Enrico G. De Giorgi

The Grouped t-Copula with an Application to Credit Risk

We describe a model that takes into account the tail dependence present in a large set of historical risk factor data using the modern concept of copulas. We extend the popular t-copula to obtain a new grouped t-copula which describes more accurately the dependence among risk factors of different classes. We explain how to estimate the parameters of the grouped t-copula and apply the method to a problem in credit risk management with a large number of risk factors. We measure the downside risk over one month for an internationally diversified credit portfolio and we observe that the new model gives different results to the t-copula and seems better able to capture the risk in a large set of risk factors.

Two Paradigms and Nobel Prizes in Economics: A Contradiction or Coexistence?

Markowitz and Sharpe won the Nobel Prize in Economics for the development of Mean-Variance (M-V) analysis and the Capital Asset Pricing Model (CAPM). Kahneman won the Nobel Prize in Economics for the development of Prospect Theory. In deriving the CAPM, Sharpe, Lintner and Mossin assume expected utility (EU) maximisation in the face of risk aversion. Kahneman and Tversky suggest Prospect Theory (PT) as an alternative paradigm to EU theory. They show that investors distort probabilities, make decisions based on change of wealth, exhibit loss aversion and maximise the expectation of an S-shaped value function, which contains a risk-seeking segment. Can these two apparently contradictory paradigms coexist? We show in this paper that although CPT (and PT) is in conflict to EUT, and violates some of the CAPMs underlying assumptions, the Security Market Line Theorem (SMLT) of the CAPM is intact in the CPT framework. Therefore, the CAPM is intact also in CPT framework.

Dynamic Portfolio Choice and Asset Pricing with Narrow Framing and Probability Weighting

This paper shows that the framework proposed by Barberis and Huang (2009) to incorporate narrow framing and loss aversion into dynamic models of portfolio choice and asset pricing can be extended to also account for probability weighting and for a value function that is convex on losses and concave on gains. We show that the addition of probability weighting and a convex–concave value function reinforces previous applications of narrow framing and cumulative prospect theory to understanding the stock market non-participation puzzle and the equity premium puzzle. Moreover, we show that a convex–concave value function generates new wealth effects that are consistent with empirical observations on stock market participation.

Loss Aversion with a State-Dependent Reference Point

This study investigates reference-dependent choice with a stochastic, state-dependent reference point. The optimal reference-dependent solution equals the optimal consumption solution (no loss aversion) if the reference point is selected fully endogenously. Given that loss aversion is widespread, we conclude that the reference point generally includes an important exogenously fixed component. We develop a choice model in which adjustment costs can cause stickiness relative to an initial, exogenous reference point. Using historical U.S. investment benchmark data, we show that this model is consistent with diversification across bonds and stocks for a wide range of evaluation horizons, despite the historically high-risk premium of stocks compared to bonds. This paper was accepted by Peter Wakker, decision analysis.

Aspirational Preferences and Their Representation by Risk Measures

We consider choice over uncertain, monetary payoffs and study a general class of preferences. These preferences favor diversification, except perhaps on a subset of sufficiently disliked acts over which concentration is instead preferred. This structure encompasses a number of known models (e.g., expected utility and several variants under a concave utility function). We show that such preferences share a representation in terms of a family of measures of risk and targets. Specifically, the choice function is equivalent to selection of a maximum index level such that the risk of beating the target at that level is acceptable. This representation may help to uncover new models of choice. One that we explore in detail is the special case when the targets are bounded. This case corresponds to a type of satisficing and has descriptive relevance. Moreover, the model is amenable to large-scale optimization. This paper was accepted by Teck Ho, decision analysis.

Financial Market Equilibria with Cumulative Prospect Theory

The paper shows that financial market equilibria need not exist if agents possess cumulative prospect theory preferences with piecewise-power value functions. The reason is an infinite short-selling problem. But even when a short-sell constraint is added, non-existence can occur due to discontinuities in agents demand functions. Existence of equilibria is established when short-sales constraints are imposed and there is also a continuum of agents in the market.

Monetary Policy Regimes: Implications for the Yield Curve and Bond Pricing

We develop a multivariate dynamic term structure model, which takes into account the nonlinear (time-varying) relation between interest rates and the state of the economy. In contrast to the classical term structure literature, in which nonlinearities are captured by increasing the number of latent state variables or by latent regime shifts, in our no-arbitrage framework the regimes are governed by thresholds and are directly linked to economic fundamentals. Specifically, starting from a simple monetary policy model for the short rate, we introduce a parsimonious and tractable model for the yield curve, which takes into account the possibility of regime shifts in the behavior of the Federal Reserve. In our empirical analysis, we show the merit of our approach three dimensions: interpretable bond dynamics, accurate short end yield curve pricing, and yield curve implications.

Loss Aversion with Multiple Investment Goals

This paper presents a time-continuous portfolio selection model with loss averse investors, who possess multiple investment goals at different time horizons. The model assumes partial narrow framing. Investors follow a two-step approach. First, they optimally allocate wealth among investment goals. Second, they determine an optimal investment strategy for each investment goal separately. We show that when loss aversion is according to the experimental findings, investors mainly invest their wealth to reach long-term goals and adopt investment strategies with high leverage to reach short-term goals. The overall strategy also display high leverage. The same patterns is observed when loss aversion is extreme and goals are very ambitious. By contrast, when loss aversion is extreme but goals are not too ambitious, investors mainly invest to reach short-term goals and adopt safe investment strategies for this purpose.

A note on reward-risk portfolio selection and two-fund separation

This paper presents a general reward-risk portfolio selection model and derives sufficient conditions for two-fund separation. In particular we show that many reward-risk models presented in the literature satisfy these conditions.

Evolutionary portfolio selection with liquidity shocks

The wealth dynamics of insurance companies strongly depends on the success of their investment strategies, but also on liquidity shocks which occur during unfavorable years, when indemnities to be paid to the clients exceed collected premia. An investment strategy that does not take liquidity shocks into account, exposes insurance companies to the risk of bankruptcy. This paper analyzes the behavior of insurance companies in an evolutionary framework. We show that an insurance company that merely satisfies regulatory constraints will eventually vanish from the market. We give a more restrictive no-bankruptcy condition on investment strategies. Moreover, we characterize trading strategies that are evolutionary stable, i.e., able to drive out any mutation. We study the existence of such strategies and the conditions under which financial and insurance markets are stable.