EXTREME VALUE AT RISK: A SCENARIO FOR RISK MANAGEMENT

This paper uses the generalised extreme value (GEV) distribution to model the extreme losses that are likely to occur during market crashes, in the case of an investor who has long positions in stocks and currencies. The null hypothesis – which tests for normality of asset returns – is rejected due to asymmetry of these returns. We assume that the asymmetric behaviour and volatility of the returns are captured by the shape and scale parameters, respectively, of a GEV distribution. The data set includes stock indices for the United States, Japan, the United Kingdom, Germany, France and South Africa, and the South African rand exchange rates against the US dollar observed from 3 January 2005 to 30 December 2009. In addition, we divide this sample period into two periods: the pre‐crisis period, from 3 January 2005 to 31 December 2007 and the crisis period, from 1 January 2008 to 30 December 2009. We compared the estimates of value at risk (VaR) using an extreme value theory (EVT) model, with the estimates derived from the traditional variance–covariance method and found that during the crisis the 99% extreme VaR estimates are more reliable as they lie within the Basel II green zone. These results suggest that, at higher quintiles, the VaR estimates based on EVT are reliable and more accurate than estimates from the traditional method.     

APPLYING A GENETIC ALGORITHM TO INTERNATIONAL DIVERSIFICATION OF EQUITY PORTFOLIOS: A SOUTH AFRICAN INVESTOR PERSPECTIVE

This paper uses the genetic algorithm (GA) approach to generate a portfolio optimisation scenario of a South African investor who seeks to maximise return from investing in S&P500, FTSE100, NASDAQ, DOWJONES, CAC40 and the DAX from January 1, 2005, to January 31, 2008, but facing exchange rate risk. The GA searches for the optimal solution in the entire set of financial constraints without looking for partial derivatives of the utility function. Whereas most financial problems require a non‐linear and time‐varying model, the GA, with its survival principle of offspring chromosomes, is better suited to this type of problem than local optimisation methods. The performance of the GA is compared with two non‐linear models, namely the quadratic mean‐variance (QMV), which maximises the portfolio mean‐variance, and the quadratic variance minimisation (QVM), which minimises the portfolio variance. The results show that neither the QMV nor the QVM takes into account the domestic investors' risk attitude towards investing in foreign equities and therefore does not provide any international diversification benefits. In addition, the bootstrapping scenario of 10,000 simulations reveals that neither the QMV nor the QVM outperforms the GA in terms of Sharpe ratio and flexibility in dealing with investors' risk attitude towards investing in foreign equities denominated in foreign currencies.     

Growth and Public Debt: What Are the Relevant Trade‐Offs?

The interplay between growth and public debt is addressed considering a Barro‐type (1990) endogenous growth model where public spendings are financed through taxes on income and public debt. The government has a target level of public debt relative to GDP, and the long‐run debt‐to‐GDP ratio is used as a policy parameter. We show that when debt is a large enough proportion of GDP, two distinct balanced‐growth paths (BGPs) may coexist, one being indeterminate. We exhibit two types of important trade‐offs associated with self‐fulfilling expectations. First, we show that the lowest BGP is always decreasing with respect to the debt‐to‐GDP ratio while the highest one is increasing. Second, we show that the highest BGP, which provides the highest welfare, is always locally indeterminate while the lowest is always locally determinate. Therefore, local and global indeterminacy may arise and self‐fulfilling expectations appear as a crucial ingredient to understand the impact of debt on growth, welfare, and macroeconomic fluctuations. Finally, a simple calibration exercise allows to provide an understanding of the recent experiences of many OECD countries.     

HOTELLING'S BEACH WITH LINEAR AND QUADRATIC TRANSPORTATION COSTS: EXISTENCE OF PURE STRATEGY EQUILIBRIA*

In Hotelling type models consumers have the same transportation cost function. We deviate from this assumption and introduce two consumer types. Some consumers have linear transportation costs, while the others have quadratic transportation costs. If at most half the consumers have linear transportation costs, a subgame perfect equilibrium in pure strategies exists for all symmetric locations. Furthermore, no general principle of differentiation holds. With two consumer types, the equilibrium pattern ranges from maximum to intermediate differentiation. The degree of product differentiation depends on the fraction of consumer types.     

Social Networks and Credit Card Overspending Among Young Adult Consumers

Research that has looked at the reasons why young individuals overspend using their credit cards has not paid attention to the perceptions that they have about important others' credit card debt, their expectations as to how much to spend when they consume in the presence of them, and how the strength of the social relationships within their social network potentially influences the extent to which they overspend using their credit cards. A survey of 225 US university students composing a culturally diverse sample revealed that these social norms and network variables have interactive effects on credit card overspending. Specifically, the results show that the perceptions that young adult consumers have about important others' credit card debt impact their overspending using credit cards when they feel that they are expected to consume at the same level as important others in shared experiences, and when they are strongly connected to these individuals.     

Helping Consumers Choose a Credit Card

Choosing an economically appropriate credit card requires that two kinds of information be available: knowledge of one's credit card usage and comparison information on credit card costs. This article examines a recent Canadian information program on credit card costs and presents the results of a study designed to test the effectiveness of changes in the information presentation format.     

Protecting Minorities through the Average Voting Rule

In the average voting rule, the outcome is some weighted average of votes. The unique average voting outcome is characterized by a median formula, which depends on voters' preferred allocations and some parameters constructed from voters' weights. A minority is said to be protected by a switch in voting rule if the outcome becomes closer to the median bliss point of the minority. Sufficient conditions for minority protection are that, either the minority's weight is sufficiently large or the majority outcome is too unfavorable to the minority. Applications to the composition of public goods and to public expenditures level are considered. We explore the combined use of average and majority voting in a two‐stage procedure for determining the level and the composition of public expenditures.     

Optimal Emission Policy under the Risk of Irreversible Pollution

We consider an optimal consumption and pollution problem that has two important features. Environmental damages due to economic activities may be irreversible and the level at which the degradation becomes irreversible is unknown. Particular attention is paid to the situation where agents are relatively impatient and/or do not care a lot about the environment and/or Nature regenerates at low rate. We show that the optimal policy of the uncertain problem drives the economy in the long run toward a steady state while, when ignoring irreversibility, the economy follows a balanced growth path accompanied by a perpetual decrease in environmental quality and consumption, both asymptotically converging toward zero. Therefore, accounting for the risk of irreversibility induces more conservative decisions regarding consumption and polluting emissions. In general, however, we cannot rule out situations where the economy will optimally follow an irreversible path and consequently will also be left, in the long run, with an irreversibly degraded environment.