5.7 Measuring Business Risk in Practice: De ning a
Measure of Earnings at Risk
In general terms, earnings at risk (EaR) can be identifi ed with the losses generated by a
given business unit under the maximum adverse variation in its earnings within a given
time horizon and con dence interval. For instance, for the asset management business,
one could try to build a distribution of the earnings produced by the fund management
company and identify EaR at a 99% con dence level as the one one-hundreth quantile
of the earnings distribution. The fi rst thorough discussion of the EaR concept for business
risk is contained in Matten (2000). Matten identi es EaR as a multiple of the standard
deviation of earnings of a given business unit. Let us assume, for instance, the hypotheti-
cal revenue volatility model of a business unit presented in Table 5-5.
If we assume revenues have a standard deviation equal to 1000 around their expected
value of 5000, variable costs are 10% of revenues, and taxes 40% of net pro t before
taxes, then the table allows us to transform revenue scenarios into corresponding scenar-
ios for net profi t before taxes and net profi t. Of course, absolute differences between a
+1/1 standard deviation scenario decrease as we move from revenues to net pro t, as a
consequence of variable costs and taxes. Earnings at risk could hence be identifi ed with
a given multiple of earnings volatility. Matten (2000) suggests that this measure does not
represent capital allocated to fee-based businesses, which should be considered equal,
instead, to earnings at risk divided by the risk-free rate. In practice, capital at risk for
business risk should be identifi ed with the amount of capital that should be invested at
the risk-free rate to compensate for the earnings that could be missed in an adverse
scenario.
The link between EaR measures and economic capital for business risk are discussed
in the next section, but it is useful to discuss in greater detail the issues involued in deriv-
ing an estimate of earnings volatility:
1. The choice of the starting point (revenues rather than earnings directly) for EaR
calculation and the consequent role of fi xed and variable cost estimates
2. The availability and size of the desired time series
3. The problems in rescaling of data series
4. The choice to include or exclude expected earnings
First of all, earnings volatility can be modeled either directly or by modeling revenues
so as to derive a net profi t distribution from revenue distribution. In the second case,
TA B L E 5 -5 Example of Earnings Volatility Model for Business Unit Alpha
-2s -1s Mean +1s +2s
Revenues 3000 4000 5000 6000 7000
Fixed costs (2500) (2500) (2500) (2500) (2500)
Variable costs (300) (400) (500) (600) (700)
Net profi t before taxes 200 1100 2000 2900 3800
Taxes (80) (440) (800) (1160) (1520)
Net profi t 120 660 1200 1740 2280
Source: Adapted, with modi cations, from Matten (2000).
MEASURING BUSINESS RISK IN PRACTICE 137

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