gender differential paper IJCRB

ijcrb.webs.com
JUNE 2011
INTERDISCIPLINARY JOURNAL OF CONTEMPORARY RESEARCH IN BUSINESS VOL 3, NO 2
winning $Y will be accepted if Ln(99)+Ln(109+Y) ≥ 2Ln(109) if Y ≥ 1,211.11. Thus for the
utility function and with a starting wealth level of $109, the individual will turn down the 50-50
chance of losing $10 and winning $11, but will accept a bet of losing $100 and winning any
amount Y in excess of $1,211.11.
Watt (2002) explained that for someone with a very high initial level of wealth, this bet
poses very little risk, and so turning it down requires an extraordinarily high level of risk
aversion. But if the person has an extraordinarily high level of risk aversion in turning down the
bet for even moderate stakes, then the person will also have an extraordinarily high level of risk
aversion in turning down bets for large stakes. Using Pratt’s approximation, Watt showed that
absolute risk aversion at wealth w is approximately equal to [2(w+E(L)-C(L, w]/V(L) where L
denotes a lottery with expected value E(L), variance V(L) and certainty equivalent at wealth w of
C(L,w). The rejection of the 50-50 bet of gaining $105 and losing $100, with the initial wealth
$350,000 implies that relative risk aversion would have to be greater than 166.57. Watt
concluded that for a person with a high level of wealth to turn down a bet of moderate stakes that
has a positive expected value would require either an unreasonably high level of risk aversion, or
some other unusual peculiarity in the utility function. Otherwise, the individual will not reject
both large-scale bets and moderate-scale bets. Therefore, the Expected utility theory certainly
faces its share of problems in explaining certain kinds of empirical evidence, as do other
competing theories.
3.2 Qualitative
3.2.1 Reference Level
How psychological findings suggest modifying the utility function that economists
employ through years. Researchers have identified a pervasive feature of reference dependence.
In a wide variety of domains, people are significantly more averse to losses than they are
attracted to same-sized gains (Kahneman et al., 1990). One realm where such loss aversion plays
out is in preferences over wealth levels. Tversky and Kahneman (1992) suggest that in the
domain of money (and in others where the size of losses and gains can be measured), people
value modest losses roughly twice as much as equal-sized gains. That the displeasure from a
monetary loss is greater than the pleasure from same-sized gain is also implied by a concave
utility function, which typically use as the explanation for risk aversion. But loss aversion says
that the value function abruptly changes slope at the reference level, so that people prefer their
status quo to a 50/50 bet of losing $10 or gaining $11. The standard concave-utility-function
explanation for risk aversion is simply not a plausible explanation of such risk attitude.
Mehra and Prescott (1985) and Esptein and Zin (1990) have, for instance, observed that
the utility-function framework cannot simultaneously explain both small-scale and large-scale
risk attitudes implied by macro data. Rabin (2000) also supported this claim by providing a
“calibration theorem” that indeed show that no concave utility function can simultaneously
explain plausible small-scale and large-scale risk attitudes.
4. Conclusion
We have focused on some of the major theories of economic behavior towards risks and
its efficiency of explanation toward large risks and small risks. Due to the inability of the
expected utility theory to provide a plausible account of risk aversion over modest stakes, we
also discuss the possibilities that may cause an ambiguous explanation of modest-scale risk
aversion. This is crucial especially for the research methods that rely extensively on the expected
utility interpretation.
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