An inequality for uniform deviations of sample averages from their means

We derive a new inequality for uniform deviations of averages from their means. The inequality is a common generalization of previous results of Vapnik and Chervonenkis (1974) and Pollard (1986). Usingthe new inequality we obtain tight bounds for empirical loss minimization learning.

Model selection and error estimation

We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be converted into a data-based penalty function and the performance of the estimate is governed by the quality of the error estimate. We consider several penalty functions, involving error estimates on independent test data, empirical {\sc vc} dimension, empirical {\sc vc} entropy, andmargin-based quantities. We also consider the maximal difference between the error on the first half of the training data and the second half, and the expected maximal discrepancy, a closely related capacity estimate that can be calculated by Monte Carlo integration. Maximal discrepancy penalty functions are appealing for pattern classification problems, since their computation is equivalent to empirical risk minimization over the training data with some labels flipped.

Adaptive model selection using empirical complexities

Given $n$ independent replicates of a jointly distributed pair $(X,Y)\in {\cal R}^d \times {\cal R}$, we wish to select from a fixed sequence of model classes ${\cal F}_1, {\cal F}_2, \ldots$ a deterministic prediction rule $f: {\cal R}^d \to {\cal R}$ whose risk is small. We investigate the possibility of empirically assessingthe {\em complexity} of each model class, that is, the actual difficulty of the estimation problem within each class. The estimated complexities are in turn used to define an adaptive model selection procedure, which is based on complexity penalized empirical risk.The available data are divided into two parts. The first is used to form an empirical cover of each model class, and the second is used to select a candidate rule from each cover based on empirical risk. The covering radii are determined empirically to optimize a tight upper bound on the estimation error. An estimate is chosen from the list of candidates in order to minimize the sum of class complexity and empirical risk. A distinguishing feature of the approach is that the complexity of each model class is assessed empirically, based on the size of its empirical cover.Finite sample performance bounds are established for the estimates, and these bounds are applied to several non-parametric estimation problems. The estimates are shown to achieve a favorable tradeoff between approximation and estimation error, and to perform as well as if the distribution-dependent complexities of the model classes were known beforehand. In addition, it is shown that the estimate can be consistent,and even possess near optimal rates of convergence, when each model class has an infinite VC or pseudo dimension.For regression estimation with squared loss we modify our estimate to achieve a faster rate of convergence.

Market Index Biases and Minimum Risk Indices

Markets, in the real world, are not efficient zero-sum games where hypotheses of the CAPM are fulfilled. Then, it is easy to conclude the market portfolio is not located on Markowitz"s efficient frontier, and passive investments (and indexing) are not optimal but biased. In this paper, we define and analyze biases suffered by passive investors: the sample, construction, efficiency and active biases and tracking error are presented. We propose Minimum Risk Indices (MRI) as an alternative to deal with to market index biases, and to provide investors with portfolios closer to the efficient frontier, that is, more optimal investment possibilities. MRI (using a Parametric Value-at-Risk Minimization approach) are calculated for three stock markets achieving interesting results. Our indices are less risky and more profitable than current Market Indices in the Argentinean and Spanish markets, facing that way the Efficient Market Hypothesis. Two innovations must be outlined: an error dimension has been included in the backtesting and the Sharpe"s Ratio has been used to select the"best" MRI

Market Index Biases and Minimum Risk Indices

Markets, in the real world, are not efficient zero-sum games where hypotheses of the CAPM are fulfilled. Then, it is easy to conclude the market portfolio is not located on Markowitz"s efficient frontier, and passive investments (and indexing) are not optimal but biased. In this paper, we define and analyze biases suffered by passive investors: the sample, construction, efficiency and active biases and tracking error are presented. We propose Minimum Risk Indices (MRI) as an alternative to deal with to market index biases, and to provide investors with portfolios closer to the efficient frontier, that is, more optimal investment possibilities. MRI (using a Parametric Value-at-Risk Minimization approach) are calculated for three stock markets achieving interesting results. Our indices are less risky and more profitable than current Market Indices in the Argentinean and Spanish markets, facing that way the Efficient Market Hypothesis. Two innovations must be outlined: an error dimension has been included in the backtesting and the Sharpe"s Ratio has been used to select the"best" MRI

A data-dependent skeleton estimate and a scale-sensitive dimension for classification

The classical binary classification problem is investigatedwhen it is known in advance that the posterior probability function(or regression function) belongs to some class of functions. We introduceand analyze a method which effectively exploits this knowledge. The methodis based on minimizing the empirical risk over a carefully selected``skeleton'' of the class of regression functions. The skeleton is acovering of the class based on a data--dependent metric, especiallyfitted for classification. A new scale--sensitive dimension isintroduced which is more useful for the studied classification problemthan other, previously defined, dimension measures. This fact isdemonstrated by performance bounds for the skeleton estimate in termsof the new dimension.

Investor protection, risk sharing and inequality

This paper studies the relationship between investor protection, financial risk sharing and income inequality. In the presence of market frictions, better protection makes investors more willing to take on entrepreneurial risk while lending to firms. This implies lower cost of external finance and better risk sharing between financiers and entrepreneurs. Investor protection, by boosting the market for risk sharing plays the twofold role of encouraging agents to undertake risky enterprises and providing them with insurance. By increasing the number of risky projects, it raises income inequality. By extending insurance to more agents, it reduces it. As a result, the relationship between the size of the market for risk sharing and income inequality is hump-shaped. Empirical evidence from a cross-section of sixty-eight countries, and a panel of fifty countries over the period 1976-2000, supports the predictions of the model.

Investor protection and income inequality: risk sharing vs risk taking

This paper studies the relationship between investor protection, entrepreneurial risk taking and income inequality. In the presence of market frictions, better protection makes investors more willing to take on entrepreneurial risk when lending to firms, thereby improving the degree of risk sharing between financiers and entrepreneurs. On the other hand, by increasing risk sharing, investor protection also induces more firms to undertake risky projects. By increasing entrepreneurial risk taking, it raises income dispersion. By reducing the risk faced by entrepreneurs, it reduces income volatility. As a result, investor protection raises income inequality to the extent that it fosters risk taking, while it reduces it for a given level of risk taking. Empirical evidence from a panel of forty-five countries spanning the period 1976-2000 supports the predictions of the model.

Salience theory of choice under risk

We present a theory of choice among lotteries in which the decision maker's attention is drawn to (precisely defined) salient payoffs. This leads the decision maker to a context-dependent representation of lotteries in which true probabilities are replaced by decision weights distorted in favor of salient payoffs. By endogenizing decision weights as a function of payoffs, our model provides a novel and unified account of many empirical phenomena, including frequent risk-seeking behavior, invariance failures such as the Allais paradox, and preference reversals. It also yields new predictions, including some that distinguish it from Prospect Theory, which we test.

The effects of poor financial information systems on the long term sustainability of local public services. Empirical evidence from the Catalan Municipalities

In this paper we describe the existence of financial illusion in public accountingand we comment on its effects for the future sustainability of local publicservices. We relate these features to the lack of incentives amongst publicmanagers for improving the financial reporting and thus management of publicassets. Financial illusion pays off for politicians and managers since it allowsfor larger public expenditure increases and managerial slack, these beingarguments in their utility functions. This preference is strengthen by the shorttime perspective of politically appointed public managers. Both factors runagainst public accountability. This hypothesis is tested for Spain by using anunique sample. We take data from around forty Catalan local authorities withpopulation above 20,000 for the financial years 1993-98. We build this databasis from the Catalan Auditing Office Reports in a way that it can be linkedto some other local social and economic variables in order to test ourassumptions. The results confirm that there is a statistical relationship between the financialillusion index (FI as constructed in the paper) and higher current expenditure.This reflects on important overruns and increases of the delay in payingsuppliers, as well as on a higher difficulties to face capital finance. Mechanismsfor FI creation have to do among other factors, with delays in paying suppliers(and thereafter higher future financial costs per unit of service), no adequateprovision for bad debts and lack of appropriate capital funding either forreposition or for new equipments. For this, it is crucial to monitor the way inwhich capital transfers are accounted in local public sheet balances. As a result,for most of the Municipalities we analyse, the funds for guaranteeing continuityand sustainability of public services provision are today at risk.Given managerial incentives at present in public institutions, we conclude thatpublic regulation recently enforced for assuring better information systems inlocal public management may not be enough to change the current state of affairs.

A unifying approach to the empirical evaluation of asset pricing models

Two main approaches are commonly used to empirically evaluate linear factor pricingmodels: regression and SDF methods, with centred and uncentred versions of the latter.We show that unlike standard two-step or iterated GMM procedures, single-step estimatorssuch as continuously updated GMM yield numerically identical values for prices of risk,pricing errors, Jensen s alphas and overidentifying restrictions tests irrespective of the modelvalidity. Therefore, there is arguably a single approach regardless of the factors being tradedor not, or the use of excess or gross returns. We illustrate our results by revisiting Lustigand Verdelhan s (2007) empirical analysis of currency returns.

Ethics and creative accounting: Some empirical evidence on accounting for intangibles in Spain

Recent research shows that financial reports are losing relevance. Mainly thisis due to the growing strategic importance of intangible assets in theperformance of a company. A possible solution is to modify accounting standardsso that statements include more self-generated intangible assets, taking intoaccount with their inherent risk and difficulty of valuation. We surveyed loanofficers who were asked to assess the credit-worthiness of a hypotheticalcompany. The only information given was a simplified version of financialstatements. Half the group got statements where research and development costshad been capitalized. The other half got statements in which these costs hadbeen treated as an expense. The findings show that capitalization wassignificantly more likely to attract a positive response to a loan request. Thepaper raises the question of whether accounting for intangibles might providemanagers with one more creative accounting technique and, in consequence, itsethical implications.

Measuring risk aversion with lists: A new bias

Various experimental procedures aimed at measuring individual risk aversion involve alist of pairs of alternative prospects. We first study the widely used method by Holt andLaury (2002), for which we find that the removal of some items from the lists yields asystematic decrease in risk aversion. This bias is quite distinct from other confoundsthat have been previously observed in the use of the Holt and Laury method. It may berelated to empirical phenomena and theoretical developments where better prospectsincrease risk aversion. Nevertheless, we have also found that the more recent elicitationmethod due to Abdellaoui et al. (2011), also based on lists, does not display anystatistically significant bias when the corresponding items of the list are removed. Ourresults suggest that methods other than the popular Holt and Laury one may bepreferable for the measurement of risk aversion.

'Biased' Risk Perceptions of Longevity and Disability in Old Age

Rational learning theories postulate that information channels and cognitive biases such as individual optimism may influence an individual¿s assessment of the risk of undesired events, especially with regard to those that have a cumulative nature. This is the case with disability in old age, which may take place upon survival to an advanced age, and such factors have been regarded as responsible for certain individual behaviours (for example, the limited incidence of insurance purchase). This paper examines the determinants of individual perceptions with regard to disability in old age and longevity. The cumulative nature of such perceptions of risk is tested, and potential biases are identified, including `optimism¿ and a set of information determinants. Empirical evidence from a representative survey of Catalonia is presented to illustrate these effects. The findings from this research suggest a significant overestimation of disability in old age, yet this is not the case with longevity. Furthermore, individual perceptions with regard to disability in old age, unlike those with regard to longevity, exhibit on aggregate an `optimistic bias¿ and, are perceived as `cumulative risks¿. Gender influences the perceived risk of disability in old age at a population level but not at the individual level, and the opposite holds true for age. Finally, self-reported health status is the main variable behind risk perceptions at both the individual and population level.

'Biased' Risk Perceptions of Longevity and Disability in Old Age

Rational learning theories postulate that information channels and cognitive biases such as individual optimism may influence an individual¿s assessment of the risk of undesired events, especially with regard to those that have a cumulative nature. This is the case with disability in old age, which may take place upon survival to an advanced age, and such factors have been regarded as responsible for certain individual behaviours (for example, the limited incidence of insurance purchase). This paper examines the determinants of individual perceptions with regard to disability in old age and longevity. The cumulative nature of such perceptions of risk is tested, and potential biases are identified, including `optimism¿ and a set of information determinants. Empirical evidence from a representative survey of Catalonia is presented to illustrate these effects. The findings from this research suggest a significant overestimation of disability in old age, yet this is not the case with longevity. Furthermore, individual perceptions with regard to disability in old age, unlike those with regard to longevity, exhibit on aggregate an `optimistic bias¿ and, are perceived as `cumulative risks¿. Gender influences the perceived risk of disability in old age at a population level but not at the individual level, and the opposite holds true for age. Finally, self-reported health status is the main variable behind risk perceptions at both the individual and population level.