STOCHASTIC

270 QUARTERLY JOURNAL OF ECONOMICS
E{-U"Woa(e-r) i }-EU"W0(l+r) je-r)
E{-U"(e-r)*W0(\-t)}
dlna _ W0(l+r)EU"(e-r)
dln(l-t) aE{-U"(e-r) 2 W0} '
The denominator of the second term on the right-hand side is ald
In a
ways positive. Hence whether — , —— is greater or less than
d In (1 — t)
unity depends on the sign of
-EU"(e-r)=E(-U"/U')U'(e-r)=E(A(W{e))
-A(W(6*))V'(e-r)+A(W($*))EU'(e-r)
where 6" is denned by e(9*) =r. The last term equals zero (since
utility maximization requires EXJ'(e—r) =0). If absolute risk aversion
increases with W, in those states of nature where
e(6)>e(6*)=r,A(W(6))>A{W(0*)),Bo-EU"(e-r)>0.
Similarly if absolute risk aversion decreases with W,-EU"(e—r)