Portfolio optimization for student t and skewed t returns

We consider the problem of valuing a European option written on an asset whose dynamics are described by an exponential Lévy-type model. In our framework, both the volatility and jump-intensity are allowed to vary stochastically in time through common driving factors—one fast-varying and one slow-varying. Using Fourier analysis we derive an explicit formula for the approximate price of any European-style derivative whose payoff has a generalized Fourier transform; in particular, this includes European calls and puts. From a theoretical perspective, our results extend the class of multiscale stochastic volatility models of Fouque et al. [Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives, 2011] to models of the exponential Lévy type. From a financial perspective, the inclusion of jumps and stochastic volatility allow us to capture the term-structure of implied volatility, as demonstrated in a calibration to S&;P500 options data.     

Portfolio selection: An extreme value approach

We show theoretically that lower tail dependence (χ), a measure of the probability that a portfolio will suffer large losses given that the market does, contains important information for risk-averse investors. We then estimate χ for a sample of DJIA stocks and show that it differs systematically from other risk measures including variance, semi-variance, skewness, kurtosis, beta, and coskewness. In out-of-sample tests, portfolios constructed to have low values of χ outperform the market index, the mean return of the stocks in our sample, and portfolios with high values of χ. Our results indicate that χ is conceptually important for risk-averse investors, differs substantially from other risk measures, and provides useful information for portfolio selection.     

Portfolio selection with two-stage preferences

We propose a model of portfolio selection under ambiguity, based on a two-stage valuation procedure which disentangles ambiguity and ambiguity aversion. The model does not imply “extreme pessimism” from the part of the investor, as multiple priors models do. Furthermore, its analytical tractability allows to study complex problems thus far not analyzed, such as joint uncertainty about means and variances of returns.     

Multivariate asset return prediction with mixture models

The use of mixture distributions for modeling asset returns has a long history in finance. New methods of demonstrating support for the presence of mixtures in the multivariate case are provided. The use of a two-component multivariate normal mixture distribution, coupled with shrinkage via a quasi-Bayesian prior, is motivated, and shown to be numerically simple and reliable to estimate, unlike the majority of multivariate GARCH models in existence. Equally important, it provides a clear improvement over use of GARCH models feasible for use with a large number of assets, such as constant conditional correlation, dynamic conditional correlation, and their extensions, with respect to out-of-sample density forecasting. A generalization to a mixture of multivariate Laplace distributions is motivated via univariate and multivariate analysis of the data, and an expectation–maximization algorithm is developed for its estimation in conjunction with a quasi-Bayesian prior. It is shown to deliver significantly better forecasts than the mixed normal, with fast and numerically reliable estimation. Crucially, the distribution theory required for portfolio theory and risk assessment is developed.     

Optimal capital growth with convex shortfall penalties

The optimal capital growth strategy or Kelly strategy has many desirable properties such as maximizing the asymptotic long-run growth of capital. However, it has considerable short-run risk since the utility is logarithmic, with essentially zero Arrow–Pratt risk aversion. It is common to control risk with a Value-at-Risk (VaR) constraint defined on the end of horizon wealth. A more effective approach is to impose a VaR constraint at each time on the wealth path. In this paper, we provide a method to obtain the maximum growth while staying above an ex-ante discrete time wealth path with high probability, where shortfalls below the path are penalized with a convex function of the shortfall. The effect of the path VaR condition and shortfall penalties is a lower growth rate than the Kelly strategy, but the downside risk is under control. The asset price dynamics are defined by a model with Markov transitions between several market regimes and geometric Brownian motion for prices within a regime. The stochastic investment model is reformulated as a deterministic programme which allows the calculation of the optimal constrained growth wagers at discrete points in time.     

The Effect of Information Quality on Optimal Portfolio Choice

Three types of agents acting on different information sets are considered: fully informed agents, insiders, and outsiders. Differences in information quality are shown to affect the properties of their optimal portfolios. For an outsider, the share of wealth invested in the stock is decreasing in the variance of the stock. However, for an insider, the effect of an increasing stock variance on the optimal portfolio weight is ambiguous. In a calibration to U.S. data, the confidence intervals of the insider's demand for the stock converge, whereas the outsider's confidence intervals become wider.     

Relative Robust Portfolio Optimization with benchmark regret

We extend Relative Robust Portfolio Optimization models to allow portfolios to optimize their performance when considered relative to a set of benchmarks. We do this in a minimum volatility setting, where we model regret directly as the maximum difference between our volatility and that of a given benchmark. Portfolio managers are also given the option of computing regret as a proportion of the benchmark’s performance, which is more in line with market practice than other approaches suggested in the literature. Furthermore, we propose using regret as an extra constraint rather than as a brand new objective function, so practitioners can maintain their current framework. We also look into how such a triple optimization problem can be solved or at least approximated for a general class of objective functions and uncertainty and benchmark sets. Finally, we illustrate the benefits of this approach by examining its performance against other common methods in the literature in several equity markets.     

Portfolio optimization with a defaultable security

In this paper we derive a closed-form solution for a representative investor who optimally allocates her wealth among the following securities: a credit-risky asset, a default-free bank account, and a stock. Although the inclusion of a credit-related financial product in the portfolio selection is more realistic, no closed-form solutions to date are given in the literature when a recovery value is considered in the event of a default. While most authors have assumed some recovery scheme in their initial model set up, they do not address the portfolio problem with a recovery when a default actually occurs. Given the tractability of the recovery of market value, we solved the optimal portfolio problem for the representative investor whose utility function is a Constant Relative Risk Aversion utility function. We find that the investor will allocate larger fraction of wealth to the defaultable security as long as the default-event risk is priced. These results are very intuitive and reasonable since it indicates that if the default risk premium is not priced properly the investor purchases less defaultable securities.     

Portfolio selection with commodities under conditional copulas and skew preferences

This article investigates the portfolio selection problem of an investor with three-moment preferences taking positions in commodity futures. To model the asset returns, we propose a conditional asymmetric t copula with skewed and fat-tailed marginal distributions, such that we can capture the impact on optimal portfolios of time-varying moments, state-dependent correlations, and tail and asymmetric dependence. In the empirical application with oil, gold and equity data from 1990 to 2010, the conditional t copulas portfolios achieve better performance than those based on more conventional strategies. The specification of higher moments in the marginal distributions and the type of tail dependence in the copula has significant implications for the out-of-sample portfolio performance.     

Portfolio construction incorporating asymmetric dependence structures: a user's guide

We outline a method of portfolio selection incorporating asymmetric dependency structures using copula functions. Assuming normally distributed marginal returns, we illustrate how asymmetric return correlations affect the efficient frontier and subsequent portfolio performance under a dynamic rebalancing framework. Implementing this methodology within the context of tactically allocating a small set of market indices, we demonstrate several key findings. First, we establish the manner by which the efficient frontier constructed under asymmetric dependence differs from a mean‐variance frontier. By establishing a paper portfolio based on these differences, we find that asymmetric correlation structures do have real economic value. The primary source of this economic value is the ability to better protect portfolio value and reduce the size of any erosion in return relative to the normal portfolio when asymmetric return correlations are accounted for.     

Portfolio selection with qualitative input

We formulate a mean-variance portfolio selection problem that accommodates qualitative input about expected returns and provide an algorithm that solves the problem. This model and algorithm can be used, for example, when a portfolio manager determines that one industry will benefit more from a regulatory change than another but is unable to quantify the degree of difference. Qualitative views are expressed in terms of linear inequalities among expected returns. Our formulation builds on the Black-Litterman model for portfolio selection. The algorithm makes use of an adaptation of the hit-and-run method for Markov chain Monte Carlo simulation. We also present computational results that illustrate advantages of our approach over alternative heuristic methods for incorporating qualitative input.     

Optimal hedge fund portfolios under liquidation risk

We use an expected utility framework to integrate the liquidation risk of hedge funds into portfolio allocation problems. The introduction of realistic investment constraints complicates the determination of the optimal solution, which is solved using a genetic algorithm that mimics the mechanism of natural evolution. We analyse the impact of the liquidation risk, of the investment constraints and of the agent's degree of risk aversion on the optimal allocation and on the optimal certainty equivalent of hedge fund portfolios. We observe, in particular, that the portfolio weights and their performance are significantly affected by liquidation risk. Finally, tight portfolio constraints can only provide limited protection against liquidation risk. This approach is of special interest to fund of hedge fund managers who wish to include the hedge fund liquidation risk in their portfolio optimization scheme.     

Marketing Period Risk in a Portfolio Context: Comment and Extension

This paper re-examines and extends the findings of Bond et al., Journal of Real Estate Finance and Economics, 34, 447–461, (2007) who consider the theoretical model of Lin and Vandell, Real Estate Economics, 35, 291–330, (2007) to determine the extent to which individual real estate asset return characteristics caused by marketing period risk disappear in a large, diversified real estate portfolio. The effects of marketing period risk are found to disappear in the limit with growth in the size of the portfolio, with ex ante variance approaching ex post variance, but only if the portfolio consists of nonsystematic risk alone, in which case both approach zero. The marketing period risk factor (MPRF), representing the ratio of ex ante to ex post variance, however, does not in general approach zero in the limit, in fact could increase or decrease depending upon the illiquidity characteristics of the individual assets and the magnitude and degree of correlation among individual property returns and marketing periods. The results suggest that even large institutional real estate portfolio managers must consider the illiquidity present in their portfolios and cannot assume that its effect will be diversified away.

Portfolio performance of linear SDF models: an out-of-sample assessment

We evaluate linear stochastic discount factor models using an ex-post portfolio metric: the realized out-of-sample Sharpe ratio of mean–variance portfolios backed by alternative linear factor models. Using a sample of monthly US portfolio returns spanning the period 1968–2016, we find evidence that multifactor linear models have better empirical properties than the CAPM, not only when the cross-section of expected returns is evaluated in-sample, but also when they are used to inform one-month ahead portfolio selection. When we compare portfolios associated to multifactor models with mean–variance decisions implied by the single-factor CAPM, we document statistically significant differences in Sharpe ratios of up to 10 percent. Linear multifactor models that provide the best in-sample fit also yield the highest realized Sharpe ratios.     

Portfolio Insurance with Liquidity Risk

This paper studies a portfolio insurance problem with liquidity risk. We consider an investor who wants to maximize the expected growth rate of wealth in a low liquid market. The investor can trade assets only at random times and his wealth must not fall below a predetermined floor. We find the optimal expected growth rate and an optimal strategy. The optimal strategy is closely related with a traditional constant proportion portfolio insurance strategy. Also we show that the same strategy maximizes the growth rate almost surely. Further we study the floor effect on the growth rate.     

Multivariate geometric expectiles

A generalization of expectiles for d-dimensional multivariate distribution functions is introduced. The resulting geometric expectiles are unique solutions to a convex risk minimization problem and are given by d-dimensional vectors. They are well behaved under common data transformations and the corresponding sample version is shown to be a consistent estimator. We exemplify their usage as risk measures in a number of multivariate settings, highlighting the influence of varying margins and dependence structures.     

International Asset Excess Returns and Multivariate Conditional Volatilities

This paper constructs a multivariate model in relating multi-asset excess returns to their conditional variances. Applying weekly data to investigate the foreign-exchange risk premium, the evidence from a multivariate GARCH model shows that the foreign-exchange excess returns are significantly correlated with economic fundamentals such as the real interest-rate differential, long-short interest-rate spread differential, and equity-premium differential. The evidence also suggests that foreign-exchange excess returns are not independent of the conditional variances of these fundamental variables, supporting the time-varying risk-premium hypothesis.     

居民最优消费与投资组合 ——基于不完全市场的分析

运用动态最优控制理论与随机金融分析方法,研究由劳动收入的特质风险与借贷约束导致的非完全市场对消费者最优投资和消费策略、波动及福利损失的影响,得到相应的动态最优投资和消费策略.研究发现:非完全市场会显著抑制消费者的消费动机和投资动机,并加剧消费波动和投资波动.此外,财务困境下非完全市场会对消费者造成高达40％ 的福利损失.     

Multivariate Tweedie lifetimes: the impact of dependence

Systematic longevity risk is increasingly relevant for public pension schemes and insurance companies that provide life benefits. In view of this, mortality models should incorporate dependence between lives. However, the independent lifetime assumption is still heavily relied upon in the risk management of life insurance and annuity portfolios. This paper applies a multivariate Tweedie distribution to incorporate dependence, which it induces through a common shock component. Model parameter estimation is developed based on the method of moments and generalized to allow for truncated observations. The estimation procedure is explicitly developed for various important distributions belonging to the Tweedie family, and finally assessed using simulation.