Using first degree stochastic dominance in allocation tasks: an experimental study

Abstract

By using subgroup analysis, this paper presents the results of an experiment designed to determine the frequency with which individuals use the first degree stochastic dominant (FSD) rule for allocation tasks. We show experimentally that some participants used the FSD rule for allocation tasks and, as a result, invest only in the dominant asset. These people did not take the mean variance (MV) rule into consideration, even though it is relevant for diversification. The other participants used the MV rule without considering the FSD rule, although they could have used it. Our analysis of the subgroups is important, because on the basis of our data it would be possible to mistakenly conclude that the different allocation rates are a result of different attitudes to risk or different utility functions.

Keywords:

• Behavioral finance
• Adaptive behavior
• Applied investment analysis
• Experimental finance

Notes

†At the time, the rate of exchange between the New Israeli Shekel (NIS) and the US dollar was approximately NIS 4 to US$ 1.

†The strength can be measured by the accumulated difference between the distributions. For example, in the high FSD case, the difference was +9% in favor of asset A (−9% for asset B). In the low FSD, it was only +3% in favor of the dominant asset. Another way to estimate the FSD strength is to look at the best and worst scenarios for each asset. For example, the difference between the best return for asset B (dominated) and the worst return for asset A (dominant) is 2% (16–14%), while the difference between the best return in asset A (dominant) and the worst return for asset B (dominated) is 20% (28–8%). Therefore, asset A has high FSD (HFSD) over asset B. When comparing assets C (dominant) and D (dominated), the difference between the best return for asset D (dominated) and the worst return for C (dominant) is 8% (20–12%), while the difference between the best return for asset C (dominant) and the worst return for D (dominated) is 14% (24–10%). Therefore, asset C has a low FSD (LFSD) over asset D.

‡Holt and Laury (2002) also infer the degree of risk-aversion using lotteries in their experiments, and Kachelmeier and Shehata (1992), Anderhub et al. (2001) and Shavit et al. (2001) infer risk-aversion by eliciting buying and/or selling prices for lotteries in experiments.

§The average payment was NIS 32, approximately $8.

¶The payment was only for the allocation task and not for the biddings for the lotteries that measure risk preference. We did not create any payment mechanism or incentives to the bidding problems since we thought that another paying mechanism could make the experiment too complicated and create a bias in the allocation tasks.

†The assets’ distributions in the examples are different from those in the investment task in order to prevent any effect or bias of the examples.

‡A participant who allocates a large share to the risky asset is less risk-averse.

§There were 10 participants (27%) who allocated their entire investment to the dominant asset in the HFSD but not in the LFSD, and only three participants (8.1%) who allocated their entire investment to the dominant asset in the LFSD but not in the HFSD.

¶As mentioned before we asked the participants to rank on a scale of 1–10 the importance of the variance in their decision-making process. The null hypothesis of the same importance in both groups is rejected.

†It is important to say that the control group could not use FSD rule since the participants in this group did not get any information on the assets’ return distribution.