Showing papers in "Journal of Risk in 2010"

Stochastic Kriging for Efficient Nested Simulation of Expected Shortfall

Abstract: We use stochastic kriging, a metamodeling technique, to speed up nested simulation of expected shortfall, a portfolio risk measure. Evaluating a risk measure of a portfolio that includes derivative securities may require nested Monte Carlo simulation. The outer level simulates financial scenarios and the inner level of simulation estimates the portfolio value given a scenario. Spatial metamodeling enables inference about portfolio values in a scenario based on inner-level simulation of nearby scenarios, reducing the required computational effort: it is not necessary to perform inner-level simulation in every scenario. Because expected shortfall involves the scenarios that entail the largest losses, our procedure adaptively allocates more computational effort to inner-level simulation of those scenarios, which also improves computational efficiency.

On correlating Lévy processes

Abstract: A relatively simple approach to correlating unit period returns of Levy processes is developed. We write the Levy process as a time changed Brownian motion and correlate the Brownian motions. It is shown that sample correlations understate the required correlation between the Brownian motions and we show how to correct for this. Pairwise tests illustrate the adequacy of the model and the signi…cant improvement o¤ered over the Gaussian alternative. We therefore advocate that the correlated time change model is a simple basic alternative to dependence modeling. From the perspective of explaining portfolio returns in higher dimensions we …nd adequacy for long-short portfolios. The long only portfolios appear to require a more complex modeling of dependency. We leave these questions for future research.

On the aggregation of risk

Abstract: The objective of this paper is to propose a general framework for aggregating economic capital across risk types. Our starting point are aggregation models that operate in a single-period framework, typically with a planning horizon of one year. As an example, we present Deutsche Bank’s EC aggregation model including calibration techniques for correlation parameters. The second part of the paper focuses on the development of multi-period extensions of the traditional single-period approach. We argue that multiperiod models provide the natural setting for aggregating risk types with different liquidity profiles. Several rollover and risk management strategies are presented and their impact is analyzed in a number of examples.

Markets, profits, capital, leverage and return

Abstract: The theory of two price markets of Cherny and Madan (2010) yields closed forms for bid and ask prices. De…ning pro…ts as the dierence be- tween the mid quote and the risk neutral expectation and capital as dif- ference between the ask and the bid price one obtains precise expressions for these entities and thereby also returns. New expressions are developed for the bid and ask prices in terms of the sensitivity of the inverse distrib- ution function to the quantile level. The latter turns out to be a measure of risk exposure at the quantile level. The theory is illustrated on un- hedged exposures in the Black Merton Scholes model, followed by variance swaps and call options for variance gamma underliers. It is argued that markets should economize capital and furthermore the maximization of expected utility may involve an uneconomic use of capital. We further observe that stock positions should be revised downwards from zero delta in left skewed markets in response to the target gamma when minimizing capital committments.

Measuring concentration risk for regulatory purposes

Abstract: The measurement of concentration risk in credit portfolios is necessary for the determination of regulatory capital under Pillar 2 of Basel II as well as for managing portfolios and allocating economic capital. Existing multi-factor models that deal with concentration risk are often inconsistent with the Pillar 1 capital requirements. Therefore, we adjust these models to achieve Basel II-compliant results. Within a simulation study we test the impact of sector concentrations on several portfolios and contrast the accuracy of the different models. In this context, we also compare Value at Risk and Expected Shortfall regarding their suitability to assess concentration risk.

Modeling extreme returns and asymmetric dependence structures of hedge fund strategies using extreme value theory and copula theory

Abstract: We use extreme value theory and copula theory to model multivariate daily return distributions of hedge fund strategy indexes. Multivariate outliers in time series of hedge fund strategies are clustered when volatilities and credit spreads increase and investors take a “flight to quality” and seek liquidity. In light of the strong “domino effect” in daily return series of hedge fund strategy indexes during the financial crisis 2008–9, the generalized Pareto distribution copula approach is an appropriate modeling choice for approximating multivariate hedge fund distributions exhibiting extreme return observations and asymmetric dependence structures. Generalized Pareto distributions are efficient approximations for the fat-tailed distributions of returns on hedge funds exceeding high thresholds. Tests for correlation symmetry show that dependence structures between several hedge fund strategies are often asymmetric. Copulas can be used to model symmetric and asymmetric dependence structures between different hedge fund strategies.

High-conviction equity portfolio optimization

Abstract: We investigate the construction of well-diversified high-conviction equity portfolios using the portfolio diversification index (PDI). This paper is the first to investigate the out-of-sample properties of the PDI. Our research applies a novel portfolio selection algorithm to maximize the PDI of a portfolio of stocks in the Standard & Poor’s S&P 500 index over the period 2000–2009. We construct equally weighted, well-diversified portfolios consisting of 5 to 30 stocks, and compare these with randomly selected portfolios of the same number of stocks. Our results indicate that investors using our algorithm to maximize the PDI can improve the diversification of high-conviction equity portfolios. For example, a portfolio of 20 stocks constructed using the algorithm with the PDI behaves outof-sample as if it contains 10 independent stocks, ie, a PDI score of 10. This is a significant improvement over the PDI score of 7 that occurs with a randomly selected portfolio. Our research is robust with respect to the number of stocks in the investment portfolio and the time period under consideration.