726 CHAPTER 19. SETTING THE COST OF INTERNATIONAL CAPITAL
Table 19.2:Exchange Rate Exposure: Good or Bad?Example 1: Example 2:
covariance> 0 covariance< 0 Comment
Wus(incad) 12,000 16,000 12,000 16,000 same distribution forWus...
S(cad/usd) 1.00 1.50 1.50 1.00 and same distribution forS;
Wus∗ (inusd) 12,000 10,667 8,000 16,000 but the positive-cov case has ...
E(Wus∗) 11,333 12,000 – a lower meanWus∗ ...
stdev(Wus∗) 667 4,000 – and a lower stdevWus∗being the same, the higher theircadwealth, the higher also their wealth inusd.
The fact that, holding constant the exchange rate, they care aboutcad-expressed
wealth then explains why the first half of the efficiency condition looks like the
Canadian investor’s condition. Butusinvestors will all the time also think of the
exchange rate, because deep down they care aboutusd-measured wealth only. It is
this concern about the exchange rate that induces a second item. But, as we shall
see, it is less obvious whether theusinvestor, thinking incadterms but caring
aboutusdnumbers, likes exchange-rate exposure or not.
Example 19.9
In Table 19.2 we have picked two examples where, in each example, there are two
equally probable scenarios forcadwealth and the exchange rate. The means and
variances are the same across the two examples, but the first one has a positive
association betweencadwealth and the exchange rate while in the second example
the correlation is negative. We see that a larger positive covariance is a mixed
blessing: it lowers both the mean (bad!) and the variance (good!). So whether
on balance the effect is preferred depends on your degree of risk aversion, notably
whether you attach more weight to the rise in return than to the rise of risk.
It can, in fact, be shown that investors with risk aversion equal to 1 ignore
covariance withS. More risk-averse investors (λ > 1) like it because they like
the variance-reduction effect, while less risk-averse people dislike it: the drop in
the mean is viewed as too high a price for the lower risk. But note that, among
financial economists, the consensus probably is that lambda exceeds unity. (Macro-
economists are not so sure.) Thus, the modal investor probably prefers the hedging
effect and is willing to accept a lower mean return on assetjif it does help as a
hedge.
What assets would be especially attractive tousinvestors from that perspective?
One might guess thatusstocks may be more appealing than Canadian stocks. But
such a view may be simplistic, as the next subsection argues.