Market Efficiency with Nonspeculative Assets

The important concept of market efficiency was introduced. The theorem that
was proved was a “no trade” theorem. If investors had common prior beliefs  then even
if they had different information, they would all refrain from trading purely speculative
claims, and each asset would be priced so that its expected return was equal to the riskless
return.
The basic intuition for this result was that in a purely speculative market the risk of the
assets was not inherent to the economy and could be avoided by every investor. Investors
would trade therefore only when they believed they were receiving a favorable “bet.” Each
investor realized that all of the other investors also thought this way, so whenever some other
investor was willing to take the opposite side of a transaction, this had to be understood as
being based on some information that the first investor did not know. Realizing this, both
investors would revise their beliefs until they came into concordance.
If markets are not purely speculative, then this result no longer holds. Investors may
be willing to take unfavorable “bets” if they offset some of the risk of their other holdings.
That is, an investor may trade to get a favorable return or to reduce risk. It is, however,
possible to separate these two motives for trade and derive a “no trade” theorem in other
than purely speculative markets. Like the previous theorem in this chapter, this result also
depends on the market being effectively complete.
The basic structure of the economy is as follows. There is an initial round of trading in
which a Pareto optimal allocation of period-0 consumption and period-i wealth is achieved.
That is, the initial round of trading takes place in an effectively complete market. After
this equilibrium is reached, investors consume. Then they receive private information, and
the market reopens for trading. In this second round, investors may also learn from the
equilibrium price or other public information. Each investor knows that this is the structure
of the economy and knows before the first round of trading all the possible states (i.e., the
private information does not cause any investor to believe that the structure of the economy
is changed or that any new states are possible).

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