I begin my series on risk aversion, competition and gender with a review paper by Catherine Eckel and Philip J. Grossman in The Handbook of Experimental Economics Results. In their paper, Eckel and Grossman cover several papers that assess risk aversion. So what do we mean by risk aversion? We mean the tendency to avoid risk, to avoid a probability of winning or losing money relative to winning or losing some certain amount of money.  For example, do you put your money under your bed, in property, in bonds, or in stocks? The level of risk increases as you move from the one to the other, but the potential rewards increase too - leading to the well-known relationship between risk and reward.  Eckel and Grossman look at three methods used in economics to assess risk aversion - Abstract Gambles, Contextual Environment Experiments and Field Experiments. I deal with each in turn.

Abstract gambles are decisions where a subject has to choose the gambles that they prefer, these decisions may be hypothetical (I'm not a fan), low stakes gambles (normally with some good, like chocolates or sweets), or be gambles with money that they are given by the experimenter. For example, the subject could be given $8, then asked whether they would like to participate in a gamble in which the rewards are -$8, -$3, $0, +$3, +$8, or they could just stick with $8.  The subject could then leave with anywhere between $0 and $16.  The experimenter could then vary the probabilities with which these events are likely to occur to evaluate risk aversion. Contextual Environment Experiments are characterised by abstract gambles, except that the decisions are framed differently, i.e. in the gain domain (getting positive amounts of money) something could be framed as an 'investment', in the loss domain something could be framed as 'insurance' (paying money to avoid something occurring in the future).  Field survey and experiments, often coupled with laboratory gambles, evaluate subjects' behavior outside of the laboratory, either in some environment to which the subjects are accustomed, or in some experimental frame - seminal experiments evaluated subjects behavior in the laboratory compared to their behavior in an activity to which they are accustomed, in this case trading sports cards, or collecting coins, others simply report survey results and chart behavior.

Using abstract gambles with material incentives, the evidence indicates the following results, either men are less risk averse than women, meaning that men, particularly men from adolescence to about 40-years-old, choose more risky gambles than women do, or there are no statistically significant differences between men's and women's behavior.  There is no evidence that men are more risk averse than women for gains.  However, for losses, women are less risk averse than men, i.e. when faced with the option of losing money, women will take a risky gamble to lose a large amount of money, rather than lose money with certainty. 

In the contextual environment experiments, the frames change and behavior also changes as a consequence.  As described above, when framing losses as insurance and gains as investments men's and women's behavior does not differ significantly in one pair of studies (Schubert et al, 1999, 2000), whereas in another (Moore and Eckel, 2003) women are significantly more risk averse than men and similar to the evidence for abstract gambles, women are more risk-seeking for insurance, i.e. risk-seeking for losses, and similarly in another study (Gysler, Kruse and Schubert, 2002) after controlling for competence, knowledge and over-confidence women are more risk averse than men with their risk aversion decreasing in their levels of expertise.  A final study by Levy, Elron and Cohen (1999) with MBA students simulating a stock market shows women significantly more risk averse than men and making substantially less money as a consequence, this experiment is particularly interesting because the subjects supposedly gambled with their own money.

Lastly, for field work, a substantial amount of data corroborates the result that women, particularly single women, are more risk averse than men.  Several articles show that men hold more risky assets than women do - women tended to hold riskless, or relatively less risky, assets. Married women were also substantially less risk averse than single women throughout these data.

The results from these papers generally indicate that women are substantially more risk averse than men for gains, and women are more risk-loving than men for losses.  Eckel and Grossman do not try to explain why women behave so, but rather try to chart the result's empirical regularity.  We'll leave speculation about why women behave this way to later papers.

References 
Eckel, Catherine and Philip J. Grossman, 2008, 'Men, Women and Risk Aversion', in The Handbook of Experimental Economics Results, Charles R. Plott and Vernon L. Smith (eds), Elsevier Science & North-Holland.
Gysler, M., J. B. Kruse, and R. Schubert. (2002).  “Ambiguity and Gender Differences in Financial  decision Making:  An Experimental Examination of Competence and Confidence Effects.”  Center for Economic Research, Swiss Federal Institute of Technology, Working Paper.
Levy, H., E. Elron and A. Cohen (1999).  "Gender Differences in Risk Taking and Investment Behavior: An Experimental Analysis."  Unpublished manuscript, The Hebrew University
Moore, E. and C. C. Eckel (2003).  “Measuring Ambiguity Aversion.” Unpublished manuscript, Department of Economics, Virginia Tech.
Schubert, R.,  M.Gysler, M. Brown and H. W. Brachinger (1999). “Financial Decision-Making:  Are Women Really More Risk Averse?” American Economic Review Papers and Proceedings 89:381-385.
Schubert, R.,  M.Gysler, M. Brown and H. W. Brachinger (2000). “Gender Specific Attitudes  Towards Risk and Ambiguity:  An Experimental Investigation.” Center for Economic Research, Swiss Federal Institute of Technology, Working Paper.