June 2007 Capital Adequacy Extension © Copyright 2007, CCRO. All rights reserved. Page 87 of 92 Plugging in these values yields a RAROC as follows: RAROC = ($165MM - $30MM)/$75MM = 180% over 5 years = 23% annualized. The Committee determined the expansion of marketing activities is a good business since its RAROC exceeds the firm’s hurdle rate. 10.2.8. Decomposing EMTCo’s Portfolio Our Equity at Risk Methodology also allows the firm to calculate the different risk components of its portfolio. While we used an incremental approach above to determine the incremental equity required to support the expansion project, we can use a decomposition method to extract the component equity36 required to support any level in the organization or any risk component. Thus we can determine the required equity to support a business unit, an investment, groups of investments, credit risk, operative risk, etc. while only running the model once. Because our available equity distribution has a default probability of 5.25% without the new marketing opportunity, we can define an equity parameter to represent the equity lost at default as being equivalent to VaR at a 94.75 percentile (1 minus 5.25%) and a 5 year time horizon37. Because the two parameters are equivalent, we can utilize the same procedures developed for VaR on our equity parameter. The decomposition would be relatively easy if our available equity distribution were normally distributed however, because of the skewness of our distribution caused by the longer time horizon and non- normal risk components, we cannot use the text book parametric solutions without inducing considerable error. Nonetheless, our simulation approach will allow us to decompose our equity utilizing the default scenarios. Because we have defined our equity parameter equivalent to VaR(P94.75, 5 years) we will use the following (altered for our equty parameter) VaR equation used to decompose the portfolio VaR to its individual components. CEQi = E( Delta Value i | Default ) Where i = individual investment, business unit or risk The component equity (CEQi) is equal to the expected change in the value of investment i when the firm defaults. Delta Value is calculated by determining the change from the investment’s initial value to its value at default. The initial value will be its MTM at t = 0 and the default value will be the sum of its realized and unrealized value at the default period. The investment’s realized value is the sum of all proceeds received prior to default and its unrealized value is the MTM at t = default period. 36 Component economic capital is an estimate of incremental economic capital 37 While VaR is normally a short term risk measure (1 day), we are using it over 5 years in this example