The hypothesis examined in this paper is that the greater the investor
's flexibility, the easier it is for him to change his portfolio depen
ding on his results, the more willing he will be to accept risks. When
the investor has no control on the size of the risky investment, but
can choose between one risky and one riskless asset, this conjecture i
s shown to be correct. However, if there is more than one risky asset
each period, counterexamples demonstrate that flexibility rarely ensur
es greater risk taking. For the standard portfolio problem in which in
vestors are free to determine the size of their investment in a risky
asset, flexibility always raises the demand for the risky asset if con
stant relative risk aversion is less than unity. But counterexamples c
an always be found when the constant relative risk aversion is larger
than unity. (C) 1997 Academic Press.