In this paper, we explore the applications of Tail Variance (TV) as a measure of tail riskiness and the confidence level of using Tail Conditional Expectation (TCE)-based risk capital. While TCE measures the expected loss of a risk that exceeds a certain threshold, TV measures the variability of risk along its tails. We first derive analytical formulas of TV and TCE for a large variety of probability distributions. These formulas are useful instruments for relevant research works on tail risk measures. We then propose a distribution-free approach utilizing TV to estimate the lower bounds of the confidence level of using TCE-based risk capital. In doing so, we introduce sharpened conditional probability inequalities, which halve the bounds of conventional Markov and Cantelli inequalities. Such an approach is easy to implement. We further investigate the characterization of tail risks by TV through an exploration of TV’s asymptotics. A distribution-free limit formula is derived for the asymptotics of TV. To further investigate the asymptotic properties, we consider two broad distribution families defined on tails, namely, the polynomial-tailed distributions and the exponential-tailed distributions. The two distribution families are found to exhibit an asymptotic equivalence between TV and the reciprocal square of the hazard rate. We also establish asymptotic relationships between TCE and VaR for the two families. Our asymptotic analysis contributes to the existing research by unifying the asymptotic expressions and the convergence rate of TV for Student-t distributions, exponential distributions, and normal distributions, which complements the discussion on the convergence rate of univariate cases in [28]. To show the usefulness of our results, we present two case studies based on real data from the industry. We first show how to use conditional inequalities to assess the confidence of using TCE-based risk capital for different types of insurance businesses. Then, for financial data, we provide alternative evidence for the relationship between the data frequency and the tail categorization by the asymptotics of TV.

This paper estimates a model using Bayesian methods and data from the USA (1990Q1–2019Q2) to explore how the financial sector contributes to business cycles through banks’ asset channel and the quality of capital adequacy constraint. The paper shows that the contribution of financial and non-financial shocks varied before, during, and after the 2008 financial crisis; housing demand and asset price shocks are the main contributors, and the credit shocks are the most persistent. In addition, the paper presents the application of macroprudential tools, along with their impact on the economy in general, and on welfare in particular. The findings illustrate that the tools which control household borrowing ability, such as loan-to-value or debt-to-income ratios, do not impact welfare significantly. However, the impact of policies on the leveraged sector is substantial. The paper proposes macroprudential policies that allow policy-makers to stabilize the economy without changing welfare. Such policies, however, should be timely, targeted, and temporary; otherwise, they may cause disruptions.

This article reinterprets the origin and evolution of the Basel Accords. We argue that the Basel I paradigm was very different from the regulatory approaches that had been applied successfully in most European countries since the Second World War. Banking systems relied on a multitude of tools including entry restrictions, liquidity rules, reserve requirements, deposit rate ceilings, lending and investment restrictions, combined with hands-on supervision and discretional interventions. By focusing exclusively on capital adequacy and credit risk, Basel I shifted attention in a very different and somewhat unexpected direction. The Basel regulations are often understood as a reaction to the bank failures of the 1970s and 1980s, but in fact their capital adequacy rules would not have prevented these failures. Indeed, even today, several of these risks are still not addressed by Basel updates, suggesting that the original and current proposals have a rather different raison d’être, placating political constituencies and banking interests.

Banking and finance are inherently pro-cyclical, a condition exacerbated by a combination of Basel II and mark-to-market accounting. But these latter measures have many advantages, so the need is to devise other counter-cyclical macro-prudential policies. This fragility was further enhanced by a decline in bank liquidity (reliance on wholesale funding) and a shift in govenance from partnerships to limited liability public companies. Some commentators have seen the solution to such pro-cyclicality in the guise of direct constraints on bank activity, such as the promotion of ‘narrow banking’ or limits on bank size. While there are arguments for toughening regulation as systemic risk increases, direct constraints are simplistic; more sensible ideas involve the adoption of better designed macro-prudential regulation, perhaps with some version of banking self-insurance. Quite what the future holds for bank regulation remains, however, to be decided.

This paper describes the dynamic financial analysis model currently being used by a property catastrophe reinsurer to manage its business. The model is-an integral part of the day-to-day operations at the Company, and is used as a decision making tool in the underwriting, investment, and capital management processes. The paper begins by describing the framework that the Company uses for risk management. This includes a classification of the risks facing the Company, which is used to define and prioritize their implementation in the model. Also included is a description of the conceptual approach the Company takes to evaluate the tradeoff between risk and return. The paper then goes on to describe the structure and operation of the dynamic financial analysis model and provides examples of its use at the Company, along with illustrative examples of the various types of output it produces.