پیش بینی دینامیکی بقای صندوق های تامینی در بازارهای مالی بحران خیز

This study focuses on dynamic changes in survival probabilities over the lifetimes of hedge funds. To model such probabilities, a mixed Cox proportional hazards (CPH) model-specifically, a survival/hazard model with time-varying covariates and fixed covariates- is employed. Resulting dynamic survival probabilities show that the mixed CPH model provides significantly higher accuracy in predicting hedge fund failure than other models in the literature, including fixed covariate CPH models and discrete logit models. Our results are useful to investors and regulators of hedge funds in crisis-prone financial markets.

Since the onset of the global financial crisis (GFC), periodic local financial crises have continued to occur worldwide. Against the backdrop of crisis-prone financial markets, possible causes of the GFC have been suggested, with varying weights assigned by experts to different hypotheses. Posited causes include the collapse of high-profile hedge funds, such as Amaranth and Bear Sterns; the bankruptcy of large financial institutions, such as Lehman Brothers and Merrill Lynch; the bailout of banks by national governments; and downturns in global stock markets. As shown by Boyson et al. (2010), hedge fund failures not only create large losses for their own investors but have detrimental effects on the entire industry and on other asset classes. Thus, the international investment community is increasingly concerned about hedge fund failures and, accordingly, increasingly desires the ability to predict financial distress of hedge funds in real-time. This need motivates the present paper to investigation into a dynamic assessment mechanism of hedge fund failure. The present paper proposes a model that can be used to predict dynamic changes in the survival probabilities of hedge funds in crisis-prone financial markets. Dynamic prediction is especially necessary in crisis-prone financial markets because well-understood relationships that exist in stable markets are observed not to hold in crisis-prone markets. Several academic efforts to predict hedge fund failure have adopted survival analysis or qualitative response models. For example, Brown et al., 2001, Brown et al., 2009, Bares et al., 2001, Boyson, 2002, Gregoriou, 2002, Rouah, 2005, Grecu et al., 2007, Chapman et al., 2008, Ng, 2008 and Baba and Goko, 2009, and Liang and Park (2010) use the Cox proportional hazards (CPH) model to examine factors affecting hedge fund failure, while Chan et al., 2006 and Baquero et al., 2005, and Malkiel and Saha (2005) use logit or probit models to investigate hedge fund survival. Since the study of Rouah (2005), several studies have used a CPH model that incorporates time-varying covariates to examine hedge fund survival (Chapman et al., 2008, Grecu et al., 2007, Ng, 2008, Baba and Goko, 2009 and Liang and Park, 2010). In these studies, however, survival probabilities are not calculated over a fund’s lifetime; rather, such studies examine only the relationships between covariates and hazard rates. By contrast, the present study uses a mixed CPH model that incorporates both time-varying and fixed covariates to generate dynamic changes in hedge fund survival probabilities over a fund’s lifetime. Note that the effects of the time-varying covariates of the mixed CPH model typically occur contemporaneously and are thus difficult to capture in a CPH model that incorporates only fixed covariates. Using two datasets, the “live funds2” and the “dead funds3” datasets provided by Hedge Fund Research, Inc. (HFR), the current study establishes a mixed survival/hazards model with covariates that are both fixed and time-varying. The sample of failed hedge funds is drawn from the “dead funds” dataset by applying filter criteria based on returns and assets under management. After estimating the model, dynamic changes in survival probabilities are predicted, and the predictive power of the model is evaluated using the relative operating characteristic (ROC) curve as a prediction accuracy metric. The dynamic survival probabilities derived from the model indicate that non-failed funds have higher survival probabilities than failed funds across a given time horizon. Furthermore, the survival probabilities of failed funds decrease much more rapidly than those of non-failed funds along the timeline. In addition, the ROC curve shows that the mixed CPH model is far superior in predicting survival probabilities than the fixed CPH model, which only incorporates fixed covariates and a discrete-time hazard logit model of Shumway (2001) that also incorporates mixed covariates. Therefore, the mixed model developed in this study provides an effective tool for real-time predictions of survival probabilities of hedge funds. Importantly, our study shows how crisis-prone financial markets distort well-known effects of covariates on hedge fund failure in non-crisis-prone markets and demonstrates how the mixed CPH model with time-varying covariates successfully adapts to dynamic market conditions. These results are useful for investors and regulators monitoring potential fund failures in real-time.

This study has sought to incorporate time-varying predictors into the CPH model. Specifically, we have proposed a survival/hazard model, with both time-varying and fixed covariates, which we have used to predict dynamic changes in survival probabilities over the lifetimes of hedge funds. This process involves estimating baseline hazards for each time period in the time-varying covariate model. A SAS Macro program is developed to generate survival probabilities predicted by a mixed CPH model that incorporates both fixed and time-varying covariates. In addition, the predictive performance of the model is evaluated, using an ROC curve and AUROC statistics, and the results are compared with those of the CPH model that incorporates only fixed covariates and a discrete-time hazard model proposed by Shumway (2001). Various variables that significantly affect hedge fund failure have been identified. In particular, a fund’s risk of return appears to be the most important factor in hedge fund failure. Low-risk funds are more likely to survive longer than high-risk funds. Fund performance and size are also important. Hedge funds with high returns or large size have lower hazard rates of failure. Interestingly, leverage is found to play a significant role in failure prediction, and funds with higher incentive fees are likely to survive longer. Additionally, minimum investment requirements are found to positively affect hedge fund failure, and offshore hedge funds are more likely to fail than funds based in the United States. As shown in our empirical results, however, the mixed CPH model does not confirm the widespread view that high-water marks, hurdle rates, and liquidity covariates have meaningful effects on hedge fund failure. Finally, it is interesting to note that use of a relative value arbitrage strategy is a strong predictor of fund failure. The main contribution of this study is the generation of dynamic survival probabilities by the means of a mixed CPH model. The resulting dynamic survival probabilities illustrate that non-failed funds have higher survival probabilities than failed funds across the same failure time horizon. Moreover, the survival probabilities of failed funds decrease much more rapidly than those of non-failed funds along the timeline. In addition, ROC curve analysis and AUROC statistics indicate that the mixed CPH model can predict hedge fund failures with relatively high accuracy compared to the fixed covariate CPH model or the discrete-time hazard model of Shumway (2001). This improvement in predictive ability of the mixed CPH model can be explained by the model property known as “overfitting to time-varying data.” Although this property might prevent the model from proving some well-known hypotheses regarding covariates, this property is desirable in a market in which crises are frequent. Additionally, this study provides advanced information to investors and regulators in crisis-prone financial markets, as discussed in Section 4.5. Future research along these lines is clearly desirable.