |
355 |
8.25 |
9.29 |
23.20 |
-0.10 |
27.10 |
50.50 |

Event Driven |
169 |
13.03 |
9.84 |
22.20 |
4.30 |
27.00 |
55.80 |

Fixed Income Arbitrage |
62 |
9.50 |
8.35 |
22.10 |
4.10 |
35.90 |
64.40 |

Multi-Strategy |
59 |
10.79 |
10.32 |
21.00 |
2.20 |
28.20 |
59.70 |

Emerging Markets |
102 |
20.41 |
14.77 |
18.00 |
0.00 |
36.30 |
62.70 |

Long/Short Equity Hedge |
520 |
14.59 |
13.12 |
12.80 |
-0.10 |
36.00 |
59.70 |

Equity Market Neutral |
83 |
8.09 |
10.00 |
9.10 |
1.80 |
32.60 |
57.00 |

Global Macro |
54 |
11.38 |
15.54 |
5.80 |
2.60 |
43.10 |
52.20 |

Dedicated Short Bias |
10 |
5.98 |
6.70 |
5.50 |
2.80 |
25.50 |
73.60 |

Managed Futures |
114 |
13.64 |
27.97 |
2.50 |
4.70 |
40.10 |
Several of the hedge fund styles use leverage to enhance the returns of the portfolios. If the implied leverage of the linear clones is beyond the range that can be obtained through the use of additional debt or futures contracts, then the returns of the clones would have to be adjusted. To adjust for the use of leverage, we use a renormalization factor. An analysis of the values for the renormalization factors indicates that leverage can be replicated using futures contracts. Therefore, the implied leverage in the clones is within the range that could be easily implemented. The mean renormalization factor is reported to be 2.05, which implies that the leverage on the fixed-weight clones is 105% of the equity position (or equity is 48.8% of the total portfolio value, 1/(2.05)), compared to the margin required on the S&P 500 futures contract that requires an initial margin of approximately 6.1%, or a renormalization (leverage) factor of 16.3, 1/(0.061). Therefore, futures could be used to easily obtain the leverage that is implied in the linear clones. The renormalization (leverage) factors can be viewed in Figure 5. The highest renormalization factor is reported for the Managed Futures style at 2.76, and the lowest renormalization factor is 1.69 for the Fund of Funds style. |

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