Roy Kouwenberg

Scenario generation and stochastic programming models for asset liability management

In this paper, we develop and test scenario generation methods for asset liability management models. We propose a multi-stage stochastic programming model for a Dutch pension fund. Both randomly sampled event trees and event trees fitting the mean and the covariance of the return distribution are used for generating the coefficients of the stochastic program. In order to investigate the performance of the model and the scenario generation procedures we conduct rolling horizon simulations. The average cost and the risk of the stochastic programming policy are compared to the results of a simple fixed mix model. We compare the average switching behavior of the optimal investment policies. Our results show that the performance of the multi-stage stochastic program could be improved drastically by choosing an appropriate scenario generation method.

Optimal Portfolio Choice under Loss Aversion

This paper analyzes the optimal investment strategy for loss averse investors, assuming a complete market and general Ito processes for the asset prices. The loss-averse investor follows a partial portfolio insurance strategy. When the investors planning horizon is short (less than 5 years), he or she considerably reduces the initial portfolio weight of stocks compared to an investor with smooth power utility. The empirical section of the paper estimates the level of loss aversion implied by historical U.S. stock market data, using a representative agent model. We find that loss aversion and risk aversion cannot be disentangled empirically.

Stochastic programming models for asset liability management

Publisher Summary This chapter reviews stochastic programming models for asset and liability management (ALM). It introduces the basics of stochastic programming and formulates a canonical model for portfolio management. It elaborates the key issue of generating probabilistic data for a stochastic programming ALM system on scenario-generation methods. It discusses the performance of a stochastic programming ALM model for pension funds in conjunction with alternative scenario-generation methods. It places stochastic programming models in the context of the traditional portfolio choice literature from financial economics, and discusses its advantages and limitations. It provides a review of stochastic programming applications to ALM in several institutional settings. It hinges upon solution techniques illustrating the size of problems that are solvable with current state-of-the-art software. Stochastic programming is a powerful modelling paradigm for ALM problems. It incorporates in a common framework multiple correlated sources of risk for both the asset and liability side, takes a long time horizon perspective, accommodates different levels of risk aversion and allows for dynamic portfolio rebalancing while satisfying operational or regulatory restrictions and policy requirements.

Ambiguity Aversion and Household Portfolio Choice Puzzles: Empirical Evidence

We test the relation between ambiguity aversion and five household portfolio choice puzzles: nonparticipation in equities, low allocations to equity, home-bias, own-company stock ownership, and portfolio under-diversification. In a representative US household survey, we measure ambiguity preferences using custom-designed questions based on Ellsberg urns. As theory predicts, ambiguity aversion is negatively associated with stock market participation, the fraction of financial assets in stocks, and foreign stock ownership, but it is positively related to own-company stock ownership. Conditional on stock ownership, ambiguity aversion is related to portfolio under-diversification, and during the financial crisis, ambiguity-averse respondents were more likely to sell stocks.

High-Performance Computing for Asset-Liability Management

Financial institutions require sophisticated tools for risk management. For companywide risk management, both sides of the balance sheet should be considered, resulting in an integrated asset-liability management approach. Stochastic programming models suit these needs well and have already been applied in the field of asset-liability management to improve financial operations and risk management. The dynamic aspect of the financial planning problems inevitably leads to multiple decision stages trading dates in the stochastic program and results in an explosion of dimensionality. In this paper we show that dedicated model generation, specialized solution techniques based on decomposition and high-performance computing, are the essential elements to tackle these large-scale financial planning problems. It turns out that memory management is a major bottleneck when solving very large problems, given an efficient solution approach and a parallel computing facility. We report on the solution of an asset-liability management model for an actual Dutch pension fund with 4,826,809 scenarios; 12,469,250 constraints; and 24,938,502 variables; which is the largest stochastic linear program ever solved. A closer look at the optimal decisions reveals that the initial asset mix is more stable for larger models, demonstrating the potential benefits of the high-performance computing approach for ALM.

Ambiguity Attitudes in a Large Representative Sample

Using a theorem showing that matching probabilities of ambiguous events can capture ambiguity attitudes, we introduce a tractable method for measuring ambiguity attitudes and apply it in a large representative sample. In addition to ambiguity aversion, we confirm an ambiguity component recently found in laboratory studies: a-insensitivity, the tendency to treat subjective likelihoods as 50-50, thus overweighting extreme events. Our ambiguity measurements are associated with real economic decisions; specifically, a-insensitivity is negatively related to stock market participation. Ambiguity aversion is also negatively related to stock market participation, but only for subjects who perceive stock returns as highly ambiguous. This paper was accepted by James Smith, decision analysis .

Options and earnings announcements: an empirical study of volatility, trading volume, open interest and liquidity

In this paper we study the impact of earnings announcements on implied volatility, trading volume, open interest and spreads in the stock options market. We find that implied volatility increases before announcement days and drops afterwards. Also option trading volume is higher around announcement days. During the days before the announcement open interest tends to increase, while it returns to regular levels afterwards. Changes in the quoted spread largely respond to higher trading volume and changes in implied volatility. The effective spread increases on the event day and on the first two days following the earnings announcement.

Hedging Options under Transaction Costs and Stochastic Volatility

In this paper, we consider the problem of hedging a contingent claim on a stock under transaction-costs and stochastic volatility. Extensive research during the last two decades has clearly demonstrated that the volatility of most stocks is not constant over time. Writers of over-the-counter stock options should take account of the effects of stochastic volatility while pricing and hedging contracts, as the volatility of the underlying is the crucial factor in estimating the price of options. Pricing methods for options under stochastic volatility processes are widely available, but practical methods for hedging under stochastic volatility are rare. The simple delta-vega hedging scheme adds option contracts to the portfolio in order to neutralize the volatility exposure during a short interval of time. This method requires frequent rebalancing of the portfolio, which could be costly due to the bid-ask spread on traded option contracts. Static hedging aims at replication of the final payoff with a fixed portfolio of traded options. The static hedging approach fails however when the traded claims do not match the maturity and the moneyness of the over-the-counter products. In this paper we use a stochastic optimization approach to construct short term delta-vega hedges that take account of future rebalancing and transaction costs. The size of the stochastic optimization model grows exponentially with the number of trading dates considered. We show that the decomposition method PDCGM combined with the interior point solver HOPDM allows for an efficient implementation of the stochastic optimization model in a parallel computing environment. This integration of high performance computing and state-of-the-art decomposition methods provides the means for solving the stochastic volatility hedging model with multiple portfolio rebalancing dates.

A Primal-Dual Decomposition Algorithm for Multistage Stochastic Convex Programming

This paper presents a new and high performance solution method for multistage stochastic convex programming. Stochastic programming is a quantitative tool developed in the field of optimization to cope with the problem of decision-making under uncertainty. Among others, stochastic programming has found many applications in finance, such as asset-liability and bond-portfolio management. However, many stochastic programming applications still remain computationally intractable because of their overwhelming dimensionality. In this paper we propose a new decomposition algorithm for multistage stochastic programming with a convex objective and stochastic recourse matrices, based on the path-following interior point method combined with the homogeneous self-dual embedding technique. Our preliminary numerical experiments show that this approach is very promising in many ways for solving generic multistage stochastic programming, including its superiority in terms of numerical efficiency, as well as the flexibility in testing and analyzing the model.

Childhood Roots of Financial Literacy

Financial literacy predicts informed financial decisions, but what explains financial literacy? We use the concept of financial socialization and aim to represent three major agents of financial socialization: family, school and work. Thus we compile twelve relevant childhood characteristics in a new survey study and examine their relation to financial literacy, while controlling for established socio-demographic characteristics. We find in a mediation analysis that both family and school positively affect the financial literacy of adults. Moreover, financial literacy and school related variables also have a direct effect on financial behavior. This suggests that family factors and schooling work through complementary channels.