19.2. THE SINGLE-COUNTRYCAPM 711
The shortfall of 2 (=125 – 123) is due to the fact that highfdkcash flows tend to go
together with low exchange rates and vice versa. This effect is lost if one just multiplies
through the two expectations, because that computation implicitly assigns probabilities 0.25
to each cell:
E(S ̃)E(C ̃∗) = [(0. 50 × 1 .2) + (0. 50 × 0 .8)]×[(0. 50 ×150) + (0. 50 ×100)],
= (0. 25 ×180) + (0. 25 ×120) + (0. 25 ×120) + (0. 25 ×80). (19.6)So when we use the Translate First approach, the expectedgbpcash flow isgbp
123 not 125.^2 This number is to be discounted at the appropriate home currency
discount rate, that is, thegbprisk-free rate plus a risk premium that reflects the risk
of thegbpcash flows to the British investor.^3 The Capital Asset Pricing Model, to
be discussed in Sections 19.2 and 19.3, provides a way to estimate the appropriate
discount rate.
While the Translate First approach is very general, it requires explicit exchange-
rate forecasts, and the covariance. These do not come in explicitly if we take the
Discount First route, and compute aPVfor the expected flow E(C ̃∗) = 125, using
thefdkrisk free rate and risk premium. This would be all right if the Freedonian
and British markets are well integrated.
We have seen how to obtain expected cash flows, but not how to obtain appro-
priate discount rates when cash flows are risky. This is the task in the remainder
of this chapter. Section 2 reviews the single-countryCAPM. Section 3 extends the
model to a multi-country setting.
19.2 The Single-Country CAPM
Our discussion of the traditional (single-country)CAPMstarts from asset demand
theory. The key assumption of this asset demand theory is that investors rank
portfolios on the basis of two numbers, the expected nominal portfolio return and
the variance of the nominal portfolio return. Implicit in the use of nominal returns
is an assumption that inflation is deterministic, or at least that inflation uncertainty
has little impact on asset pricing. The theory of optimal portfolios, as developed
by Markowitz (1952), can also be interpreted as a theory that tells us how expected
(^2) In the above example, the cov-correction is relatively small. But the link between exchange
rate and cash-flow is weak too, in the above story: it just works via general economic activity. In
reality, there often is a strong, direct link, for instance if the firm is an exporter or importer, and
then the covariance would be bigger.
(^3) Recall that if capital markets within, say, theOECDare well integrated, theukvalue would also
be correct for any other investor from any otherOECDcountry. (TheOECDis just a for-example
term: the world market now counts many non-OECDmembers.)