Costas Xiouros

Credit risk optimization using factor models

We study portfolio credit risk management using factor models, with a focus on optimal portfolio selection based on the tradeoff of expected return and credit risk. We begin with a discussion of factor models and their known analytic properties, paying particular attention to the asymptotic limit of a large, finely grained portfolio. We recall prior results on the convergence of risk measures in this “large portfolio approximation” which are important for credit risk optimization. We then show how the results on the large portfolio approximation can be used to reduce significantly the computational effort required for credit risk optimization. For example, when determining the fraction of capital to be assigned to particular ratings classes, it is sufficient to solve the optimization problem for the large portfolio approximation, rather than for the actual portfolio. This dramatically reduces the dimensionality of the problem, and the amount of computation required for its solution. Numerical results illustrating the application of this principle are also presented.

Disagreement, Habit and the Dynamic Relation Between Volume and Prices

Dynamic asset pricing models typically do not generate trading volume whereas empirically trading volume is strongly related to asset prices; volume is usually high when returns are high and during periods of high return volatility. Stock prices on the other hand are known to be quite volatile and require a high equity premium while the risk-free rate of return is low and quite stable. We attempt to reconcile all these price and volume characteristics in a new model of disagreement where agents have external habit formation preferences that generate time-variation in risk-aversion. The model is flexible enough to be able to generate in a number of ways the dynamic relation between prices and volume whereas it also provides a configuration by which prices are also fitted well. The paper additionally shows that the information structure and the asset structure have important implications for the correlation between stock returns and volume.

Risk Aversion Sensitive Real Business Cycles

Technology choice allows for substitution of production across states of nature and depends on state dependent risk aversion. In equilibrium, endogenous technology choice can counter a persistent negative productivity shock with an increase in investment. An increase in risk aversion intensifies transformation across states, which directly leads to higher investment volatility. In our model and the data, the conditional volatility of investment correlates negatively with the price-dividend ratio and predicts excess stock market returns. In addition, the same mechanism generates predictability of consumption and produces fluctuations in the risk-free rate.

Differences of Opinion and the Price Volume Relation

This paper solves a dynamic general equilibrium asset pricing model of disagreement that draws a direct link between asset prices and the financial volume of trade. The model exhibits two risk averse agents that hold heterogeneous beliefs about the conditional mean of the aggregate consumption growth. The differences in opinions is supported by the fact that agents interpret public information differently. The connecting link between prices and volume is an exogenously time varying disagreement intensity that determines the magnitude of disagreement about new information. The model is able to explain a number of seemingly unrelated asset pricing facts namely the positive correlation between price changes and volume, the contemporaneous relation between volume and return volatility, the excess volatility, the volatility persistence and the negative correlation between price levels and volatility.

Trading and Asset Prices

A model is presented with counter-cyclical belief heterogeneity and habit-formation preferences. Belief heterogeneity stems from disagreement in the interpretation of common signals. The model accounts for the positive relation between the magnitude of returns and trading volume, the asymmetric relation between returns and volume, the equity premium and the stock return volatility. If agents are able to create leverage without borrowing, using instead a levered security, the model also accounts for the positive relation between returns and volume. Further, the endogenous belief heterogeneity is negatively correlated with the price-dividend ratio and predicts interest rates; new empirical evidence supports both predictions.

Stock and Bond Prices with Disagreement and Habit Formation Preferences

We solve analytically a pure exchange general equilibrium model of heterogeneous beliefs with habit forming preferences. Equilibrium prices depend on three factors: (i) the habit formation parameter; ii) the degree of disagreement; iii) the dynamics of disagreement. We show that in the absence of time-varying disagreement, it is possible to construct an observational equivalent economy with homogeneous beliefs, despite the fact that investors update their beliefs in a Bayesian way. We assume time-varying disagreement as a reduced-form model for an economy in which behavioral biases, asymmetric information or cultural differences might explain why information coming to the market is processed differently by different individuals. When the factor of disagreement is time-varying, its time varying properties have significant effects on the interest rate and its volatility. An increase in disagreement increases the interest rate when risk aversion is higher than logarithmic (myopic investor); negative correlation between disagreement and risk aversion (lower disagreement implies higher aggregate risk-aversion), results in lower volatility of interest rates. There is evidence that disagreement and risk aversion are negatively correlated: in recessions risk-aversion goes up while disagreement tends to go down (investors become pessimistic and markets dry up). In addition, time-varying disagreement affects the correlation between stock prices and the discount factor and, therefore, the equity premium.