CHAPTER 18.
18.1. The maximization problem for the speculator’s is:
fppcEUmax f*
f
Let us rewrite the program in the spirit of Chapter IV:
fppcUEfW f*
. The FOC can then be written
0ppfppc‘UEf‘W ff*
. From (U”<0) we find
0ppfppc‘‘UEf‘‘W 2
ff*
. This means that f>0 iff
0ppEc‘U0‘W f*
. From U’>0 we have f>0 iff
0ppE f
. The two other
cases follow immediately.
18.2. Let us reason with the help of an example. Suppose the current futures price pf is $100.-.
The marginal cost of producing the corresponding commodity is $110. The producer’s
expectation as to the t=1 spot price for her output is $120.
The producer could speculate in the sense of deciding to produce an extra unit of output
The rule we have derived in this chapter would, however, suggest that this is the wrong
It is easy to see, indeed, that if the producer wants to take a position on the basis of her
expectations on the t=1 spot price, she will make a larger unit profit by speculating on the
18.3. When the object exchanged is a financial asset and investors have heterogeneous
information, a price increase may reveal some privately held information leading some
18.4. When investors share the same information, the only source of trading are liquidity needs
of one or another group of investors. In the CCAPM with homogeneous investors, there
simply is no trading. Prices support the endowment allocations. In a world of
heterogeneous information, the liquidity-based trades are supplemented by exchanges
18. 5
2
y
2
1
eyp
~
E
)q
~
,e
~
cov(ypz2q
~
varze
~
varyp
~
var 222
FOC:
This is a marginal product = marginal cost condition where the latter includes a risk
premium.
z : z varq p ycov(e,q) 0
% %%
q
~
var
)q
~
,e
~
cov(yp
z
p y = value placed at risk by fluctuations of exchange rates.
Optimal position in hedging instrument 2 is the product of py by a coefficient that we
~