We compare the performance of the perturbation-based (local) portfolio solution method of Devereux and Sutherland (2010a, 2011) with a global solution method. We find that the local method performs very well when the model is designed to capture stylized macroeconomic facts and countries/agents are symmetric, i.e. when the latter have similar size, face similar risks and trade assets with similar risk properties. It performs less satisfactory when the agents engaged in financial trade are asymmetric. The global solution method performs substantially better when the model is parameterized to match the observed equity premium, a key stylized finance fact. (authors' abstract) / Series: Department of Economics Working Paper Series

This paper solves a long-standing open problem in mathematical finance: to find a solution to the problem of maximizing utility from terminal wealth of an agent with a random endowment process, in the general, semimartingale model for incomplete markets, and to characterize it via the associated dual problem. We show that this is indeed possible if the dual problem and its domain are carefully defined. More precisely, we show that the optimal terminal wealth is equal to the inverse of marginal utility evaluated at the solution to the dual problem, which is in the form of the regular part of an element of(L∞)* (the dual space of L∞). (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

We show that, for a utility function U: R to R having reasonable asymptotic elasticity, the optimal investment process H. S is a super-martingale under each equivalent martingale measure Q, such that E[V(dQ/dP)] < "unendlich", where V is conjugate to U. Similar results for the special case of the exponential utility were recently obtained by Delbaen, Grandits, Rheinländer, Samperi, Schweizer, Stricker as well as Kabanov, Stricker. This result gives rise to a rather delicate analysis of the "good definition" of "allowed" trading strategies H for the financial market S. One offspring of these considerations leads to the subsequent - at first glance paradoxical - example. There is a financial market consisting of a deterministic bond and two risky financial assets (S_t^1, S_t^2)_0<=t<=T such that, for an agent whose preferences are modeled by expected exponential utility at time T, it is optimal to constantly hold one unit of asset S^1. However, if we pass to the market consisting only of the bond and the first risky asset S^1, and leaving the information structure unchanged, this trading strategy is not optimal any more: in this smaller market it is optimal to invest the initial endowment into the bond. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Using a stylized two period model we obtain portfolio solutions from two solution approaches that belong to the class of local approximation methods - the approach of Judd and Guu (2001, hereafter 'JG') and the approach of Devereux and Sutherland (2010, 2011,hereafter 'DS') - and compare them with the true portfolio solution. We parameterize the model to match mean, standard deviation, skewness and kurtosis of return data on aggregate MSCI stock market indices. The optimal equity holdings in the true solution depend on the size of uncertainty, and the precise form of this relationship is determined by the distributional properties of equity returns. While the DS method and the JG approach provide the same portfolio solution as the size of uncertainty goes to zero, else the two solutions can differ substantially. Because under the DS method portfolio holdings are never approximated in the direction of the size of uncertainty, even higher-order approximations lead to the (zero-order) constant solution in our example model. In contrast, the JG solution generally varies as the size of uncertainty changes, and already a second-order JG solution can account for effects of skewness and kurtosis of equity returns. (authors' abstract) / Series: Department of Economics Working Paper Series

Bitcoin is an unregulated digital currency originally introduced in 2008 without legal tender status. Based on a decentralized peer-to-peer network to confirm transactions and generate a limited amount of new bitcoins, it functions without the backing of a central bank or any other monitoring authority. In recent years, Bitcoin has seen increasing media coverage and trading volume, as well as major capital gains and losses in a high volatility environment. Interestingly, an analysis of Bitcoin returns shows remarkably low correlations with traditional investment assets such as other currencies, stocks, bonds or commodities such as gold or oil. In this paper, we shed light on the impact an investment in Bitcoin can have on an already well-diversified investment portfolio. Due to the non-normal nature of Bitcoin returns, we do not propose the classic mean-variance approach, but adopt a Conditional Value-at-Risk framework that does not require asset returns to be normally distributed. Our results indicate that Bitcoin should be included in optimal portfolios. Even though an investment in Bitcoin increases the CVaR of a portfolio, this additional risk is overcompensated by high returns leading to better return-risk ratios.

There is an ongoing debate over the role that equity markets play in determining and influencing international equity flows. The first chapter of this dissertation describes the large portfolio equity flows into China and India, in order to understand the buying behavior of US investors. The rapid growth of the Chinese and Indian economies, coupled with the recent development and liberalization of their financial markets has attracted significant portfolio investment from U.S. investors. It is commonly assumed that domestic investors have an informational advantage over foreign investors; however, some recent empirical literature has questioned this assumption. Essay one dissects the nature of the relationship between foreign equity flows, equity returns, and related variables. The results of my empirical investigation provides evidence that U.S. institutional investors are making investment decisions based on long-run determinants of value rather than responding to price signals or ‘chasing returns'. I anticipate that the strong relationship between equity flows and fundamentals will strengthen as information asymmetries decline and US investors continue to develop more sophisticated methods of assessing underlying value in China and India. The second essay of this dissertation explores a new panel data set based on US gross cross-border equity flows to 20 industrialized nations combined with measures of market valuation for the period of 1977-2005. Empirical evidence of imperfect integration across world equity markets indicates that valuation matters. Consistent with relative value trading as a determinant of equity flow patterns, I find that equity flows decrease sharply with host-country market valuations—in particular the component of valuation that is forecasted to revert the following year. I also find that equity flows increase sharply with US equity market valuations. These results suggest the existence of a valuation channel for cross-border equity flows. The findings of this chapter show that US investors are informed about both domestic markets and foreign markets. Peripheral findings of this essay confirm the findings of other researches, but with a longer sample period. Consistent with existing literature, I find a negative influence of interest rates spreads, and information asymmetries on cross-border trade in equities.

In recent years socially responsible investing has become an increasingly more popular subject with both private and institutional investors. At the same time, a number of scientific papers have been published on socially responsible investments (SRIs), covering a broad range of topics, from what actually defines SRIs to the financial performance of SRI funds in contrast to non-SRI funds. In this paper, we revisit Markowitz' Portfolio Selection Theory and propose a modification allowing to incorporate not only asset-specific return and risk but also a social responsibility measure into the investment decision making process. Together with a risk-free asset, this results in a three-dimensional capital allocation plane that allows investors to custom-tailor their asset allocations and incorporate all personal preferences regarding return, risk and social responsibility. We apply the model to a set of over 6,231 international stocks and find that investors opting to maximize the social impact of their investments do indeed face a statistically significant decrease in expected returns. However, the social responsibility/risk-optimal portfolio yields a statistically significant higher social responsibility rating than the return/risk-optimal portfolio.

Using a stylized two-period model we compare portfolio solutions from two local solution approaches - the approach of Judd and Guu (2001) and the approach of Devereux and Sutherland (2010, 2011) - with the true nonlinear portfolio solution.

We theoretically and empirically study portfolio optimization under transaction costs and establish a link between turnover penalization and covariance shrinkage with the penalization governed by transaction costs. We show how the ex ante incorporation of transaction costs shifts optimal portfolios towards regularized versions of efficient allocations. The regulatory effect of transaction costs is studied in an econometric setting incorporating parameter uncertainty and optimally combining predictive distributions resulting from high-frequency and low-frequency data. In an extensive empirical study, we illustrate that turnover penalization is more effective than commonly employed shrinkage methods and is crucial in order to construct empirically well-performing portfolios.

We examine in an experiment the causes, consequences and possible cures of myopic loss aversion (MLA) for investment behaviour under risk. We find that both, investment horizons and feedback frequency contribute almost equally to the effects of MLA. Longer investment horizons and less frequent feedback lead to higher investments. However, when given the choice, subjects prefer on average shorter investment horizons and more frequent feedback. Exploiting the status quo bias by setting a long investment horizon or low feedback frequency as a default turns out to be a successful behavioural intervention that increases investment levels. (author´s abstract) / Series: Department of Economics Working Paper Series