We propose a model of portfolio selection that adjusts an investors’ portfolio allocation in accordance with changing market liquidity environments and market conditions. We found that market liquidity provides a useful “leading indicator” in dynamic asset allocation. Specifically, market liquidity risk premium cycles anticipate economic and market cycles. Investors can therefore act to avoid markets with low liquidity premiums, waiting to extract liquidity risk premiums when the likelihood of extracting a liquidity premium improves. The result, meaningfully enhanced portfolio performance through economic and market cycles, and is robust to transactions costs and alternate specifications.

We propose that fund performance can be predicted by its R2, obtained from a regression of its returns on a multifactor benchmark model. Lower R2 indicates greater selectivity, and it significantly predicts better performance. Stock funds sorted into lowest-quintile lagged R2 and highest-quintile lagged alpha produce significant annual alpha of 3.8%. Across funds, R2 is positively associated with fund size and negatively associated with its expenses and manager's tenure.

Since Lehman Brothers collapsed in 2008, tail-risk hedging has become an increasingly important concern for investors. Traditional approaches, such as purchasing options or variance swaps as insurance, are often expensive, illiquid, and result in a substantial drag on performance. A more prudent, cost-effective way to maintain a constant risk exposure is to actively manage portfolio exposure according to the prevailing volatility level within underlying assets. The authors implement a robust methodology based on Dybvig’s payoff distribution model to target a constant level of volatility and normalize monthly returns. This approach to portfolio and risk management can help investors obtain their desired risk exposures over both short and longer time frames, reduce exposure to tail risk, and in general increase portfolios’ risk-adjusted performance.

Portfolio optimization problems involving value at risk (VaR) are often computationally intractable and require complete information about the return distribution of the portfolio constituents, which is rarely available in practice. These difficulties are compounded when the portfolio contains derivatives. We develop two tractable conservative approximations for the VaR of a derivative portfolio by evaluating the worst-case VaR over all return distributions of the derivative underliers with given first- and second-order moments. The derivative returns are modelled as convex piecewise linear or—by using a delta–gamma approximation—as (possibly nonconvex) quadratic functions of the returns of the derivative underliers. These models lead to new worst-case polyhedral VaR (WPVaR) and worst-case quadratic VaR (WQVaR) approximations, respectively. WPVaR serves as a VaR approximation for portfolios containing long positions in European options expiring at the end of the investment horizon, whereas WQVaR is suitable for portfolios containing long and/or short positions in European and/or exotic options expiring beyond the investment horizon. We prove that—unlike VaR that may discourage diversification—WPVaR and WQVaR are in fact coherent risk measures. We also reveal connections to robust portfolio optimization.

A common challenge in portfolio risk analysis is that certain assets have shorter return histories than others. Unfortunately, many standard portfolio risk analysis techniques—including historical tail risk measurement, regime-dependent risk analysis, and bootstrapping simulations—require full return histories for all assets or risk factors. The author presents easy instructions on how to efficiently combine data for investments whose histories differ in length and offers a new model to better account for non-normal distributions.

Going beyond the simple bid–ask spread overlay for a particular Value at Risk, the author introduces an innovative framework that integrates liquidity risk, funding risk, and market risk. He overlaid a whole distribution of liquidity uncertainty on future market risk scenarios and allowed the liquidity uncertainty to vary from one scenario to another, depending on the liquidation or funding policy implemented. The result is one easy-to-interpret, easy-to-implement formula for the total liquidity-plus-market-risk profit and loss distribution.

This paper proposes a framework for the modeling, inference and forecasting of volatility in the presence of level shifts of unknown timing, magnitude and frequency. First, we consider a stochastic volatility model comprising both a level shift and a short-memory component, with the former modeled as a compound binomial process and the latter as an AR(1). Next, we adopt a Bayesian approach for inference and develop algorithms to obtain posterior distributions of the parameters and the two latent components. Then, we apply the model to daily S&P 500 and NASDAQ returns over the period 1980.1–2010.12. The results show that although the occurrence of a level shift is rare, about once every two years, this component clearly contributes most to the variation in the volatility. The half-life of a typical shock from the AR(1) component is short, on average between 9 and 15 days. Interestingly, isolating the level shift component from the overall volatility reveals a stronger relationship between volatility and business cycle movements. Although the paper focuses on daily index returns, the methods developed can potentially be used to study the low frequency variation in realized volatility or the volatility of other financial or macroeconomic variables.

We test the performance of different volatility estimators that have recently been proposed in the literature and have been designed to deal with problems arising when ultra high-frequency data are employed: microstructure noise and price discontinuities. Our goal is to provide an extensive simulation analysis for different levels of noise and frequency of jumps to compare the performance of the proposed volatility estimators. We conclude that the maximum likelihood estimator filter (MLE-F), a two-step parametric volatility estimator proposed by Cartea and Karyampas (2011a; The relationship between the volatility returns and the number of jumps in financial markets, SSRN eLibrary, Working Paper Series, SSRN), outperforms most of the well-known high-frequency volatility estimators when different assumptions about the path properties of stock dynamics are used.

This paper proposes a simple model for incorporating wrong-way and right-way risk into CVA (credit value adjustment) calculations. These are the calculations, involving Monte Carlo simulation, made by a dealer to determine the reduction in the value of its derivatives portfolio because of the possibility of a counterparty default. The model assumes a relationship between the hazard rate of the counterparty and variables whose values can be generated as part of the Monte Carlo simulation. Numerical results for portfolios of 25 instruments dependent on five underlying market variables are presented. The paper finds that wrong-way and right-way risk have a significant effect on the Greek letters of CVA as well as on CVA itself. It also finds that the percentage effect depends on the collateral arrangements.

We propose a new method for measuring the quality of banks' credit portfolios. This method makes use of information embedded in bank share prices by exploiting differences in their sensitivity to credit default swap spreads of borrowers of varying quality. The method allows us to derive a credit risk indicator (CRI). This indicator represents the perceived share of high-risk exposures in a bank's portfolio and can be used as a risk weight for computing regulatory capital requirements. We estimate CRIs for the 150 largest U.S. bank holding companies. We find that their CRIs are able to forecast bank failures and share price performances during the crisis of 2007–2009, even after controlling for a variety of traditional asset quality and general risk proxies.

We investigate a new non-stationary non-parametric volatility model, in which the conditional variance of time series is modelled as a non-parametric function of an integrated or near-integrated covariate. Importantly, the model can generate the long memory property in volatility and allow the unconditional variance of time series to be time-varying. These properties cannot be derived from most existing non-parametric or semi-parametric volatility models. We show that the kernel estimate of the model is consistent and its asymptotic distribution is mixed normal. For an empirical application of the model, we study the daily S&P 500 index return volatility using the VIX index as the covariate. It is shown that our model performs reasonably well both in within-sample and out-of-sample forecasts.

Numerous issues have arisen over the past few decades relating to the implied volatility smile in the options market; however, the extant literature reveals that relatively little effort has thus far been placed into comparing the various implied volatility models, essentially as a result of the lack of any theoretical foundation on which to base such comparative analysis. In this study, we use a comprehensive options database and employ methods of combining the various hypothesis tests to compare the different implied volatility models. To the best of our knowledge, this is the first study of its kind to address this issue using combination tests. Our empirical results reveal that the linear piecewise model is the most appropriate model for capturing the implied volatility smile, with additional robustness checks confirming the validity of this finding.

We develop a new approach to approximating asset prices in the context of continuous-time models. For any pricing model that lacks a closed-form solution, we provide a solution, which relies on the approximation of the intractable model through a known, "auxiliary" one. We derive an expression for the difference between the true (but unknown) price and the auxiliary one, which we approximate in closed-form, and use to create increasingly improved refinements to the initial mispricing induced by the auxiliary model. The approach is intuitive, simple to implement and leads to fast and extremely accurate approximations. We illustrate this method in a variety of contexts, including option pricing with stochastic volatility, volatility contracts and the term-structure of interest rates.

The usage pattern is based on an offline phase to calibrate and generate model libraries. Valuation and simulation algorithms are planned offline with portfolio specific optimizations. The interactive user-driven phase includes a coherent global market simulation taking a few minutes and a real time data exploration phase with response time below 10 seconds.

Data exploration includes 3-dimensional risk visualization of portfolio loss distributions and sensitivities. It also includes risk resolution capability for outliers from the global portfolio level down to the single instrument level and hedge ratio optimization. The network bottleneck is bypassed by using heterogeneous boards with acceleration. The memory bottleneck is avoided at the algorithmic level by adapting the mathematical framework to revolve around a handful of compute-bound algorithms.

The main contribution of the paper is the back-testing and comparison of market-neutral PCA- and ETF- based strategies over the broad universe of U.S. equities. Back-testing shows that, after accounting for transaction costs, PCA-based strategies have an average annual Sharpe ratio of 1.44 over the period 1997 to 2007, with a much stronger performances prior to 2003: during 2003-2007, the average Sharpe ratio of PCA-based strategies was only 0.9. On the other hand, strategies based on ETFs achieved a Sharpe ratio of 1.1 from 1997 to 2007, but experience a similar degradation of performance after 2002. We introduce a method to take into account daily trading volume information in the signals (using "trading time'' as opposed to calendar time), and observe significant improvements in performance in the case of ETF-based signals. ETF strategies which use volume information achieve a Sharpe ratio of 1.51 from 2003 to 2007.