Kris Boudt

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

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.

Robust M-estimation of multivariate GARCH models

The Gaussian quasi-maximum likelihood estimator of Multivariate GARCH models is shown to be very sensitive to outliers in the data. A class of robust M-estimators for MGARCH models is developed. To increase the robustness of the estimators, the use of volatility models with the property of bounded innovation propagation is recommended. The Monte Carlo study and an empirical application to stock returns document the good robustness properties of the M-estimator with a fat-tailed Student t loss function.

The Gaussian rank correlation estimator: robustness properties

The Gaussian rank correlation equals the usual correlation coefficient computed from the normal scores of the data. Although its influence function is unbounded, it still has attractive robustness properties. In particular, its breakdown point is above 12%. Moreover, the estimator is consistent and asymptotically efficient at the normal distribution. The correlation matrix obtained from pairwise Gaussian rank correlations is always positive semidefinite, and very easy to compute, also in high dimensions. We compare the properties of the Gaussian rank correlation with the popular Kendall and Spearman correlation measures. A simulation study confirms the good efficiency and robustness properties of the Gaussian rank correlation. In the empirical application, we show how it can be used for multivariate outlier detection based on robust principal component analysis.

Asset Allocation with Conditional Value-at-Risk Budgets

Risk budgets are frequently used to estimate and allocate the risk of a portfolio by decomposing the total portfolio risk into the risk contribution of each component position. Many approaches to portfolio allocation use ex post methods for constructing risk budgets and take the variance as a risk measure. In this paper, however, we use ex ante methods to evaluate the component contribution to Conditional Value at Risk (CVaR) and to allocate risk. The proposed minimum CVaR concentration portfolio draws a balance between the investors return objectives and the diversification of risk across the portfolio. For a portfolio invested in bonds, commodities, equities, and real estate, we show that the minimum CVaR concentration portfolio offers an attractive compromise between the good risk-adjusted return properties of the minimum CVaR portfolio and the positive return potential and low portfolio turnover of an equal-weighted portfolio.

Jump Robust Two Time Scale Covariance Estimation and Realized Volatility Budgets

We estimate the daily integrated variance and covariance of stock returns using high-frequency data in the presence of jumps, market microstructure noise and non-synchronous trading. For this we propose jump robust two time scale (co)variance estimators and verify their reduced bias and mean square error in simulation studies. We use these estimators to construct the ex-post portfolio realized volatility (RV) budget, determining each portfolio component’s contribution to the RV of the portfolio return. These RV budgets provide insight into the risk concentration of a portfolio. Furthermore, the RV budgets can be directly used in a portfolio strategy, called the equal-risk-contribution allocation strategy. This yields both a higher average return and lower standard deviation out-of-sample than the equal-weight portfolio for the stocks in the Dow Jones Industrial Average over the period October 2007–May 2009.

Jump robust daily covariance estimation by disentangling variance and correlation components

A jump robust positive semidefinite rank-based estimator for the daily covariance matrix based on high-frequency intraday returns is proposed. It disentangles covariance estimation into variance and correlation components. This allows us to account for non-synchronous trading by estimating correlations over lower sampling frequencies. The efficiency gain of disentangling covariance estimation and the jump robustness of the estimator are illustrated in a simulation study. In an application to the Dow Jones Industrial Average constituents, it is shown that the proposed estimator leads to more stable portfolios.

Block Rearranging Elements within Matrix Columns to Minimize the Variability of the Row Sums

Several problems in operations research, such as the assembly line crew scheduling problem and the k-partitioning problem can be cast as the problem of finding the intra-column rearrangement (permutation) of a matrix such that the row sums show minimum variability. A necessary condition for optimality of the rearranged matrix is that for every block containing one or more columns it must hold that its row sums are oppositely ordered to the row sums of the remaining columns. We propose the block rearrangement algorithm with variance equalization (BRAVE) as a suitable method to achieve this situation. It uses a carefully motivated heuristic—based on an idea of variance equalization—to find optimal blocks of columns and rearranges them. When applied to the number partitioning problem, we show that BRAVE outperforms the well-known greedy algorithm and the Karmarkar–Karp differencing algorithm.

Implied returns and the choice of mean-variance efficient portfolio proxy

Implied expected returns are the expected returns for which a supposedly mean–variance efficient portfolio is effectively efficient, given a covariance matrix. The authors analyze the properties of monthly implied expected stock returns and study their sensitivity to the choice of mean–variance efficient portfolio proxy. For the universe of S&P 100 stocks over the period from 1984 to 2014, they find that using as risk-based portfolio proxy with respect to a market capitalization or fundamental value portfolio brings its biggest gains in return forecasts’ stability and precision. For all the proxies considered, they report that the implied expected returns outperform forecasts based on a time-series model in stability and precision.

Asset allocation with risk factors

In this paper, we propose to build portfolios that offer diversification over so-called ‘risk factors’ and this within a minimum variance portfolio construction framework. We believe this approach is an important advancement compared with traditional asset allocation as it achieves a higher level of true risk diversification, taking into account the common and unique risk factors that each asset class is exposed to. We apply the methodology to a portfolio invested in European government bonds, corporate bonds, high-yield bonds and equity. The first application consists of an ex post factor risk contribution analysis where we decompose the portfolio risk into the risk associated with the economic activity, inflation, interest rate, exchange rate, credit risk, market risk and idiosyncratic asset class-specific risk factors. In the second application, we construct minimum variance portfolios that satisfy ex ante constraints on the factor risk contributions.

The Impact of Covariance Misspecification in Risk-Based Portfolios

The equal-risk-contribution, inverse-volatility weighted, maximum-diversification and minimum-variance portfolio weights are all direct functions of the estimated covariance matrix. We perform a Monte Carlo study to assess the impact of covariance matrix misspecification to these risk-based portfolios. Our results show that the equal-risk-contribution and inverse-volatility weighted portfolio weights are relatively robust to covariance misspecification, but that the minimum-variance and maximum-diversification portfolios are highly sensitive to errors in the estimated variance and correlation, respectively.