On a class of law invariant convex risk measures

We consider the class of law invariant convex risk measures with robust representation r_h,p(X)=sup_fò₀¹ [AV@R_s(X)f(s)-f^p(s)h(s)] ds\rho_{h,p}(X)=\sup_{f}\int_{0}^{1} [AV@R_{s}(X)f(s)-f^{p}(s)h(s)]\,ds, where 1≤p<∞ and h is a positive and strictly decreasing function. The supremum is taken over the set of all Radon–Nikodym derivatives corresponding to the set of all probability measures on (0,1] which are absolutely continuous with respect to Lebesgue measure. We provide necessary and sufficient conditions for the position X such that ρ _h,p (X) is real-valued and the supremum is attained. Using variational methods, an explicit formula for the maximizer is given. We exhibit two examples of such risk measures and compare them to the average value at risk.     

The demand for residential domestic service in the London of 1901†

This article concerns the effect of income and other variables on the demand for residential domestic service in London in 1901 and presents the first estimated model of the demand for residential service known to the author. It uses previously unexploited data consisting of the incomes and household details of some 500 civil servants. An extension of Becker's model of household production is set out and an ordered probit statistical model of servant demand is estimated. The results confirm the importance of income but also show that the demographic composition of the household was of significance. These results are interpreted in terms of age‐ and gender‐related differences in the supply of labour and the demand for market goods. The results are consistent with the view that middle‐class Edwardian households should be understood as sites of production as well as consumption. A comparison of the statistical results with contemporary recommendations in manuals of household management suggests that those recommendations were typically over‐optimistic. The article presents a ‘ready reckoner’ whereby household income may be estimated from the number of resident servants, but caution in its use is urged.     

How trading activity scales with company size in the FTSE 100

This paper investigates the scaling dependencies between measures of ‘activity’ and of ‘size’ for companies included in the FTSE 100. The ‘size’ of companies is measured by the total market capitalization. The ‘activity’ is measured with several quantities related to trades (transaction value per trade, transaction value per hour, tick rate), to the order queue (total number of orders, total value), and to the price dynamic (spread, volatility). The outcome is that systematic scaling relations are observed: (1) the value exchanged by hour and value in the order queue have exponents of less than 1, respectively 0.90 and 0.75; (2) the tick rate and the value per transaction scale with the exponents 0.39 and 0.44; (3) the annualized volatility is independent of the size, and the tick-by-tick volatility decreases with the market capitalization with an exponent of ?0.23; (4) the spread increases with the volatility with an exponent of 0.94. A theoretical random walk argument is given that relates the volatility exponents to the exponents in points 1 and 2.     

Volatility forecasts and at-the-money implied volatility: a multi-component ARCH approach and its relation to market models

This article explores the relationships between several forecasts for the volatility built from multi-scale linear ARCH processes, and linear market models for the forward variance. This shows that the structures of the forecast equations are identical, but with different dependencies on the forecast horizon. The process equations for the forward variance are induced by the process equations for an ARCH model, but postulated in a market model. In the ARCH case, they are different from the usual diffusive type. The conceptual differences between both approaches and their implication for volatility forecasts are analysed. The volatility forecast is compared with the realized volatility (the volatility that will occur between date t and t + ΔT), and the implied volatility (corresponding to an at-the-money option with expiry at t + ΔT). For the ARCH forecasts, the parameters are set a priori. An empirical analysis across multiple time horizons ΔT shows that a forecast provided by an I-GARCH(1) process (one time scale) does not capture correctly the dynamics of the realized volatility. An I-GARCH(2) process (two time scales, similar to GARCH(1,1)) is better, while a long-memory LM-ARCH process (multiple time scales) replicates correctly the dynamics of the implied and realized volatilities and delivers consistently good forecasts for the realized volatility.     

A mean/variance approach to long-term fixed-income portfolio allocation

Abstract

Long-term investments in bonds offer known returns, but with risks corresponding to defaults of the underwriters. The excess return for a risky bond is measured by the spread between the expected yield and the risk-free rate. Similarly, the risk can be expressed in the form of a default spread, measuring the difference between the yield when no default occurs and the expected yield. For zero-coupon bonds and for actual market data, the default spread is proportional to the probability of default per year. The analysis of market data shows that the yield spread scales as the square root of the default spread. This relation expresses the risk premium over the risk-free rate that the bond market offers, similarly to the risk premium for equities. With these measures for risk and return, an optimal bond allocation scheme can be built following a mean/variance utility function. Straightforward computations allow us to obtain the optimal portfolio, depending on a pre-set risk-aversion level. As for equities, the optimal portfolio is a linear combination of one risk-free bond and a risky portfolio. Using the scaling law for the default spread allows us to obtain simple expressions for the value, yield and risk of the optimal portfolio.     

Persistent misalignments of the European exchange rates: some evidence from non-linear cointegration

The asymmetric and persistent adjustment of the European real exchange rates is investigated using the framework of non-linear cointegration. The episodes of slow mean-reversion dynamics over the period from 1979 to 1999 are explained. A test of unit root against STAR cointegration is proposed and some complete estimations and stochastic simulations of ESTAR models are presented. The presence of effective non-linear adjustment during the moving of the currencies to their long-run fundamental equilibrium exchange rate value is discussed.     

Private Label Development: The Large Food Retailer Faced with the Supplier's Opportunism

For the last 20 years, large food retailers have had an important place in fast-moving consumer good sales. This article describes their buying strategies, focusing on supplier selection in the case of private label contracts. It introduces the concept of opportunism to explain recent and probably irreversible developments in retail buying organisations, integrating a growing number of technologists and scientists. New businesses, with close relationships to industrial purchasing, have appeared in the retailing industry. In the end, they will require a new ‘species’ of managers, able to simultaneously monitor logistical, technical and commercial interfaces between large food retailers and their private label producers.     

Too much of a good thing? Why altruism can harm the environment?

Success of eco-labeling schemes, broadly defined, varies among products and across countries. Based on a simple theoretical framework, we show that the nature of environmental attributes among products (i.e., private versus public) and the consumer type (i.e., egoist versus altruist) shape the overall performance of such schemes. In addition, we demonstrate that altruistic consumers exhibiting a too high willingness to pay for the eco-labeled product can inadvertently prevent egoistic consumers from purchasing it, leading to a sub-optimal outcome in terms of environmental performance. Several policy and managerial implications are drawn.