13.3. MEASURING AND HEDGING OF OPERATING EXPOSURE 507
Figure 13.5:Results for the non-linear exposure example
Non-linear exposure350004000045000500005500060000650000.75 0.8 0.85 0.9 0.95 1 1.05
S_TV(S_T)General Issues in Minimum-Variance Hedging
The above problems were kept simple, which is fine if the purpose is to explain the
concept. Still, in fairness it must be added that the hedging of operations exposure
is a bit of a minefield once you go to reality. Here is a list of the steps to be taken,
and the issues to be solved:
- Getting dataOne can either go for data from the past, or numbers about
possible future scenarios.- Past data One can proceed the way one estimates a market beta: collect
past data on stock prices and exchange rates, and regress. We see the
following problems. (i) This allows you, at best, to estimate the risk of
the firm as a whole, not a new project or a separate business. (ii) The
assumption is that the future is like the past, which is often not true:PPP
deviations come in long swings, for instance, and exposure during a pe-
riod of dollar overvaluation is a poor guide to exposure in the subsequent
period of undervaluation. (iii) Even past exposure is estimated poorly
because, for most firms, exchange risk is only a weak determinant of re-
turns, which means that estimates are imprecise. (iv) If you nevertheless
go for this data-mining approach, you should realise that, with time-series
data, there is a problem of unit roots (ask your statistics teacher). This
means that one has to use return data (percentage changes in values),
not the value data themselves. The regression coefficient one gets from
a returns regression is an elasticity (that is, (∂V/∂S)(S/V)) whereas the
Bwe need is a partial derivative,∂V/∂S. So one would need an adjust-
ment, multiplying the slope coefficient byV/S. Then a decision needs to
- Past data One can proceed the way one estimates a market beta: collect