Cash management using multi-stage stochastic programming

We consider a cash management problem where a company with a given financial endowment and given future cash flows minimizes the Conditional Value at Risk of final wealth using a lower bound for the expected terminal wealth. We formulate the optimization problem as a multi-stage stochastic linear program (SLP). The company can choose between a riskless asset (cash), several default- and option-free bonds, and an equity investment, and rebalances the portfolio at every stage. The uncertainty faced by the company is reflected in the development of interest rates and equity returns. Our model has two new features compared to the existing literature, which uses no-arbitrage interest rate models for the scenario generation. First, we explicitly estimate a function for the market price of risk and change the underlying probability measure. Second, we simulate scenarios for equity returns with moment-matching by an extension of the interest rate scenario tree.     

Dynamic asset–liability management in a Markov market with stochastic cash flows

This paper provides a general model to investigate an asset–liability management (ALM) problem in a Markov regime-switching market in a multi-period mean–variance (M–V) framework. Emphasis is placed on the stochastic cash flows in both wealth and liability dynamic processes, and the optimal investment and liquidity management strategies in achieving the M–V bi-objective of terminal surplus are evaluated. In this model, not only the asset returns and liability returns, but also the cash flows depend on the stochastic market states, which are assumed to follow a discrete-time Markov chain. Adopting the dynamic programming approach, the matrix theory and the Lagrange dual principle, we obtain closed-form expressions for the efficient investment strategy. Our proposed model is examined through empirical studies of a defined contribution pension fund. In-sample results show that, given the same risk level, an ALM investor (a) starting in a bear market can expect a higher return compared to beginning in a bull market and (b) has a lower expected return when there are major cash flow problems. The effects of the investment horizon and state-switching probability on the efficient frontier are also discussed. Out-of-sample analyses show the dynamic optimal liquidity management process. An ALM investor using our model can achieve his or her surplus objective in advance and with a minimum variance close to zero.     

Optimal investment under multi-factor stochastic volatility

We consider a model for multivariate intertemporal portfolio choice in complete and incomplete markets with a multi-factor stochastic covariance matrix of asset returns. The optimal investment strategies are derived in closed form. We estimate the model parameters and illustrate the optimal investment based on two stock indices: S&P500 and DAX. It is also shown that the model satisfies several stylized facts well known in the literature. We analyse the welfare losses due to suboptimal investment strategies and we find that investors who invest myopically, ignore derivative assets, model volatility by one factor and ignore stochastic covariance between asset returns can incur significant welfare losses.     

Optimal multi-period consumption and investment with short-sale constraints

This article examines agents’ consumption-investment problem in a multi-period pure exchange economy where agents are constrained with the short-sale of state-dependent risky contingent claims. In equilibrum, agents hold options written on aggregate consumption in their optimal portfolios. Furthermore, under the specific case of quadratic utility, the optimal risk-sharing rule derived for the pricing agent leads to a multifactor conditional consumption-based capital asset pricing model (CCAPM), where excess option returns appear as factors.     

Pricing options on scenario trees

We examine valuation procedures that can be applied to incorporate options in scenario-based portfolio optimization models. Stochastic programming models use discrete scenarios to represent the stochastic evolution of asset prices. At issue is the adoption of suitable procedures to price options on the basis of the postulated discrete distributions of asset prices so as to ensure internally consistent portfolio optimization models. We adapt and implement two methods to price European options in accordance with discrete distributions represented by scenario trees and assess their performance with numerical tests. We consider features of option prices that are observed in practice. We find that asymmetries and/or leptokurtic features in the distribution of the underlying materially affect option prices; we quantify the impact of higher moments (skewness and excess kurtosis) on option prices. We demonstrate through empirical tests using market prices of the S&P500 stock index and options on the index that the proposed procedures consistently approximate the observed prices of options under different market regimes, especially for deep out-of-the-money options.     

Regime switching based portfolio selection for pension funds

This paper shows how a mean variance criterion can be applied to a multi period setting in order to obtain efficient portfolios in an asset and liability context. The optimization model allows for rebalancing activities, transaction costs, stochastic volatilities for both assets and liabilities. Furthermore, a general framework for the projection of pension fund liabilities as well as for the generation of asset returns is given. In a further step the dynamics of the liability maturity structure is modeled as customized index, whose volatility and correlation with asset returns become integral components of the applied regime switching approach. The numerical results illustrate the diversification of the assets and its risk return pattern in dependency of the liability dynamics.     

Beyond Sharpe ratio: Optimal asset allocation using different performance ratios

As the assumption of normality in return distributions is relaxed, classic Sharpe ratio and its descendants become questionable tools for constructing optimal portfolios. In order to overcome the problem, asymmetrical parameter-dependent performance ratios have been recently proposed in the literature. The aim of this note is to develop an integrated decision aid system for asset allocation based on a toolkit of eleven performance ratios. A multi-period portfolio optimization up covering a fixed horizon is set up: at first, bootstrapping of asset return distributions is assessed to recover all ratios calculations; at second, optimal rebalanced-weights are achieved; at third, optimal final wealth is simulated for each ratios. Eventually, we make a robustness test on the best performance ratios. Empirical simulations confirm the weakness in forecasting of Sharpe ratio, whereas asymmetrical parameter-dependent ratios, such as the Generalized Rachev, Sortino–Satchell and Farinelli–Tibiletti ratios show satisfactorily robustness.     

Dynamic trading with uncertain exit time and transaction costs in a general Markov market

This paper investigates a dynamic trading problem with transaction cost and uncertain exit time in a general Markov market, where the mean vector and covariance matrix of returns depend on the states of the stochastic market, and the market state is regime switching in a time varying state set. Following the framework proposed by Gârleanu and Pedersen (2013), the investor maximizes his or her multi-period mean–variance utility, net of quadratic transaction costs capturing the linear price impact where trades lead to temporary linear changes in prices. The explicit expression for the optimal strategy is derived by using matrix theory technique and dynamic programming approach. Finally, numerical examples are provided to study the effects of transition cost and exit probability on the wealth process, the trading strategy, turnover rate and the total transaction cost.     

An equilibrium model of wealth distribution

I present an explicitly solved equilibrium model for the distribution of wealth and income in an incomplete-markets economy. I first propose a self-insurance model with an inter-temporally dependent preference [Uzawa, H. 1968. Time preference, the consumption function, and optimal asset holdings. In: Wolfe, J.N. (Ed.), Value, Capital, and Growth: Papers in Honour of Sir John Hicks. Edinburgh University Press, Edinburgh, pp. 485-504]. I then derive an analytical consumption rule which captures stochastic precautionary saving motive and generates stationary wealth accumulation. Finally, I provide a complete characterization for the equilibrium cross-sectional distribution of wealth and income in closed form by developing a recursive formulation for the moments of the distribution of wealth and income. Using this recursive formulation, I show that income persistence and the degree of wealth mean reversion are the main determinants of wealth-income correlation and relative dispersions of wealth to income, such as skewness and kurtosis ratios between wealth and income.     

A robust optimization approach to asset-liability management under time-varying investment opportunities

This paper presents an asset liability management model based on robust optimization techniques. The model explicitly takes into consideration the time-varying aspect of investment opportunities. The emphasis of the proposed approach is on computational tractability and practical appeal. Computational studies with real market data study the performance of robust-optimization-based strategies, and compare it to the performance of the classical stochastic programming approach.     

A systematic approach to multi-period stress testing of portfolio credit risk

We propose a new method for analysing multi-period stress scenarios for portfolio credit risk more systematically than in current macro stress tests. The plausibility of a scenario is quantified by its distance from an average scenario. For a given level of plausibility, we search systematically for the most adverse scenario. This ensures that no plausible scenario will be missed. We show how this method can be applied to some models already in use by practitioners. While worst case search requires numerical optimisation we show that we can work with reasonably good linear approximations to the portfolio loss function. This makes systematic multi-period stress testing computationally efficient and easy to implement. Applying our approach to data from the Spanish loan register we show that, compared to standard stress test procedures, our method identifies more harmful scenarios that are equally plausible.     

A Critique of the Stochastic Discount Factor Methodology

In this paper, we point out that the widely used stochastic discount factor (SDF) methodology ignores a fully specified model for asset returns. As a result, it suffers from two potential problems when asset returns follow a linear factor model. The first problem is that the risk premium estimate from the SDF methodology is unreliable. The second problem is that the specification test under the SDF methodology has very low power in detecting misspecified models. Traditional methodologies typically incorporate a fully specified model for asset returns, and they can perform substantially better than the SDF methodology.     

A PROGRAMMING MODEL FOR BANK HEDGING DECISIONS

This study constructs, solves, and interprets a normative model that focuses on the risk management needs of a banking institution. The optimization model is a prototype, and it explicitly incorporates uncertainty via the two-stage linear programming format. Both the traditional asset-liability management and the newer hedging risk management strategies are included. The model suggests that although the specific risk management strategy mix depends on the economic scenario, hedging should be actively considered as a workable strategy.     

Spectral risk measures and portfolio selection

This paper deals with risk measurement and portfolio optimization under risk constraints. Firstly we give an overview of risk assessment from the viewpoint of risk theory, focusing on moment-based, distortion and spectral risk measures. We subsequently apply these ideas to an asset management framework using a database of hedge funds returns chosen for their non-Gaussian features. We deal with the problem of portfolio optimization under risk constraints and lead a comparative analysis of efficient portfolios. We show some robustness of optimal portfolios with respect to the choice of risk measure. Unsurprisingly, risk measures that emphasize large losses lead to slightly more diversified portfolios. However, risk measures that account primarily for worst case scenarios overweight funds with smaller tails which mitigates the relevance of diversification.     

Robust optimal excess-of-loss reinsurance and investment strategy for an insurer in a model with jumps

This paper considers a robust optimal excess-of-loss reinsurance-investment problem in a model with jumps for an ambiguity-averse insurer (AAI), who worries about ambiguity and aims to develop a robust optimal reinsurance-investment strategy. The AAI’s surplus process is assumed to follow a diffusion model, which is an approximation of the classical risk model. The AAI is allowed to purchase excess-of-loss reinsurance and invest her surplus in a risk-free asset and a risky asset whose price is described by a jump-diffusion model. Under the criterion for maximizing the expected exponential utility of terminal wealth, optimal strategy and optimal value function are derived by applying the stochastic dynamic programming approach. Our model and results extend some of the existing results in the literature, and the economic implications of our findings are illustrated. Numerical examples show that considering ambiguity and reinsurance brings utility enhancements.     

Asset–liability modelling and pension schemes: the application of robust optimization to USS

This paper uses a novel numerical optimization technique – robust optimization – that is well suited to solving the asset–liability management (ALM) problem for pension schemes. It requires the estimation of fewer stochastic parameters, reduces estimation risk and adopts a prudent approach to asset allocation. This study is the first to apply it to a real-world pension scheme, and the first ALM model of a pension scheme to maximize the Sharpe ratio. We disaggregate pension liabilities into three components – active members, deferred members and pensioners, and transform the optimal asset allocation into the scheme's projected contribution rate. The robust optimization model is extended to include liabilities and used to derive optimal investment policies for the Universities Superannuation Scheme (USS), benchmarked against the Sharpe and Tint, Bayes–Stein and Black–Litterman models as well as the actual USS investment decisions. Over a 144-month out-of-sample period, robust optimization is superior to the four benchmarks across 20 performance criteria and has a remarkably stable asset allocation – essentially fix-mix. These conclusions are supported by six robustness checks.     

On the Cross-Sectional Relation between Expected Returns, Betas, and Size

In this paper, I set up scenarios where the mean-variance capital asset pricing model is true and where it is false. Then I investigate whether the coefficients from regressions of population expected excess returns on population betas, and expected excess returns on betas and size, allow us to distinguish between the scenarios. I show that the coefficients from either ordinary least squares or generalized least squares regressions do not allow us to tell whether the model is true or false.     

二叉树利率期限结构模型应用初探——以寿险公司资产负债管理为例

近年来我国寿险公司经营风险加剧，寿险公司资产负债管理正逐渐成为实务界和学术界关注的焦点。本文在深入研究随机规划、利率期限结构、投资组合等相关理论的基础上，对比分析均衡模型和无套利模型的差异，指出无套利模型更适于构楚随机规划问题中利率情景树的构建。在无套利模型中，二叉树Black-Derman-Toy模型简单易操作，可以避免三叉树模型计算量大，效率不高等缺点。因此本文采用二叉树方法以Black-Derman-Toy模型构造利率情景树，与随机规划模型相结合的资产负偾管理方法，协调、管理寿险公司资产负偾现金流，减少了随机规划模型处理随机利率分布的技术性难度。     

Optimal investment for insurers

We consider a stochastic model for the wealth of an insurance company which has the possibility to invest into a risky and a riskless asset under a constant mix strategy. The total insurance claim amount is modeled by a compound Poisson process and the price of the risky asset follows a geometric Brownian motion. We investigate the resulting integrated risk process and the corresponding discounted net loss process. This opens up a way to measure the risk of a negative outcome of the integrated risk process in a stationary way. We provide an approximation of the optimal investment strategy, which maximizes the expected wealth under a risk constraint on the Value-at-Risk.     

FUNCTIONAL FORMS OF THE CAPITAL ASSET PRICING MODEL UNDER DIFFERENT MARKET RISK REGIMES

This paper demonstrates that, given the assumption that asset returns are generated by the linear market model, the same functional form for the capital asset pricing model can be derived via the simpler linear programming approach for the riskaverse, risk-neutral, and risk-loving market regimes.