budgets calculate net income as the difference between revenue and expenses. ROE is then estimated as net income divided by capital invested. In the case of risk budgets, a risk "charge"-defined as VaR or some other proxy for "risk expense"-can be associated with each line item of projected revenue and expense. Hence, a RORC can be associated with each activity as well as for the aggregation of all activities. In the case of both financial and risk budgets, presumably ROE and RORC must exceed some minimum levels for them to be deemed acceptable. Both statistics are concerned with whether the organization is sufficiently compensated-in cost/benefit terms-for the expenses and/or risks associated with generating revenues. Just as the financial budget allocates revenue and expense amounts across activities to determine their profitability, so too should a risk budget exist for each activity in order to estimate the risk-adjusted profitability of the activity. Just as financial budgets show a contribution to ROE by activity, so too can risk budgets show a contribution to overall risk capital usage by activity. For example, standard mean-variance optimization methods produce estimates of weights to be assigned to each asset class, in addition to overall estimates of portfolio standard deviation and the marginal contribution to risk8 from each allocation. Note that both RORC and ROE can and should be estimated over all time intervals that are deemed relevant. For example, if investment boards meet monthly and are likely to react to short-term performance, monthly RORC is relevant. Hence, management must define the time horizons over which risk budget allocations are to be spent and over which RORC should be measured.3 An example at this point might be helpful. Assume that an organization has a material investment portfolio. The organization is concerned about the impact of the earnings volatility of this portfolio on reported earnings and, therefore, share price. In constructing a risk budget for this portfolio, the organization might: 11 From the risk and business plan, identify acceptable levels of RORC and ROE over various time horizons. II Using mean variance optimization or other techniques, determine appropriate weights for each investment class. II Simulate the performance of a portfolio (including the behavior of related liabilities, if relevant) constructed with these weights over various time horizons, and test the sensitivity of this performance to changes in return and covariance assumptions. 8The marginal contribution to risk from any asset is defined as the change in risk associated with a small change in the underlying weight of that asset in the portfolio. sWe know that risk across different time dimensions does not simply scale by the square root of time. The path to the long term may be much bumpier than a simple scaling might imply. In fact, the long-term result may be entirely consistent with a fair number of short-term anomalies. If so, management must ensure that risk allocations are sized in such a manner that losses associated with short-term market difficulties can be negotiated effectively. Hence, in a manner analogous to financial budgeting, the risk budget helps managers size the bets in each revenue-producing area.