Since the initiation of the New Basel Capital Accord (Basel II) in 1999, when operational risk was introduced to the regulatory landscape, the attention to this risk type has risen substantially. The Basel Committee on Banking Supervision (Basel Committee, 2006) defines operational risk as “risk of loss resulting from inadequate or failed internal processes, people and systems or from external events.” The fact that events like bookkeeping errors and terrorist attacks are covered by this characterization illustrates the broad range of risks relative to credit or market risk. Taking this heterogeneity of loss events into account, the Basel Committee categorizes losses into seven event types and eight business lines. Banks are supposed to calculate risk measures for each of these 7 × 8 = 56 combinations, such as “Internal Fraud” in “Trading and Sales” or “Damage to Physical Assets” in “Commercial Banking”.
The risk measure specified by the Basel Committee is the Unexpected Loss at a confidence level of 99.9%. Generally speaking, this refers to the 99.9% quantile of the loss distribution (possibly reduced by the Expected Loss, that is, the mean of the distribution), commonly known as the 99.9% Value–at–Risk (VaR). It measures the maximum loss that will not be exceeded with the specified confidence level and is a widely used risk measure since the 1990s. The total required risk capital under the Advanced Measurement Approaches (AMA) is obtained by summing over all 56 event–type/business–line VaRs, a strategy implicitly expecting the joint occurrence of all loss types involved or, in other words, assuming perfect positive correlation between all loss processes. To allow for non–perfect correlations, the Basel Committee permits a bank “...to use internally determined correlations [...] provided it can demonstrate to the satisfaction of the national supervisor that its systems for determining correlations are sound, implemented with integrity, and take into account the uncertainty surrounding any such correlation estimates (particularly in periods of stress).” (Basel Committee, 2006, p. 148). Dropping the highly unrealistic assumption of perfect dependence (i.e., summing the Unexpected Losses of all cells) and relying on realistic correlation estimates should decrease the calculated risk capital. Therefore, banks should have a strong interest in developing and establishing adequate assessment approaches. This expected decrease in estimated risk capital due to less than perfect correlations of the loss processes is the focus here. Specifically, we investigate whether a general rule can be established about risk–capital requirements and less than perfect correlations. Second, we analyze how the model specification affects such a rule.
The electric utility industry represents the second most capital intensive sector in the United States, surpassed only by the railroad industry. Many of the industry’s costs stem directly from investments in and maintenance of the power plants, transmission and distribution lines, equipment, and structures that are used to deliver electricity where it’s needed.
Today, the electric utility industry faces the greatest challenge in its history. In order to meet the projected growth in electricity demand, major investments are needed to expand and modernize most elements of the electric utility business. At the same time, concerns about global climate change and other environmental issues have created a new industry emphasis on more energy-efficient products and services and low emission generation sources. By some estimates, the industry will need to make a total infrastructure investment of $1.5 trillion to $2.0 trillion between 2010 and 2030, net of projected savings from aggressive energy efficiency and demand response programs.
The classical theory of portfolio selection pioneered by Markowitz (1952) remains to this day an immensely prominent approach to asset allocation and active portfolio management. The key inputs to this approach are the expected returns and the covariance matrix of the assets under consideration in the portfolio selection problem. According to the classical theory, optimal portfolio weights can be found by minimizing the variance of the portfolio’s returns subject to the constraint that the expected portfolio return achieves a specified target value.
