Optimal portfolios with minimum capital requirements

We propose a novel approach to active risk management based on the recent Basel II regulations to obtain optimal portfolios with minimum capital requirements. In order to avoid regulatory penalties due to an excessive number of Value-at-Risk (VaR) violations, capital requirements are minimized subject to a given number of violations over the previous trading year. Capital requirements are based on the recent Basel II amendments to account for the ‘stressed’ VaR, that is, the downside risk of the portfolio under extreme adverse market conditions. An empirical application for two portfolios involving different types of assets and alternative stress scenarios demonstrates that the proposed approach delivers an improved balance between capital requirement levels and the number of VaR exceedances. Furthermore, the risk-adjusted performance of the proposed approach is superior to that of minimum-VaR and minimum-stressed VaR portfolios.     

Options on portfolios with higher-order moments

We develop a simple calibration approach to generate return distributions for multivariate asset distributions and use this technique to price options on portfolios given the first four co-moments of the joint distribution of returns. The technique is fast and captures the impact of covariance, and the co-skewness and co-kurtosis tensors on the value of these options. Given the technique works for a portfolio, the same is also applicable to options on individual securities as a special simpler case.     

Risk parity portfolios with risk factors

Portfolio construction and risk budgeting are the focus of many studies by academics and practitioners. In particular, diversification has spawned much interest and has been defined very differently. In this paper, we analyse a method to achieve portfolio diversification based on the decomposition of the portfolio’s risk into risk factor contributions. First, we expose the relationship between risk factor and asset contributions. Secondly, we formulate the diversification problem in terms of risk factors as an optimization program. Finally, we illustrate our methodology with a real example of building a strategic asset allocation based on economic factors for a pension fund facing liability constraints.     

Diversified minimum-variance portfolios

We build on a one parameter family of weighting schemes arising from \(L^2\)-constrained portfolio optimization problems. The parameter allows to fine tune the trade-off between the volatility and the diversification of the portfolio. We propose two criteria in order to determine two unique portfolios: the first criterion requires that no weights be negative while the second one imposes a target diversification which is median between full concentration and full diversification. Both portfolios are empirically compared to classical benchmarks. The first one behaves very much like other popular Long-Only weighting schemes while the second displays a more aggressive profile, while generating moderate turnover. We also discuss implementation issues, as well as estimation related problems.     

Constrained dynamic futures portfolios with stochastic basis

Annals of Finance - We study the problem of dynamically trading multiple futures contracts on different underlying assets subject to portfolio constraints. The spreads between futures and spot...     

Optimizing international portfolios with options and forwards

We develop a stochastic programming model to address in a unified manner a number of interrelated decisions in international portfolio management: optimal portfolio diversification and mitigation of market and currency risks. The goal is to control the portfolio’s total risk exposure and attain an effective balance between risk and expected return. By incorporating options and forward contracts in the portfolio optimization model we are able to numerically assess the performance of alternative tactics for mitigating exposure to the primary risks. We find that control of market risk with options has more significant impact on portfolio performance than currency hedging. We demonstrate through extensive empirical tests that incremental benefits, in terms of reducing risk and generating profits, are gained when both the market and currency risks are jointly controlled through appropriate means.     

Buy-and-hold mean-variance portfolios with a random exit strategy

We show how buy-and-hold investors can move from horizon uncertainty to profit opportunity. The analysis is conducted under a risk-averse framework rather than the standard Markowitz formulation in the case of i.i.d. asset processes. We make this practical achievement by considering a threshold stopping rule as the strategy to determine when to exit the market. The resulting investment horizon is random and can be correlated with the market. Under this setting, we first provide an analytical approximation to optimal weights, and then identify a class of reference variables associated with the stopping rule that leads to ex-ante improvements in portfolio allocation, vis-a-vis the fixed exit time alternative. The latter conclusion is based on a generalization of the Sharpe ratio, adjusted for horizon uncertainty. The obtained investment suggestion is simple and can be implemented empirically.     

Insurance contracts portfolios with heterogenous parametric life distributions

In this paper we consider two portfolios: one of m endowment insurance contracts and one of m whole life insurance contracts. We introduce the majorization order, Schur functions, and parametric families of distribution functions. We assume that the owners of the portfolios are exposed to different members of a known parametric family of distributions and study the effect of this stochastic heterogeneity on the premiums and death benefits of the insurance contracts. We show that the premiums paid in both contracts are Schur concave and that the death benefit awarded in the whole life contract is Schur convex. We provide upper and lower bounds for the premiums and for the death benefit, and compute the bounds for four parametric families of distribution functions used frequently in the Actuarial Sciences.     

Leveraged carry trade portfolios

Studying all possible pairs of 11 major currencies and 11 portfolios in 1976–2008 we show that, when there is no leverage, carry trade is significantly profitable for most currency pairs and portfolios. Positive returns do not diminish in time providing a strong case against the hypothesis of uncovered interest rate parity. We explain these findings with the leveraged nature of carry trade: leverage may increase profitability but it materially increases downside risk. We argue that market inefficiency is related to the level of leverage.     

Ex-ante performance of REIT portfolios

Review of Quantitative Finance and Accounting - The Real Estate Investment Trust (REIT) market has become an increasingly important vehicle for alternative investment for equity investors. While...     

Shrinkage estimation of Kelly portfolios

Although the Kelly portfolio is theoretically optimal in maximizing the long-term log-growth rate, in practice this is not always so. In this paper, we first show that the sample plug-in estimator of the Kelly portfolio weights is actually biased, and we then propose an unbiased estimator as an alternative. We further derive a shrinkage estimator under the objective of minimizing the expected growth loss of the actual growth relative to the true growth. An explicit formula for the shrinkage coefficient is established. Statistical properties for the shrinkage coefficient are studied through extensive Monte Carlo simulations, and conditions for obtaining accurate estimates for the shrinkage coefficient are also discussed. The effectiveness of the proposed unbiased and shrinkage Kelly portfolios in reducing the expected growth loss are validated by various simulation studies. It is found that our proposed shrinkage Kelly portfolio has superior performances in growth loss reduction, followed by the unbiased Kelly portfolio, and the sample plug-in Kelly portfolio. The advantages of our proposed unbiased and shrinkage Kelly portfolios for long-term investments are additionally confirmed by stock investment in the U.S. market.     

The duration of option portfolios

Duration is a value-weighted measure of average maturity which is commonly associated with portfolios of fixed-income securities. However, the concept finds application in option pricing theory also. This article shows that if options are valued by the Black (1976) formula and a comparative-statics methodology is employed, then the interest rate sensitivity of a portfolio of European options is equal to its duration. If the options are instead valued through the Black-Scholes (1973) formula, then the interest rate sensitivity is equal to only the ‘bond-equivalent duration’ inherent in a dynamic replication strategy for the option portfolio.     

Default estimation for low-default portfolios

Risk managers at financial institutions are concerned with estimating default probabilities for asset groups both for internal risk control procedures and for regulatory compliance. Low-default assets pose an estimation problem that has attracted recent concern. The problem in default probability estimation for low-default portfolios is that there is little relevant historical data information. No amount of data data-processing can fix this problem. More information is required. Incorporating expert opinion formally is an attractive option. The probability (Bayesian) approach is proposed, its feasibility demonstrated, and its relation to supervisory requirements discussed.     

Simulation-based Value-at-Risk for nonlinear portfolios

Value-at-risk (VaR) has been playing the role of a standard risk measure since its introduction. In practice, the delta-normal approach is usually adopted to approximate the VaR of portfolios with option positions. Its effectiveness, however, substantially diminishes when the portfolios concerned involve a high dimension of derivative positions with nonlinear payoffs; lack of closed form pricing solution for these potentially highly correlated, American-style derivatives further complicate the problem. This paper proposes a generic simulation-based algorithm for VaR estimation that can be easily applied to any existing procedures. Our proposal leverages cross-sectional information and applies variable selection techniques to simplify the existing simulation framework. Asymptotic properties of the new approach demonstrate faster convergence due to the additional model selection component introduced. We have also performed sets of numerical results that verify the effectiveness of our approach in comparison with some existing strategies.     

A model for tax advantages of portfolios with many assets

Taxable portfolios present challenges for optimization models with even a limited number of assets. Holding many assets, however, has a distinct tax advantage over holding few assets. In this paper, we develop a model that takes an extreme view of a portfolio as a continuum of assets to gain the broadest possible advantage from holding many assets. We find the optimal strategy for trading in this portfolio in the absence of transaction costs and develop bounding approximations on the optimal value. We compare the results in a simulation study to a portfolio consisting only of a market index and show that the multi-asset portfolio’s tax advantage can lead either to significant consumption or bequest increases.     

Optimal portfolios under worst-case scenarios

In standard portfolio theories such as Mean–Variance optimization, expected utility theory, rank dependent utility heory, Yaari’s dual theory and cumulative prospect theory, the worst outcomes for optimal strategies occur when the market declines (e.g. during crises), which is at odds with the needs of many investors. Hence, we depart from the traditional settings and study optimal strategies for investors who impose additional constraints on their final wealth in the states corresponding to a stressed financial market. We provide a framework that maintains the stylized features of the SP/A theory while dealing with the goal of security in a more flexible way. Preferences become state-dependent, and we assess the impact of these preferences on trading decisions. We construct optimal strategies explicitly and show how they outperform traditional diversified strategies under worst-case scenarios.     

Correlation dynamics of global industry portfolios

This paper investigates the time series of realized correlations between global industries and the world market over the 1979–2008 period. The behavior of industry correlations is characterized by long-term swings, with a period of historically low correlations in the late 1990s. The Telecommunications and the Financials industries show a positive secular trend. Global industry correlations move countercyclically. Furthermore, there is evidence that industry correlations are higher for market downside moves than for upside moves.