4.4. THE MARKET VALUE OF AN OUTSTANDING FORWARD CONTRACT 147
flesh out [4.20] into
Et(S ̃T)
1 +rt,T+RPt,T(βS)
=
Ft,T
1 +rt,T. (4.22)
After a minor rearrangement (line 1, below)we can then use the notationceqas in
[4.21], to conclude that
Ft,T = Et(S ̃T)
1 +rt,T
1 +rt,T+RPt,T
⇒CEQt(S ̃T) = Et(S ̃T)
1 +rt,T
1 +rt,T+RPt,T(4.23)
≈ Et(S ̃T)1
1 +RPt,T. (4.24)
The last line is only an approximation of the true relation [4.23]. We merely add it to
show why the fraction on the right-hand side of [4.23] is called the risk adjustment.
Example 4.17
Suppose your finance professor offers you a 1-percent share in the next-year royalties
from his finance textbook, with an expected value, next year, ofusd 3,450,000.
Given the high risk (^o o), the market would discount this at 10 percent—3 risk-free
plus a 7 risk premium. Theceqwould be
CEQ = 3, 450 , 0001. 03
1. 10
= 3, 450 , 000 × 0 .936363636 = 3, 090 , 000. (4.25)
Thus, the market would be indifferent between this proposition andusd3,090,000
for sure. You could unload either of these in the market at a commonPV,
3 , 450 , 000
1. 10= 3, 000 ,000 =
3 , 090 , 000
1. 03
. (4.26)
The risk-adjusted expected value plays a crucial role in the theory of international
finance. As we shall see in the remainder of this chapter and later in the book, the
risk-adjusted expectation has many important implications for asset pricing as well
as for corporate financial decisions.
4.4.5 Implications for Spot Values; the Role of Interest Rates
In principle, we can see the spot value as the expected future value of the investment—
including interest earned—corrected for risk and then discounted at the appropriate
risk-free rate. In this subsection we consider the role of interest rates and changes
therein, hoping to clear up any confusion that might exist in your mind. Notably,
we have noted that a forward discount,i.e. a relatively high foreign riskfree rate,
signals a weak currency. Yet we see central banks increase interest rates when their