Partial information about contagion risk, self-exciting processes and portfolio optimization : [Version 18 April 2013]

This paper compares two classes of models that allow for additional channels of correlation between asset returns: regime switching models with jumps and models with contagious jumps. Both classes of models involve a hidden Markov chain that captures good and bad economic states. The distinctive feature of a model with contagious jumps is that large negative returns and unobservable transitions of the economy into a bad state can occur simultaneously. We show that in this framework the filtered loss intensities have dynamics similar to self-exciting processes. Besides, we study the impact of unobservable contagious jumps on optimal portfolio strategies and filtering

Hedging the exchange rate risk in international portfolio diversification : currency forwards versus currency options

As past research suggest, currency exposure risk is a main source of overall risk of international diversified portfolios. Thus, controlling the currency risk is an important instrument for controlling and improving investment performance of international investments. This study examines the effectiveness of controlling the currency risk for international diversified mixed asset portfolios via different hedge tools. Several hedging strategies, using currency forwards and currency options, were evaluated and compared with each other. Therefore, the stock and bond markets of the, United Kingdom, Germany, Japan, Switzerland, and the U.S, in the time period of January 1985 till December 2002, are considered. This is done form the point of view of a German investor. Due to highly skewed return distributions of options, the application of the traditional mean-variance framework for portfolio optimization is doubtful when options are considered. To account for this problem, a mean-LPM model is employed. Currency trends are also taken into account to check for the general dependence of time trends of currency movements and the relative potential gains of risk controlling strategies

Portfolio Constraints and Contagion in Emerging Markets

The objective of this paper is twofold: (1) to analyze an optimal portfolio rebalancing by a fund manager in response to a "volatility shock" in one of the asset markets, under sufficiently realistic assumptions about the fund manager's performance criteria and portfolio restrictions; and (2) to analyze how the composition of the investor base determines the sensitivity of equilibrium asset prices to a shock originating in one of the fundamentally unrelated asset markets. The analysis confirms that certain combinations of portfolio constraints (notably short-sale constraints and benchmark-based performance criteria) can create an additional transmission mechanism for propagating shocks across fundamentally unrelated asset markets. The paper also discusses potential implications of recent and ongoing changes in the investor base for asset price volatility in emerging markets. Copyright 2006, International Monetary Fund

Transaction fees and optimal rebalancing in the growth-optimal portfolio

The growth-optimal portfolio optimization strategy pioneered by Kelly is based on constant portfolio rebalancing which makes it sensitive to transaction fees. We examine the effect of fees on an example of a risky asset with a binary return distribution and show that the fees may give rise to an optimal period of portfolio rebalancing. The optimal period is found analytically in the case of lognormal returns. This result is consequently generalized and numerically verified for broad return distributions and returns generated by a GARCH process. Finally we study the case when investment is rebalanced only partially and show that this strategy can improve the investment long-term growth rate more than optimization of the rebalancing period.Comment: 17 pages, 7 figure

Dynamic Credit Investment in Partially Observed Markets

We consider the problem of maximizing expected utility for a power investor who can allocate his wealth in a stock, a defaultable security, and a money market account. The dynamics of these security prices are governed by geometric Brownian motions modulated by a hidden continuous time finite state Markov chain. We reduce the partially observed stochastic control problem to a complete observation risk sensitive control problem via the filtered regime switching probabilities. We separate the latter into pre-default and post-default dynamic optimization subproblems, and obtain two coupled Hamilton-Jacobi-Bellman (HJB) partial differential equations. We prove existence and uniqueness of a globally bounded classical solution to each HJB equation, and give the corresponding verification theorem. We provide a numerical analysis showing that the investor increases his holdings in stock as the filter probability of being in high growth regimes increases, and decreases his credit risk exposure when the filter probability of being in high default risk regimes gets larger

Managerial Incentives and Financial Contagion

This paper proposes a framework for comovements of asset prices with seemingly unrelated fundamentals, as an outcome of optimal portfolio strategies by fund managers. In emerging markets, dedicated managers outperforming a benchmark index and global managers maximizing absolute returns lead to systematic interactions between asset prices, without asymmetric information. The model determines optimal portfolio weights, the incidence of relative value strategies, and prices systematically deviating from fundamentals with limits to arbitraging this differential. Managerial compensation contracts, optimal at the firm level, may lead to inefficiencies at the macroeconomic level. We identify conditions when shocks in one emerging market affect others.Financial Crises, Index Investors, Global Linkages

Managerial incentives and financial contagion

This paper proposes a framework to examine the comovements of asset prices with seemingly unrelated fundamentals, as an outcome of the optimal portfolio strategies of large institutional fund managers. In emerging markets, the dominant presence of dedicated fund managers whose compensation is linked to the outperformance of their portfolio relative to a benchmark index, and of global fund managers whose compensation is linked to the absolute returns of their portfolios, leads to portfolio decisions that result in systematic interactions between asset prices even in the absence of asymmetric information. The model endogenously determines the optimal amount of cash holdings or leverage, the incidence of relative value versus macro hedge fund strategies, and how prices can systematically deviate from the long-term fundamental value for long periods of time, with limits to the arbitrage of this differential. Managerial compensation contracts, while optimal at a firm level, may lead to inefficiencies at the macroeconomic level. We identify conditions when a negative shock to one emerging market affects another market negatively.Financial crises ; Mutual funds

Pairs Trading under Drift Uncertainty and Risk Penalization

In this work, we study a dynamic portfolio optimization problem related to pairs trading, which is an investment strategy that matches a long position in one security with a short position in another security with similar characteristics. The relationship between pairs, called a spread, is modeled by a Gaussian mean-reverting process whose drift rate is modulated by an unobservable continuous-time, finite-state Markov chain. Using the classical stochastic filtering theory, we reduce this problem with partial information to the one with full information and solve it for the logarithmic utility function, where the terminal wealth is penalized by the riskiness of the portfolio according to the realized volatility of the wealth process. We characterize optimal dollar-neutral strategies as well as optimal value functions under full and partial information and show that the certainty equivalence principle holds for the optimal portfolio strategy. Finally, we provide a numerical analysis for a toy example with a two-state Markov chain.Comment: 24 pages, 4 figure