5.7 Measuring Business Risk in Practice: Deﬁ 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 conﬁ 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% conﬁ 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 identiﬁ 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 proﬁ 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 proﬁ 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 modiﬁ cations, from Matten (2000).

MEASURING BUSINESS RISK IN PRACTICE 137

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