Quantile regression analysis of hedge fund strategies

Extending previous work on hedge fund pricing, this paper introduces the idea of modelling the conditional quantiles of hedge fund returns using a set of risk factors. Quantile regression analysis provides a way of understanding how the relationship between hedge fund returns and risk factors changes across the distribution of conditional returns. We propose a Bayesian approach to model comparison which provides posterior probabilities for different risk factor models that can be used for model averaging. The most relevant risk factors are identified for different quantiles and compared with those obtained for the conditional expectation model. We find differences in factor effects across quantiles of returns, which suggest that the standard conditional mean regression method may not be adequate for uncovering the risk-return characteristics of hedge funds. We explore potential economic impacts of our approach by analysing hedge fund single strategy return series and by constructing style portfolios.     

Tactical Industry Allocation and Model Uncertainty

We use Bayesian model averaging to analyze industry return predictability in the presence of model uncertainty. The posterior analysis shows the importance of inflation and earnings yield in predicting industry returns. The out‐of‐sample performance of the Bayesian approach is, in general, superior to that of other statistical model selection criteria. However, the out‐of‐sample forecasting power of a naive i.i.d. forecast is similar to the Bayesian forecast. A variance decomposition into model risk, estimation risk, and forecast error shows that model risk is less important than estimation risk.     

Model averaging in risk management with an application to futures markets

This paper considers the problem of model uncertainty in the case of multi-asset volatility models and discusses the use of model averaging techniques as a way of dealing with the risk of inadvertently using false models in portfolio management. Evaluation of volatility models is then considered and a simple Value-at-Risk (VaR) diagnostic test is proposed for individual as well as ‘average’ models. The asymptotic as well as the exact finite-sample distribution of the test statistic, dealing with the possibility of parameter uncertainty, are established. The model averaging idea and the VaR diagnostic tests are illustrated by an application to portfolios of daily returns on six currencies, four equity indices, four ten year government bonds and four commodities over the period 1991–2007. The empirical evidence supports the use of ‘thick’ model averaging strategies over single models or Bayesian type model averaging procedures.     

Varying risk premia in international bond markets

Cochrane and Piazzesi [Cochrane, J.H., Piazzesi, M., 2005. Bond risk premia. American Economic Review 95, 138–160] use forward rates to forecast future bond returns. We extend their approach by applying their model to international bond markets. Our results indicate that the unrestricted Cochrane and Piazzesi (2005) model has a reasonable forecasting power for future bond returns. The restricted model, however, does not perform as well on an international level. Furthermore, we cannot confirm the systematic tent shape of the estimated parameters found by Cochrane and Piazzesi (2005). The forecasting models are used to implement various trading strategies. These strategies exhibit high information ratios when implemented in individual countries or on an international level and outperform alternative approaches. We introduce an alternative specification to forecast future bond returns and achieve superior risk-adjusted returns in our trading strategy. Bayesian model averaging is used to enhance the performance of the proposed trading strategy.     

Model uncertainty and systematic risk in US banking

This paper uses Bayesian Model Averaging to examine the driving factors of equity returns of US Bank Holding Companies. BMA has as an advantage over OLS that it accounts for the considerable uncertainty about the correct set (model) of bank risk factors. We find that out of a broad set of 12 risk factors only the market, real estate, and high-minus-low Fama–French factors are reliably related to US bank stock returns over the period 1986–2010. Other factors are either only relevant over specific subperiods or for subsets of bank holding companies. We discuss the implications of our findings for empirical banking research.     

Portfolio selection with higher moments

We propose a method for optimal portfolio selection using a Bayesian decision theoretic framework that addresses two major shortcomings of the traditional Markowitz approach: the ability to handle higher moments and parameter uncertainty. We employ the skew normal distribution which has many attractive features for modeling multivariate returns. Our results suggest that it is important to incorporate higher order moments in portfolio selection. Further, our comparison to other methods where parameter uncertainty is either ignored or accommodated in an ad hoc way, shows that our approach leads to higher expected utility than competing methods, such as the resampling methods that are common in the practice of finance.     

A Bayesian approach to detecting nonlinear risk exposures in hedge fund strategies

This paper proposes a model that allows for nonlinear risk exposures of hedge funds to various risk factors. We introduce a flexible threshold regression model and develop a Bayesian approach for model selection and estimation of the thresholds and their unknown number. In particular, we present a computationally flexible Markov chain Monte Carlo stochastic search algorithm which identifies relevant risk factors and/or threshold values. Our analysis of several hedge fund returns reveals that different strategies exhibit nonlinear relations to different risk factors, and that the proposed threshold regression model improves our ability to evaluate hedge fund performance.     

The Illiquidity Discount of Life Insurance Investments

We incorporate an illiquid life insurance investment in the multi-period investment strategy of an investor with constant relative risk aversion and independent and identically distributed returns. In our setup, the liquid and the illiquid assets are risky and correlated and the illiquid investment cannot be rebalanced. We calculate the illiquidity discount as the difference in certainty equivalent rates of return between the optimal strategy with all assets being rebalanced in each period and the strategy with the illiquid investment. Calibrating our model to data of the German market we find a negative relationship between the level of risk aversion and the illiquidity discount when the investor does not rebalance at all. However, when the investor rebalances his liquid assets in each period to hedge against the illiquid investment the illiquidity discount becomes economically negligible.     

Exchange-traded funds,persistence in tracking errors and information dissemination

We estimate tracking errors from 26 exchange-traded funds (ETFs) utilizing three different methods and test their relative performance using Jensen's model. We find that tracking errors are significantly different from zero and display persistence. Based on Jensen's alpha, risk adjusted returns are significantly inferior to benchmark returns for all ETFs with two exceptions at conventional significance levels revealing that passive investment strategy does not outperform market returns. We then examine the degree to which frequently used factors such as expense ratio, dividends, exchange rate and spreads of trading prices may be underlying sources of tracking errors causing this underperformance. We find that the change in the exchange rate is a significant source of tracking errors. Our serial correlation test, runs test and panel regression analysis reveal that Asian markets display relatively greater persistence and therefore are less efficient in disseminating information and noisier in filtering the information contained in returns.     

Bayesian and Bühlmann credibility for phase-type distributions with a univariate risk parameter

Credibility theory is a statistical tool to calculate the premium for the next period based on past claims experience and the manual rate. Each contract is characterized by a risk parameter. A phase-type (or PH) random variable, which is defined as the time until absorption in a continuous-time Markov chain, is fully characterized by two sets of parameters from that Markov chain: the initial probability vector and transition intensity matrix. In this article, we identify an interpretable univariate risk parameter from amongst the many candidate parameters, by means of uniformization. The resulting density form is then expressed as an infinite mixture of Erlang distributions. These results are used to obtain a tractable likelihood function by a recursive formula. Then the best estimator for the next premium, i.e. the Bayesian premium, as well as its approximation by the Bühlmann credibility premium are calculated. Finally, actuarial calculations for the Bühlmann and Bayesian premiums are investigated in the context of a gamma prior, and illustrated by simulated data in a series of examples.     

Mixed tempered stable distribution

In this paper, we introduce a new parametric distribution, the mixed tempered stable. It has the same structure of the normal variance–mean mixtures but the normality assumption gives way to a semi-heavy tailed distribution. We show that, by choosing appropriately the parameters of the distribution and under the concrete specification of the mixing random variable, it is possible to obtain some well-known distributions as special cases. We employ the mixed tempered stable distribution which has many attractive features for modelling univariate returns. Our results suggest that it is flexible enough to accommodate different density shapes. Furthermore, the analysis applied to statistical time series shows that our approach provides a better fit than competing distributions that are common in the practice of finance.     

Detecting structural breaks and identifying risk factors in hedge fund returns: A Bayesian approach

Extending previous work on asset-based style factor models, this paper proposes a model that allows for the presence of structural breaks in hedge fund return series. We consider a Bayesian approach to detecting structural breaks occurring at unknown times and identifying relevant risk factors to explain the monthly return variation. Exact and efficient Bayesian inference for the unknown number and positions of the breaks is performed by using filtering recursions similar to those of the forward–backward algorithm. Existing methods of testing for structural breaks are also used for comparison. We investigate the presence of structural breaks in several hedge fund indices; our results are consistent with market events and episodes that caused substantial volatility in hedge fund returns during the last decade.     

Model Selection and Averaging in Financial Risk Management

Simulated asset returns are used in many areas of actuarial science. For example, life insurers use them to price annuities, life insurance, and investment guarantees. The quality of those simulations has come under increased scrutiny during the current financial crisis. When simulating the asset price process, properly choosing which model or models to use, and accounting for the uncertainty in that choice, is essential. We investigate how best to choose a model from a flexible set of models. In our regime-switching models the individual regimes are not constrained to be from the same distributional family. Even with larger sample sizes, the standard model-selection methods (AIC, BIC, and DIC) incorrectly identify the models far too often. Rather than trying to identify the best model and limiting the simulation to a single distribution, we show that the simulations can be made more realistic by explicitly modeling the uncertainty in the model-selection process. Specifically, we consider a parallel model-selection method that provides the posterior probabilities of each model being the best, enabling model averaging and providing deeper insights into the relationships between the models. The value of the method is demonstrated through a simulation study, and the method is then applied to total return data from the S&P 500.     

Predictive regressions with time-varying coefficients

We evaluate predictive regressions that explicitly consider the time-variation of coefficients in a comprehensive Bayesian framework. For monthly returns of the S&P 500 index, we demonstrate statistical as well as economic evidence of out-of-sample predictability: relative to an investor using the historic mean, an investor using our methodology could have earned consistently positive utility gains (between 1.8% and 5.8% per year over different time periods). We also find that predictive models with constant coefficients are dominated by models with time-varying coefficients. Finally, we show a strong link between out-of-sample predictability and the business cycle.     

A Bayesian encompassing test using combined value-at-risk estimates

The Value at Risk (VaR) is a risk measure that is widely used by financial institutions in allocating risk. VaR forecast estimation involves the conditional evaluation of quantiles based on the currently available information. Recent advances in VaR evaluation incorporate conditional variance into the quantile estimation, yielding the Conditional Autoregressive VaR (CAViaR) models. However, the large number of alternative CAViaR models raises the issue of identifying the optimal quantile predictor. To resolve this uncertainty, we propose a Bayesian encompassing test that evaluates various CAViaR models predictions against a combined CAViaR model based on the encompassing principle. This test provides a basis for forecasting combined conditional VaR estimates when there are evidences against the encompassing principle. We illustrate this test using simulated and financial daily return data series. The results demonstrate that there are evidences for using combined conditional VaR estimates when forecasting quantile risk.     

Hedge fund pricing and model uncertainty

This article uses Bayesian model averaging to study model uncertainty in hedge fund pricing. We show how to incorporate heteroscedasticity, thus, we develop a framework that jointly accounts for model uncertainty and heteroscedasticity. Relevant risk factors are identified and compared with those selected through standard model selection techniques. The analysis reveals that a model selection strategy that accounts for model uncertainty in hedge fund pricing regressions can be superior in estimation/inference. We explore potential impacts of our approach by analysing individual funds and show that they can be economically important.     

Forecasting the performance of hedge fund styles

This article predicts the relative performance of hedge fund investment styles using time-varying conditional stochastic dominance tests. These tests allow for the construction of dynamic trading strategies based on nonparametric density forecasts of hedge fund returns. During the recent financial turmoil, our tests predict a superior performance for the Global Macro investment style compared with the other strategies of ‘Directional Traders’. The Dedicated Short Bias investment style is stochastically dominated by the other directional styles. These results are confirmed by simple nonparametric tests constructed from realized excess returns. Further, by utilizing a cross-validation method for optimal bandwidth parameter selection, we discover the factors that have predictive power regarding the density of hedge fund returns. We observe that different factors have forecasting power for different regions of the returns distribution and, more importantly, that the Fung and Hsieh factors have power not only for describing the risk premium but also, if appropriately exploited, for density forecasting.     

Prediction of Individual Bond Prices via a Dynamic Bond Pricing Model: Application to Japanese Government Bond Price Data

In this paper, we propose a dynamic bond pricing model and report the usefulness of our bond pricing model based on analysis of Japanese Government bond price data. We extend the concept of the time dependent Markov (TDM) model proposed by Kariya and Tsuda (Financial Engineering and the Japanese Markets, Kluwer Academic Publishers, Dordrecht, The Netherlands, Vol. 1, pp. 1–20) to a dynamic model, which can obtain information for future bond prices. A main feature of the extended model is that the whole stochastic process of the random cash-flow discount functions of each individual bond has a time series structure. We express the dynamic structure for the models by using a Bayesian state space representation. The state space approach integrates cross-sectional and time series aspects of individual bond prices. From the empirical results, we find useful evidence that our model performs well for the prediction of the patterns of the term structure of the individual bond returns.