Contributions published at Financial Economics (Thorsten Hens)

null

We examine the dynamics of extreme values of overnight borrowing rates in an inter-bankmoney market before a financial crisis during which overnight borrowing rates rocketed up to (simple annual) 4000 percent. It is shown that the generalized Pareto distribution fits well to the extreme values of the interest rate distribution. We also provide predictions of extreme overnight borrowing rates using pre-crisis data. The examination of tails (extreme values) provides answers to such issues as to what are the extreme movements to be expected in financial markets; is there a possibility for even larger movements and, are there theoretical processes that can model the type of fat-tails in the observed data? The answers to such questions are essential for proper management of financial exposures and laying ground for regulations.

null

We consider a simple CAPM with heterogenous expectations on assets mean returns while keeping the assumption of homogenous expectations on the covariance of returns. Our first result derives the security market line as an aggregation result without using the two-fund-separation property. In particular every investor can hold optimal portfolios that are underdiversified.In our model alpha-opportunities can be explained as a feature of financial market equilibria and we can show that alpha-opportunities erode with the assets under management and that the hunt for alphaopportunities is a zero-sum game. Then we endogenize the agents information by allowing them to be either passive, in which case they invest according to the average expectation embodied in the market returns, or to be active, in which case they can acquire superior information at some cost. It is shown that expecting a positive alpha is not necessarily a good criterion for becoming active. Moreover, the less risk averse investors are more inclined to be active and delegating active investment to portfolio managers only makes sense if the performance fee increases with the skill of the portfolio manager. Finally, in our model it turns out that only a market in which all investors are passive and share the same correct belief is stable with respect to information acquisition. Hence the standard CAPM with homogenous beliefs can be seen as the long run outcome of our model.

We study properties of structured financial products optimizing a utility functional of a customer. The conventional method may have the disadvantage that the a priori restriction to a certain number of assets could make it impossible to find the optimal portfolio. So instead of optimizing the distribution of given assets, we impose only the price constraint as given by the CAPM and optimize the return distribution. In particular on nowadays markets where a multitude of asset types is available, it seems helpful to optimize first in the general framework, assuming a complete market, and then to find assets whose return distribution and conjoint probability distribution with the market portfolio resemble the theoretically optimal portfolio as closely as possible. We introduce a method to construct such optimal portfolios numerically and present some results for the cases of expected utility and cumulative prospect theory

In June 2003 Swiss banks held over CHF 500 billion in mortgages. This important segment accounts for about 63% of all loan portfolios of Swiss banks. Since default insurance is not common in Switzerland, the corresponding risks are a severe threat for the health of the financial system. We focus the analysis on portfolios of residential mortgages and model the probability distribution of the number of defaults using a non-parametric approach, where the intensity processes associated to the time-to-default is linked to a set of predictors through general smooth functions: A generalized additive model is used to condition default intensities of mortgages on relevant economic risk drivers. We calibrate our model on a large mortgage servicing data set and compare the resulting loss distributions to a well-known benchmark, i.e. the loss distribution from CreditRisk+ as commonly applied in the industry. The conditional loss distribution and risk measures for a large mortgage portfolio are shown to be greatly sensitive to the prevailing socio-economic scenario. We present evidence that aggregated res- idential mortgage default risk is not only driven by the rating but also by variables such as the loan-to-value ratio, contract age, regional unemployment as well as contract rate changes and the contract type. Hence, it is crucial to integrate the significant factors into any reasonable bank risk, portfolio or capital management framework or approaches for structuring and pricing of related products. We illustrate the severe shortcomings of the unconditional ap- proaches. With our results we are able to contribute significantly to the ongoing international discussion about the drivers of residential mortgage risk as well as to suggestions for improved risk management approaches. Finally, our findings are highly relevant for the implementation of the Basel II accord. Keywords: reduced-form, structural approach, default risk, default intensity, mortgages, generalized additive model, CreditRisk+.

null

The disposition effect is the observation that investors hold winning stocks too long and sell losing stocks too early. A standard explanation of the disposition effect refers to prospect theory and in particular to the asymmetric risk aversion according to which investors are risk averse when faced with gains and risk-seeking when faced withnlosses. We show that for reasonable parameter values the disposition effect can however not be explained by prospect theory as proposed by Kahneman and Tversky. The reason is that those investors who sell winning stocks and hold loosing assets would in the first place notnhave invested in stocks. That is to say the standard prospect theory argument is sound ex-post, assuming that the investment has takennplace, but not ex-ante, requiring that the investment is made in the first place.

We consider a repeated stochastic coordination game with imperfect public monitoring. In the game any pattern of coordinated play is a perfect Bayesian Nash equilibrium. Moreover, standard equilibrium selection argumentsneither have no bite or they select an equilibrium that is not observed in actual plays of the game. We give experimental evidence for a unique equilibrium selection and explain this very robust finding by equilibrium selection based on behavioral arguments, in particular focal point analysis,nprobability matching and over-confidence. Our results have interesting applicationsnin finance because the observed equilibrium exhibits momentum,nreversal and excess volatility. Moreover, the results may help to explain why technical analysis is a commonly observed investment style.

Von den turbulenten Börsenringen zum virtuellen Wertpapiermarkt, von sieben kantonalen Börsen zur SWX, von den Anfängen des Optionen- und Futureshandels zur grössten Derivatbörse der Welt. Die SWX Swiss Exchange blickt heute auf zehn Jahre elektronischen Börsenhandel, der Börsenplatz Schweiz auf eine 25-jährige Geschichte des Wandels.

Identifying investment strategies that will survive in the long run is a main endeavor in the eld of evolutionary nance. The evolutionary perspective on the nancial market considers rather long time horizons, making the creation and disappearance of rms a highly relevant factor in determining such strategies. However, this factor has not been examined in existing research. This paper seeks to ll the gap in the literature by simulating dividends and investment strategies on the basis of initial public offerings (IPOs) and defaults. This paper simulates the evolution of the wealth shares of various investment strategies in a setup wherein dividends are nonstationary. The results show that a modied version of the generalized Kelly rule dominates competing investment strategies in terms of nal wealth. This nding agrees with the existing literature, which suggests that the generalized Kelly rule has good chances of surviving or even taking over the entire market in different setups. However, the creation and dissolution of a rm can only be observed once in the life of a company; therefore, using only a long time series of one company alone is not the most optimal method of estimating the probability that a rm will default. Instead, the dividend process must be understood by examining similar companies. This completely alters the implementation of the generalized Kelly rule compared with the way it is applied in the existing evolutionary nance literature, even when the dividend processes of the companies involved are independent of each other.

Starting from the reward-risk model for portfolio selection introduced in DeGiorgi (2005), we derive the reward-risk Capital Asset Pricing Model (CAPM) analogously to the classical mean-variance CAPM. In contrast to the mean-variance model, reward-risk portfolio selection arises from an axiomatic definition of reward and risk measures based on few basic principles, including consistency with second order stochastic dominance. With complete markets, we show that at any financial market equilibrium, reward-risk investors' optimal allocations are comonotonic and therefore our model reduces to a representative investor model. Moreover, the pricing kernel is an explicitly given, non-increasing function of the market portfolio return, reflecting the representative investor's risk attitude. Finally, an empirical application shows that the reward-risk CAPM better captures the cross-section of US stock returns than the mean-variance CAPM does.

This paper studies the evolution of wealth shares of portfolio rules in incomplete markets with short-lived assets. Prices are determined endogenously. The performance of a portfolio rule in the process of repeated reinvestment of wealth is determined by the wealth share eventually conquered in competition with other portfolio rules. Using random dynamical systems theory, we derive necessary and sufficient conditions for the evolutionary stability of portfolio rules. In the case of Markov (in particular i.i.d.) payoffs these local stability conditions lead to a simple portfolio rule that is the unique evolutionary stable strategy. This rule possesses an explicit representation. Moreover, it is demonstrated that mean–variance optimization is not evolutionary stable while the CAPM-rule always imitates the best portfolio rule and survives.

The paper analyzes the process of market selection of investment strategies in an incomplete market of short-lived assets. In the model under study, asset payoffs depend on exogenous random factors. Market participants use dynamic investment strategies taking account of the available information about current and previous events. It is shown that an investor allocating wealth across the assets according to their conditional expected payoffs eventually accumulates total market wealth, provided the investor’s strategy is asymptotically distinct from the portfolio rule suggested by the Capital Asset Pricing Model (CAPM). This assumption turns out to be essentially necessary for the result.

We consider economies with additively separable utility functions and give conditions for the two-agents case under which the existence of sunspot equilibria is equivalent to the occurrence of the transfer paradox. This equivalence enables us to show that sunspots cannot matter if the initial economy has a unique spot market equilibrium and there are only two commodities or if the economy has a unique equilibrium for all distributions of endowments induced by asset trade. For more than two agents the equivalence breaks and we give an example for sunspot equilibria even though the economy has a unique equilibrium for all distributions of endowments induced by asset trade.