Risk Management and Value Creation in ... - Arabictrader.com

Rationales for Risk Management in Banks 117
Tax
Convex
Linear
Pretax Income
Figure 3.8 Tax schedules.
Source: Adapted from Smithson et al. (1995), p. 103.
In a tax system with a linear tax schedule risk management cannot have
any impact on firm value, since—as we know from statistics:
E(g(X)) = g(E(X)) (3.6)
where g = Linear tax function
X = Random variable = pretax income
E(·) = Expected value of (·).
So when, for instance, a firm can have pretax income of +300 or –100
with equal probability and the tax rate is fixed at 50%, g(X) = 0.5X 343 and
hence E(g(X)) = g(E(X)) = 50.
If the effective tax schedule is convex (as indicated by function f(X) in
Figure 3.9), risk management will reduce the firm’s expected taxes, because
Jensen’s inequality 344 indicates that a reduction in the volatility of pretax
income X (hedged position) induced by (financial price) risk will decrease
the tax liability (the expected value of the unhedged position), because:
E(f(X)) ≥ f(E(X)) (3.7)
343 This is equivalent to allowing for unrestricted tax-loss carry forwards.
344 See Smith (1995), p. 26, and Bamberg and Baur (1991), p. 121.