Evaluation of Hedge Fund Returns Value at Risk Using GARCH Models

The aim of this research paper is to evaluate hedge fund returns Value-at-Risk by using GARCH models. To perform the empirical analysis, one uses the HFRX daily performance hedge fund strategy subindexes and spans the period March 2003 – March 2008. I found that skewness and kurtosis are substantial in the hedge fund returns distribution and the clustering phenomenon is pointed out. These features suggest the use of GARCH models to model the volatility of hedge fund return indexes. Hedge fund return conditional variances are estimated by using linear models (GARCH) and non-linear asymmetric models (EGARCH and TGARCH). Performance of several Value at Risk models is compared; the Gaussian VaR, the student VaR, the cornish fisher VaR, the normal GARCH-type VaR, the student GARCH-type VaR and the cornish fisher GARCH-type VaR. Our results demonstrate that the normal VaR underestimates accurate hedge fund risks while the student and the cornish fisher GARCH-type VaR are more reliable to estimate the potential maximum loss of hedge funds.Hedge Fund, Value at Risk, GARCH models.

A-KA Model: an Optimization of the Stock’s Portofolio

The elaborate proposes a compact alternative methodology to the classical stocks portfolio optimization based on the normal distribution of the returns of the assets named Adaptable - Kurtosis Asymmetry model (A-KA). In the financial theory is well-known that odd-order moments of a distribution describe a particular performance characteristic; on the contrary, the even-order moments tell a precise sense of risk of a distribution of returns. If it is true that, in general terms, minimizing the variance also minimizes the volatility of portfolio return is also true that we should minimize the kurtosis to get away from unpleasant situations in case “Extreme” events occur, especially if negative. The idea behind this paper is to exploit the four moments of return’s distributions, optimizing an alternative risk indicator to variance, such as the kurtosis of the final distribution of the portfolio, making constraints on distributive asymmetry, in a dynamic underlying logic

Evaluating dynamic covariance matrix forecasting and portfolio optimization

In this thesis we have evaluated the covariance forecasting ability of the simple moving average, the exponential moving average and the dynamic conditional correlation models. Overall we found that a dynamic portfolio can gain significant improvements by implementing a multivariate GARCH forecast. We further divided the global investment universe into sectors and regions in order to investigate the relative portfolio performance of several asset allocation strategies with both variance and conditional value at risk as a risk measure. We found that the choice of risk measure does not seem to heavily impact the asset allocation. As comparison to the dynamic portfolios we added regional/sector portfolios which where rebalanced after a 3% threshold rule. The regional portfolio was constructed to mimic the current strategy of the Norwegian Pension Fund Global. The max Sharpe portfolio for regions had the highest risk adjusted return, but suffered from a very high turnover. After being modified however, this strategy turned out to be superior even after transaction costs were imposed

Predicting Hedge Fund failure : the role of risk across time

This study focuses on the relation between the risk profile of a hedge fund and its probability to fail. We propose to model the failure event using survival analysis through a Cox Hazards Model while incorporating piecewise effects in the risk covariate. Empirical results suggest that there has been a shift in the relationship between the risk profile of a hedge fund and its probability of failure. For the period between 1995 and 2006, larger risk was associated with higher probability of failure whereas since 2007, increasing risk levels reduce the risk of failure of hedge funds. We are the first to show this effect and use this model in Hedge Funds literature. These findings allow investors to better understand the dynamics of risk and probability to fail and may have huge implications in portfolio composition

Proper use of the modified Sharpe ratios in performance measurement : rearranging the Cornish Fisher expansion

Performance analysis is a key process in finance to evaluate or compare investment opportunities, allocations, or management. The classical method is to compute the market or sub-market returns and volatilities, and then calculate the standard performance measure, namely, the Sharpe ratio. This measure is based on the first two moments of a return distribution. Therefore, a significant weakness of this method is that it implicitly assumes that the distribution is Gaussian (if it is not Gaussian, the approach may lead to a bad fit). In fact, risk comes from not only volatility, but also from higher moments of distribution such as skewness and kurtosis. The standard method to resolve this issue is to use the modified Sharpe ratio; this method replaces the classical Sharpe ratio volatility with the value at risk. The latter is computed using the Cornish Fisher expansion, a tool based on the first four moments of return distribution. This methodology, however, may present a major pitfall: in some cases, quantile functions do not stay monotone. In this paper, we show how this tool can be used effectively through a specific procedure, rearrangement. We compare various metrics using rank correlation, and demonstrate how and in which cases the proposed procedure delivers ranking different from the standard Sharpe ratio ranking. Furthermore, we show how our technique offers better distribution approximations and is therefore a more useful performance metric. Institutional investors may find the technique proposed here useful in that it allows for considering non-normality in performance analysi

Alternative Approaches for Estimating Value at Risk

In this paper the alternative value-at-risk (VaR) and expected shortfall (ES) analysis were made according to different error distribution assumptions by using stock market daily return series of Turkey (ISE100), United Kingdom (FTSE100), Japan (NIKKEI225) and France (CAC40). The backtesting procedures examining the performance of the alternative VaR models appointed that the estimations under Cornish-Fisher expansion are more consistent for the financial asset returns frequently possessing fat tails and asymmetric distributionValue-at-Risk, APGARCH, Expected Shortfall, Cornish-Fisher Expansion, Backtesting

MODELLING OPERATIONAL RISK MEASUREMENT IN ISLAMIC BANKING: A THEORETICAL AND EMPIRICAL INVESTIGATION

With the emergence and development of Islamic banking industry, the need to cater operational risks issues has attracted the attention of academics in recent years. Such studies commonly agree that operational risk is relatively higher and serious than credit risk and market risk for Islamic banks. However, there is not any single research in the context of Islamic banking which thoroughly tackles the issue of operational risks by tackling it in three main aspects: theoretical, methodological, and empirical. This may be due to the fact that operational risk is relatively new area, which requires further research to understand the complexities it carries. This is the sources of motivation for the research, which aims to fill this observed gap in the literature by responding to the mentioned three aspects. This research, hence, aims to develop a new measurement model of operational risk exposures in Islamic banking with the objective of theoretically determining the underlying features of operational risk exposures and its measurement particularly for Islamic banks. In its attempt to develop a theoretical framework of the proposed model, the research provides a classification of operational risks in major Islamic financial contracts. In addition, rather than adopting the existing operational risk measurement methods, this research develops a proposed measurement model attributed as Delta Gamma Sensitivity Analysis- Extreme Value Theory (DGSA-EVT) model. DGSA-EVT is a model to measure high frequency-low severity (HF-LS) and low frequency-high severity (LF-HS) type of operational risks. This is the core of this research’s methodological contribution. As regards to the empirical contributions, in analysing operational value at risk (opVaR), this research carefully analyses the behaviour of the data by taking into account volatility, skewness and kurtosis of the variables. In the modelling, volatility analysis employs two models: constant-variance model and exponential weighted moving average (EWMA) model. Results of the empirical tests show that the operational risk variables in this research are non-normal; thus, non-normality involving skewness and kurtosis as well as volatility has to be taken into account in the estimation of VaR. In doing so, this research employs Cornish-Fisher expansion upon which the confidence interval of operational variables is an explicit function of the skewness and kurtosis as well as the volatility. Empirical findings by deploying a set of econometrics tests reveal that for financing activities, the role of maintaining operational efficiency as part of an Islamic bank’s fiduciary responsibilities is immensely high. However, people risk is enormous and plays a dominant role in affecting the level of operational risk exposures in Islamic banks in investment activities

Estimating Portfolio Risk for Tail Risk Protection Strategies

We forecast portfolio risk for managing dynamic tail risk protection strategies, based on extreme value theory, expectile regression, Copula-GARCH and dynamic GAS models. Utilizing a loss function that overcomes the lack of elicitability for Expected Shortfall, we propose a novel Expected Shortfall (and Value-at-Risk) forecast combination approach, which dominates simple and sophisticated standalone models as well as a simple average combination approach in modelling the tail of the portfolio return distribution. While the associated dynamic risk targeting or portfolio insurance strategies provide effective downside protection, the latter strategies suffer less from inferior risk forecasts given the defensive portfolio insurance mechanics