A single-period model and some empirical evidences for optimal asset allocation with value-at-risk constraints

In this paper, we consider the optimal asset allocation problems under VaR constraints. It is shown that the separation property holds to a certain extent. The optimal allocation of funds in risky assets is dependent on the distribution of the returns of risky assets and the VaR level, but independent of the acceptable loss ratio; the amount to be borrowed or lent at the risk free rate depends on the acceptable loss ratio. A general asset allocation model under VaR constraints is derived. As an application of our model, we address the optimal asset allocation between two categories of assets—bonds and stocks. Interesting empirical results are obtained for the US, Australia and the UK. The empirical results show that the mechanism of asset allocation under VaR constraints is fundamentally different from the classical mean-variance approach. The empirical results appear to support our model and demonstrate the potential usefulness of our approach.Value at Risk, optimal asset allocation, separation property, empirical

Dynamic asset (and liability) management under market and credit risk

We introduce a modelling paradigm which integrates credit risk and market risk in describing the random dynamical behaviour of the underlying fixed income assets. We then consider an asset and liability management (ALM) problem and develop a mul- tistage stochastic programming model which focuses on optimum risk decisions. These models exploit the dynamical multiperiod structure of credit risk and provide insight into the corrective recourse decisions whereby issues such as the timing risk of default is appropriately taken into consideration. We also present a index tracking model in which risk is measured (and optimised) by the CVaR of the tracking portfolio in relation to the index. Both in- and out-of-sample (backtesting) experiments are undertaken to validate our approach. In this way we are able to demonstrate the feasibility and flexibility of the chosen framework

Asset Allocation under the Basel Accord Risk Measures

Financial institutions are currently required to meet more stringent capital requirements than they were before the recent financial crisis; in particular, the capital requirement for a large bank's trading book under the Basel 2.5 Accord more than doubles that under the Basel II Accord. The significant increase in capital requirements renders it necessary for banks to take into account the constraint of capital requirement when they make asset allocation decisions. In this paper, we propose a new asset allocation model that incorporates the regulatory capital requirements under both the Basel 2.5 Accord, which is currently in effect, and the Basel III Accord, which was recently proposed and is currently under discussion. We propose an unified algorithm based on the alternating direction augmented Lagrangian method to solve the model; we also establish the first-order optimality of the limit points of the sequence generated by the algorithm under some mild conditions. The algorithm is simple and easy to implement; each step of the algorithm consists of solving convex quadratic programming or one-dimensional subproblems. Numerical experiments on simulated and real market data show that the algorithm compares favorably with other existing methods, especially in cases in which the model is non-convex

Optimal Contracts for Teams of Money Managers

The optimal organizational form and optimal incentive contract are characterized for a team of money managers, assuming that the investor (principal) is risk averse and that each manager's (agent's) actions affect both that manager's expected return and the correlation of returns between managers. If the managers are risk tolerant, then a noncooperative team organization and a strictly competitive contract, in which each manager is rewarded both for doing well and for doing better than the team, is the most efficient way to discourage herding within the team. This is despite the fact that, in such a contract total wages paid are a concave function of total returns, and so using the contract to discourage herding (and thus achieve lower risk) is in direct conflict with the investor's objective of using the contract to transfer risk onto the managers. As the risk aversion of both the investor and the managers increases, cooperation among managers becomes the optimal way to organize the team. For some parameter values, if everyone is risk averse, first-best can be achieved under cooperation. First-best without herding can never be achieved if the managers are risk tolerant, or if cooperation is infeasiblecontracts for teams, money managers

Data-driven satisficing measure and ranking

We propose an computational framework for real-time risk assessment and prioritizing for random outcomes without prior information on probability distributions. The basic model is built based on satisficing measure (SM) which yields a single index for risk comparison. Since SM is a dual representation for a family of risk measures, we consider problems constrained by general convex risk measures and specifically by Conditional value-at-risk. Starting from offline optimization, we apply sample average approximation technique and argue the convergence rate and validation of optimal solutions. In online stochastic optimization case, we develop primal-dual stochastic approximation algorithms respectively for general risk constrained problems, and derive their regret bounds. For both offline and online cases, we illustrate the relationship between risk ranking accuracy with sample size (or iterations).Comment: 26 Pages, 6 Figure

RM-CVaR: Regularized Multiple β\beta-CVaR Portfolio

The problem of finding the optimal portfolio for investors is called the portfolio optimization problem. Such problem mainly concerns the expectation and variability of return (i.e., mean and variance). Although the variance would be the most fundamental risk measure to be minimized, it has several drawbacks. Conditional Value-at-Risk (CVaR) is a relatively new risk measure that addresses some of the shortcomings of well-known variance-related risk measures, and because of its computational efficiencies, it has gained popularity. CVaR is defined as the expected value of the loss that occurs beyond a certain probability level ($\beta$). However, portfolio optimization problems that use CVaR as a risk measure are formulated with a single $\beta$ and may output significantly different portfolios depending on how the $\beta$ is selected. We confirm even small changes in $\beta$ can result in huge changes in the whole portfolio structure. In order to improve this problem, we propose RM-CVaR: Regularized Multiple $\beta$-CVaR Portfolio. We perform experiments on well-known benchmarks to evaluate the proposed portfolio. Compared with various portfolios, RM-CVaR demonstrates a superior performance of having both higher risk-adjusted returns and lower maximum drawdown.Comment: accepted by the IJCAI-PRICAI 2020 Special Track AI in FinTec

Data Envelopment Analysis Models of Investment Funds

Publisher PD