Balance Sheet Additivity of Risk Measures

This paper has explored a problem presented by introducing formal measures of risk into firm decision making. Risk measured in the firm's asset collection may not equal risk in the claims against the assets, with a resulting inequality of valuations in an a priori balance sheet. This nonadditivity problem does not occur if covariance with some external portfolio is used as the risk measure. Computer testing has suggested that the nonadditivity problem could occur in considerable magnitude if variance were used as a risk measure, and to a substantially lesser extent if standard deviation (or the coefficient of variation) were used. Nonadditivity problems in the measures were worse in rather high (but not ultra-high) debt-use ranges and did not exist at all as long as debt was used so moderately that no chance of default was foreseen. While no findings were stated on this point, intuition and some unreported work done by one of the authors both suggest that nonadditivity would also be a problem in mixed risk measures, in which both covariance with an external portfolio and a measure of dispersion in the firm's own portfolio are employed.