Cross-Sectional Analysis of Performance and Risk

The empirical analyses of this study continue with cross-sectional analysis of hedge fund performance after examining the determinants of options use. The purpose of cross-sectional performance and risk analysis is to provide a detailed picture of the use of options and control for other variables that may explain hedge fund performance and risk. The dummy variables for the use of other de-rivatives and options for each asset class (1 = use options or other dede-rivatives) form variables for asset classes respectively. These variables are used to indicate whether the use of particular derivatives has an impact on hedge fund perform-ance and risk. Other primary focuses, other invested asset classes, and hedge fund strategies are controlled for as in the previous analysis.

The empirical model for the cross-sectional performance and risk characteristic analyses of hedge funds is the following (Model 2):

(46) MEASURE

_ji

=

_i

+

_j

CONTROL

_ji

j=1 N

⁺

^j

^DERIVATIVE

^ji

^{+ e}

ⁱ

j=1 N

^,

where MEASURE

_ji

defines a risk/performance measure j of fund i;

CONTROL

_ji

defines an additional control variable j of fund i, and DERIVATIVE

_ji

defines a dummy variable for the use of a derivative j by fund i (1 if the derivative

is used, and 0 otherwise). Model 2 is used to test Hypotheses 1, 2 and 5a.

Statisti-cally significant values of

_j

imply derivatives use affecting the performance and

risk characteristics of hedge funds.

To test the impact of the complexity of derivative strategies on the risk and per-formance characteristics of a hedge fund Model 2 is reformulated and the empiri-cal model for the cross-sectional analysis of the complexity, which tests Hypothe-ses 3, 4, and 5b, is the following (Model 3):

(46) MEASURE

_ji

=

_i

+

_j

CONTROL

_ji

j=1 N

⁺

¹

^COMPLEX

ⁱ

^{+ e}

ⁱ

^,

where MEASURE

_ji

defines a measure associated with higher moments j of fund i; CONTROL

_ji

defines an additional control variable j of fund i, and COMPLEX

_i

defines the number of different derivatives used by a hedge fund. Statistically significant and positive values of imply supportive evidence for the hypothe-ses examined.

The number of different derivatives used by a hedge fund is considered to be a proxy for complexity of derivative strategies. As there is no more detailed infor-mation available on the use of derivatives for a sufficient sample of hedge funds, the variable constructed may be considered as the most reasonable proxy for the complexity of derivative strategy. Intuitively, the more a hedge fund uses differ-ent types of derivatives, the more complex its derivative strategy is. The variable for the complexity is slightly similar to the variable for complexity of a hedge fund used by Tiu (2005) as the complexity variable used by Tiu (2005) counts for the number of significant strategy exposures of a hedge fund to 15 different in-dices.

Different options counted in the construction of the complexity variable are

op-tions for equity, fixed-income, commodity, and currency. Futures and forwards,

respectively, for fixed-income, currency, and commodity are counted for the

vari-able but for equity the Lipper TASS database reports only the use of equity index

futures. Also, warrants issued with equity securities, warrants issued with

fixed-income securities, interest rate swaps, and cross-currency interest rate swaps are

counted for the variable. To sum up, data in the Lipper TASS database allows a

proxy variable to be constructed for the complexity of derivative strategies by a

hedge fund ranging from 0 to 15. As an example of the complexity, if a hedge

fund uses equity index futures and equity index options, the strategy is assumed to

be more complex than if the hedge fund had used only one of these two

deriva-tives. A hedge fund may have a long position on an index futures option and short

position on the same index using index futures as an attempt to profit from price

inefficiency between the securities. The strategy appears to be simple and hedged

but a hedge fund may be exposed to many other risk factors such as the liquidity

of the underlying assets. This risk may be intensified as a result of leverage use

once the market exposure is hedged. As such, the term “complexity” compre-hends risks that may be unexpected or should be nonexistent as a result of hedg-ing and diversification. A practical example of such complexity is the failure of the LTCM, a hedge fund, which used a wide range of different derivatives and derivative strategies. The fund positions were supposed to be hedged and diversi-fied but the fund was eventually exposed to liquidity squeeze during the Russian Crisis 1998 (see, e.g., Lowenstein 2002). Considering the complexity from the viewpoint of a formal model, it appears that the more financial derivatives are used, the more inputs there are in the model used. For example, also investing also in stock options in addition to fixed-income options increases the number of the inputs by definition as for these options the underlying assets are different.

The model presented above assumes a linear relation between the complexity of a derivative strategy of a hedge fund and its performance but the relation may also be nonlinear. For instance, the use of a few derivatives may be relatively less profitable than the use of many derivatives as a result of economies of scale.

Therefore, a polynomial relation of degree 2 between MEASURE

_ji

and COMPLEX

_i

is also analysed using the following model (Model 4):

(48) MEASURE

_ji

=

_i

+

_j

CONTROL

_ji

j=1 N

⁺

¹

^COMPLEX

ⁱ

⁺

²

^(COMPLEX

ⁱ

⁾

²

^{+ e}

ⁱ

^,

where the only difference from Model 3 is that the series of squared numbers of different derivatives used is included in the model. Thus, Model 4 also tests Hy-potheses 3, 4, 5b. Models 3 and 4 are compared with one another using the Akaike information criterion (AIC) and the Schwarz information criterion (SIC).

A disadvantage of the OLS analysis is that it can only consider the relation

be-tween the mean of performance and risk measures and the complexity of

deriva-tive strategy. However, the complexity may affect the performance and risk of a

hedge fund differently for different segments of the sample. For instance, the

complexity may have a relation only with best performing funds but not with

those performing poorly. Thus, quantile regression can provide more insights into

the analysis of this study. Thus, the results of quantile regression analysis is

pre-sented for nine equally spaced quantiles of the sample using selected risk and

per-formance measures which are alpha, appraisal ratio, the Sharpe ratio, the

Cornish-Fischer expansion and standard deviation.

In document Do investors benefit from the use of options and complexity of derivative strategy of a hedge fund? (sivua 105-108)