A margin account is a type of brokerage account that allows investors to buy and sell financial securities using credit. The account’s margin requirement is the amount of collateral required, from the investor, to cover the funds or securities extended by the broker to the investor. In Canada, the primary driver of an account’s margin requirement is the account’s Capital Charge [CC] which is calculated using a set of regulatory rules. The regulations are degenerate in that hundreds of valid CCs often exist for a single account. This work outlines a linear optimization model for selecting the minimal CC out of the set of valid CCs for a given margin account. The method proposed is consistent with all of the regulatory requirements and is guaranteed optimal in most cases. Relative to existing methods, the new method produced an average CC reduction of approximately 2% and displayed qualitatively better run-times.

A margin account is a type of brokerage account that allows investors to buy and sell financial securities using credit. The account’s margin requirement is the amount of collateral required, from the investor, to cover the funds or securities extended by the broker to the investor. In Canada, the primary driver of an account’s margin requirement is the account’s Capital Charge [CC] which is calculated using a set of regulatory rules. The regulations are degenerate in that hundreds of valid CCs often exist for a single account. This work outlines a linear optimization model for selecting the minimal CC out of the set of valid CCs for a given margin account. The method proposed is consistent with all of the regulatory requirements and is guaranteed optimal in most cases. Relative to existing methods, the new method produced an average CC reduction of approximately 2% and displayed qualitatively better run-times.

This work undertakes the first comprehensive theoretical assessment of syndicated loans. It is shown that syndicated and bilateral (single lender) loans should be good substitutes in meeting a borrower's financing requirements, but that syndicated loans are more complex and impose additional risks to the parties in the way they are arranged. The existing explantions of loan syndication - that they are hybrids of private bank loans and public debt instruments, that syndication is a portfolio management tool, and that loans are syndicated where they are too large to be provided bilaterally - are unable to substantially explain both the nature of syndicated loans and practice in the loan markets. A rigorous new explanation is developed, which shows that syndication reduces the rate of lending costs, so that the return to the loan originator is greater, and the borrower's cost of financing is lower, where a loan is syndicated rather than provided bilaterally. This explanation is shown to hold in competitive loan markets and to be consistent with the observation that syndicated loans are generally larger than other loans. Incidental to this new explanation, new expressions of the return to a bank from providing a loan on a bilateral basis and from originating a syndicated loan are also developed. New algorithms are also developed for determining the distribution of the commitments from syndicate participants and thus the originator's final hold, the amount it must lend itself, where the loan is underwritten. This provides, for the first time, a rigorous basis for assessing the expected return, and the risk, for the originator of a given syndicated loan. Finally, empirical testing finds that a bank's observed lending history is significant to its decision to participate in a new syndicated loan but that predictions of participation, which are fundamental inputs into the final hold algorithms, based on this information have relatively little power. It follows that there is competitive advantage to loan originators that have access to other, private information on potential participants' lending intentions.

Notre thèse consiste à expliquer, en apportant quelques éléments théoriques, les imperfections des stress tests macro-prudentiels d’EBA/BCE, et de proposer une nouvelle méthodologie de leur application ainsi que deux stress tests spécifiques en complément. Nous montrons que les stress tests macro-prudentiels peuvent être non pertinents lorsque les deux hypothèses fondamentales du modèle de base de Gordy-Vasicek utilisé pour évaluer le capital réglementaire des banques en méthodes internes (IRB) dans le cadre du risque de crédit (portefeuille de crédit asymptotiquement granulaire et présence d’une seule source de risque systématique qui est la conjoncture macro-économique), ne sont pas respectées. Premièrement, ils existent des portefeuilles concentrés pour lesquels les macro-stress tests ne sont pas suffisants pour mesurer les pertes potentielles, voire inefficaces si ces portefeuilles impliquent des contreparties non cycliques. Deuxièmement, le risque systématique peut provenir de plusieurs sources ; le modèle actuel à un facteur empêche la répercussion propre des chocs « macro ».Nous proposons un stress test spécifique de crédit qui permet d’appréhender le risque spécifique de crédit d’un portefeuille concentré, et un stress test spécifique de liquidité qui permet de mesurer l’impact des chocs spécifiques de liquidité sur la solvabilité de la banque. Nous proposons aussi une généralisation multifactorielle de la fonction d’évaluation du capital réglementaire en IRB, qui permet d’appliquer les chocs des macro-stress tests sur chaque portefeuille sectoriel, en stressant de façon claire, précise et transparente les facteurs de risque systématique l’impactant. Cette méthodologie permet une répercussion propre de ces chocs sur la probabilité de défaut conditionnelle des contreparties de ces portefeuilles et donc une meilleure évaluation de la charge en capital de la banque. / Our thesis consists in explaining, by bringing some theoretical elements, the imperfections of EBA / BCE macro-prudential stress tests, and proposing a new methodology of their application as well as two specific stress tests in addition. We show that macro-prudential stress tests may be irrelevant when the two basic assumptions of the Gordy-Vasicek core model used to assess banks regulatory capital in internal methods (IRB) in the context of credit risk (asymptotically granular credit portfolio and presence of a single source of systematic risk which is the macroeconomic conjuncture), are not respected. Firstly, they exist concentrated portfolios for which macro-stress tests are not sufficient to measure potential losses or even ineffective in the case where these portfolios involve non-cyclical counterparties. Secondly, systematic risk can come from several sources; the actual one-factor model doesn’t allow a proper repercussion of the “macro” shocks. We propose a specific credit stress test which makes possible to apprehend the specific credit risk of a concentrated portfolio, as well as a specific liquidity stress test which makes possible to measure the impact of liquidity shocks on the bank’s solvency. We also propose a multifactorial generalization of the regulatory capital valuation model in IRB, which allows applying macro-stress tests shocks on each sectorial portfolio, stressing in a clear, precise and transparent way the systematic risk factors impacting it. This methodology allows a proper impact of these shocks on the conditional probability of default of the counterparties of these portfolios and therefore a better evaluation of the capital charge of the bank.