Showing papers in "Journal of Risk in 2008"

Estimation and decomposition of downside risk for portfolios with non-normal returns

Abstract: We propose a new estimator for expected shortfall that uses asymptotic expansions to account for the asymmetry and heavy tails in financial returns. We provide all the necessary formulas for decomposing estimators of value-at-risk and expected shortfall based on asymptotic expansions and show that this new methodology is very useful for analyzing and predicting the risk properties of portfolios of alternative investments.

On Testing the Equality of the Multiple Sharpe Ratios, with Application on the Evaluation of Ishares

Abstract: Extending the work of Jobson and Korkie (1981), Lo (2002) and Memmel (2003), this paper applies the technique of the repeated measures design to develop the Multiple Sharpe ratio test statistic to test the hypothesis of the equality of the multiple Sharpe ratios. We also work out the asymptotic distribution of the statistic and its properties. To demonstrate the superiority of our proposed statistic over the traditional pair-wise Sharpe ratio test, we illustrate our approach by testing the equality of Sharpe ratios for the eighteen iShares. Whereas the pair-wise Sharpe ratio test show that the performance of all the 18 iShares are indistinguishable, our test results reject the equality of the Sharpe ratios in each year as well as in the entire sample; implying that the 18 iShares perform differently in each year as well as in the entire sample, with some outperforming others in the market. The test in our paper provides investors with a tool to evaluate their portfolio performances and enables them to make wiser decisions in their investments.

How much structure is best? A comparison of market model, factor model and unstructured equity covariance matrices

Abstract: This paper compares three approaches to estimating equity covariance matrices: a factor model, a market model and an unstructured asset-by-asset model. These approaches make different trade-offs between estimation variance and model specification error. We explore this trade-off with a simulation experiment and with an empirical analysis of UK equity portfolios. The factor model is found to perform best for large investment universes and typical sample lengths. The market model underperforms due to excessive specification error while an asset-by-asset model with a short half-life of 22 days underperforms due to high estimation variance. The importance of properly accounting for serial correlation is highlighted.

Evaluating value-at-risk measures in the presence of long memory conditional volatility

Abstract: This work analyze different approaches in the evaluation of Value-atRisk measures when returns show long memory patterns in conditional variance. In a Montecarlo study we follow the approaches of Kupiec (1995), Christoffersen (1998), Christoffersen, Hahn and Inoue (2001) and Lopez (1998) using the suggested test and loss functions in choosing the best model among a group of alternatives (GARCH, IGARCH, the true FIGARCH DGP and the EWMA). Our Montecarlo analysis shows that the test of Kupiec and the loss function approach lead to the choice of a misspecified model, while the test of Christoffersen et al. (2001) correctly identify long memory. We apply then all the previous tests and measures in the comparison of different models for the Value-at-Risk of the returns of the FIB30, the future on the italian stock market index.

Algorithms for handling CVaR-constraints in dynamic stochastic programming models with applications to finance

Abstract: We propose dual decomposition and solution schemes for multistage CVaR-constrained problems. These schemes meet the need for handling multiple CVaR-constraints for different time frames and at different confidence levels. Hence they allow shaping distributions according to the decision maker's preference.With minor modifications, the proposed schemes can be used to decompose further types of risk constraints in dynamic portfolio management problems. We consider integrated chance constraints, second-order stochastic dominance constraints, and constraints involving a special value-of-information risk measure. We also suggest application to further financial problems. We propose a dynamic risk-constrained optimization model for option pricing. Moreover we propose special mid-term constraints for use in asset-liability management.

Empirical likelihood for value-at-risk and expected shortfall

Abstract: When estimating risk measures, whether from historical data or by Monte Carlo simulation, it is helpful to have confidence intervals that provide information about statistical uncertainty. We provide asymptotically valid confidence intervals and confidence regions involving value-at-risk (VaR), conditional tail expectation and expected shortfall (conditional VaR), based on three different methodologies. One is an extension of previous work based on robust statistics, the second is a straightforward application of bootstrapping, and we derive the third using empirical likelihood. We then evaluate the small-sample coverage of the confidence intervals and regions in simulation experiments using financial examples. We find that the coverage probabilities are approximately nominal for large sample sizes, but are noticeably low when sample sizes are too small (roughly, less than 500 here). The new empirical likelihood method provides the highest coverage at moderate sample sizes in these experiments. We want to measure the risk of a given portfolio that has random profits at the end of a predetermined investment period. We can sample from the distribution of the portfolio’s profits using Monte Carlo simulation based on a stochastic model of financial markets. Our focus will be on estimating risk measures for our portfolio based on simulated profits and providing information in the form of confidence intervals and regions about the statistical uncertainty of these estimates. We address only this Monte Carlo sampling error in estimating risk, not the model risk that includes errors introduced by using an incorrect model of financial markets and statistical error in estimating the model’s parameters from data. We will emphasize moderate Monte Carlo sample sizes, which are appropriate when

Value-at-risk and extreme value distributions for financial returns

Abstract: The ability of the Generalised Extreme Value (GEV) and Generalised Logistic (GL) distributions to fit extreme financial returns in the stock, commodities and bond markets is assessed. The empirical results indicate that the too much celebrated GEV is not the most appropriate model for the data since the fatter tailed GL is found to provide better descriptions of the extreme returns. Extreme Value Theory (EVT) based VaR estimates are then derived and compared to those generated by traditional methods. The results show that when the focus is on the really ruinous events which are located deep into the tails of the returns distribution, the EVT methods used in this study can be particularly useful since they produce VaR estimates that outperform those derived by the traditional methods at high confidence levels. However, these estimates were found to be considerably higher than those derived by traditional VaR models; consequently leading to higher capital reserves for financial institutions.

Overcoming dimensional dependence of worst case scenarios and maximum loss

Abstract: Maximum Loss shows a peculiar kind of dimensional dependence: for a fixed portfolio and fixed probability of the admissibility domain, the inclusion of additional irrelevant risk factors increases Maximum Loss. For elliptical distributions we propose a definition of Maximum Loss which we show to be free of this undesirable property. If we characterise the admissibility domain by its Mahalanobis radius instead of its probability mass, the inclusion of irrelevant risk factors, or of risk factors which are highly correlated to other risk factors, does not affect Maximum Loss.

Hedging under alternative stickiness assumptions: an empirical analysis for barrier options

Abstract: In this study, we empirically analyze dynamic hedges of barrier options in the local volatility model using more than five years of data on the DAX, a major German equity index. The emphasis is on the comparison of the hedge performance of different hedging strategies under alternative stickiness assumptions on the dynamics of the implied volatility surface. We compare sticky-strike, sticky-moneyness and local volatility-implied (model-consistent) hedges for barrier options with a maturity of one and two years. We find that sticky-strike performs best, with the choice of the hedging strategy being a much more important factor for successful risk management than the stickiness assumption.

The long-term risk caused by the stock market bubble

Abstract: In this paper we quantify the risk caused by the crash of a pricing bubble in the US stock market by utilizing a recently introduced econometric bubble model. The skewness and kurtosis are shown to vary widely with the price-dividend ratio. Simulation experiments quantify how the moments and VaR of the predictive distribution depend on the holding period, the price-dividend ratio and inflation. This information is useful in deciding on market timing and needed risk capital. In addition the analysis of higher moments support the old wisdom that stocks are a more attractive investment in the long run than in the short run.

Firm specific option risk and implications for asset pricing

Abstract: This paper examines the benefits and costs of investing in firm specific options as an additional investment in a portfolio. We examine twelve option strategies and find that there is significant negative (positive) abnormal return to buying (selling) puts from January 1996 through July 2006. There is almost no additional benefit from going long any option, and some benefit from selling calls, dependent on the amount option leverage taken. Additionally, we find that the premiums from selling puts are not related to any specific firm characteristic, suggesting a pervasive premium for puts. Asset pricing tests that include market option return factors are unable to explain the returns to firm specific options. Tests on delta-hedged portfolios confirm that the gains to puts are related to idiosyncratic volatility and not market volatility. This is indicative an idiosyncratic volatility risk premium that is distinct from idiosyncratic price risk.

Hedging Portfolios of Financial Guarantees

Abstract: We propose a framework a la Davis et al. (1993) and Whalley and Wilmott (1997) to study dynamic hedging strategies on portfolios of financial guarantees in the presence of transaction costs. We contrast four dynamic hedging strategies including a utility-based dynamic hedging strategy, in conjunction with using an asset-based index, with the strategy of no hedging. For the proposed utility-based strategy, the portfolio rebalancing is triggered by the tradeoff between transaction costs and utility gains. Overall, using a Froot and Stein (1998) and Perold (2005) type of risk-adjusted performance measurement metric, we find the utility-based strategy to be a good compromise between the delta hedging strategy and the passive stance of doing nothing. This result is even stronger with higher transaction costs. However, if the insured firms assets are not traded or in a high transaction costs environment, the guarantor can use an index-based security as hedging instrument. JEL classification code: G11, G13, G22.