in this case. When zt≥1, there is no such problem because losses are penal-
ized at a single rate: 2.25 for zt=1, and higher than 2.25 for zt>1.
We adopt the following technique for dealing with the case of zt≤1: we
take the loss aversion component of the investor’s utility, namely
and for St=1 and a risk-free rate of Rf,t=3.86 percent, we compute E(v),
the expected loss aversion when the excess stock return is distributed as
logRt+ 1 – logRfN(0.06, 0.2^2 ),a good approximation to the historical distribution of the excess stock re-
turn. We then compute the quantity for which an investor with utility
function
would have exactly the same expected loss aversion for this distribution of
the excess stock return, again with St=1. This λis our measure of the in-
vestor’s effective loss aversion for any particular zt<1.
vX SSR R
RRRR
RR
tttt ft
tfttft
tft(,)()
()for,
,,
,++
++
+=−
−≥
<
11
11
λSt 1λvX S zSR SR
SzR R SR zRRzR
ttt RzRtt tft
ttft ft t t t ftttft
ttft(,,)
()( )for
,,
,, ,,
,++
++
+=−
−+ −≥
<
11
11
λ 1268 BARBERIS, HUANG, SANTOS