A =(.5, $10; .5, $ -10) B = (.2, $20; .8, $ - 5) C =(.8, $5; .2, $ -
20).
The vector (p, $7; 1 — p, $xf ) denotes an alternative which has a p-chance
of getting $.7; and a 1-p-chance of getting $7Z. All three alternatives have the
same expected value and the same variance. However, most subjects judge
C to be the most risky alternative: they seem to dislike the relatively large
loss potential in alternative C.
To model risk perception, the literature on behavioral decision making
has proposed and tested different theories [see Brachinger and Weber (1997)
and Jia, Dyer and Butler (1999) for an overview]. An exponential model
[Sarin 1984] and a power function model [Luce and E. Weber 1986] were
found to fit the data quite well [Keller et al. 1986 and E. Weber and Bottom
1990]. These models define risk as the expected value of a function of the
outcomes or of the deviations of the outcomes from a possibly endogenous
benchmark. Thus, the risk of a random variable e can be written as
Risk(e) = E[F (e — e)]
(1)
F is a function with F(0) = 0, e denotes the random payoff of the alter-
native and e the benchmark. This risk measure is general enough to include
risk measures which describe people’s risk perception, e.g. the exponential
risk measure. Jia and Dyer (1996) define a standard measure of risk as in
equation (1) with (-F) being a von Neumann-Morgenstern utility function.
The benchmark e equals the expected payoff.
There are two fundamental ways for defining a benchmark: exogenously
or endogenously. An exogenous benchmark is set by the investor, e.g., it
can be the outcome level the investor wants to surpass. This benchmark can
have any sign. This benchmark may be affected by portfolio gains or losses in