Abstract

In the evolution of bank regulation over the last thirty years, the Value-at-Risk (VaR) measure has been a key metric in determining the amount of regulatory capital a bank must hold to deal prudently with its exposure to market, credit and operational risk. The security supposedly provided by VaR was certainly challenged by the financial crisis in 2008. The risk analysis in place at the time appeared to be too narrowly focused, as other issues (particularly liquidity risk) came to the fore.

This thesis has maintained the VaR objective, but extends the traditional analysis along two dimensions. First, we have analyzed a notion of business risk associated with fluctuations in a bank’s business income that are not tied to specific market, credit or operational events. Rather the fluctuations that we analyze are more the consequences of ongoing strategic decisions. Second, we have attempted to operationalize a sectoral approach where the losses potentially faced by a particular bank are those that are shared by its competitors.

We first develop in Chapter 2 a general framework for analyzing the core notion Residual Profit & Loss (RPL) using the income statements as reported in Capital IQ which also provides data on Interest Earning Assets (IEA). We then construct a business income data set based on RPL/IEA for a US Retail Banking Sector. There are twenty-two banks in the sector. RPL/IEA is determined for these banks over the period 2002-2015. Using more recent data, we will be able in the thesis to focus on the post-crisis 2008 period.

A data set is also constructed in Chapter 2 for the Canadian banking sector. It is more concentrated than the US sector studied and was less severely affected by the 2008 crisis. But the methodological approach followed in this chapter faces an additional complexity in so far as accounting standards were significantly changed in 2011. Moreover, it is not possible to reconstruct income statements prior to 2011 using the new standards. We pursue several avenues of adjustment to render the treatment of the data over the entire sample as coherent as possible. We then construct RPL/IEA for this typical banking sector following the same methodology as used for the US retail sector.

The remainder of Chapter 2 transforms the time series of business returns (RPL/IEA ratio) for each bank into the US and Canadian sectoral loss datasets. A loss (gain) for a particular bank is characterized as the deviation from its expected return defined as its average return over the sample.

Chapter 3 proposes two approaches to determine the values of VaR corresponding to two ways of looking at the loss datasets. One approach assumes that an individual bank’s loss time series follows a sectoral moving average process. The common parameter is estimated across the time series using maximum likelihood. The VaR for an individual bank can readily be retrieved in this multivariate characterization. The second approach ignores the time series dimension and pools the data into a single sample for each sector. In this context, we propose to use the saddlepoint approximation technique that involves the use of sample moments to estimate the percentiles of the underlying loss distribution.
The saddlepoint approach is not commonly use in the applied financial literature. The basic features of this technique are reviewed in Chapter 3 along with several examples to illustrate how it has been applied in finance. The second part of the Chapter presents an extensive Monte Carlo simulation study that contrasts the performance of the saddlepoint percentile estimates with those obtained by the maximum likelihood structural approach.

Chapter 4 returns to the calculation of business risk faced by the US and Canadian sectors considered in the thesis. For each of the associated business loss data sets, there are the two estimation procedures that were introduced in the previous chapter. The VaRs for different confidence levels are determined and contrasted across the two models for each of the two sectors. We include several comparisons with the economic capital held by specific banks in the Canadian sector.