Thus, risk-seeking investors exhibit FDSD (SDSD, TDSD) if their utility functions u belong to [U.sup.D.sub.1] ([U.sup.D.sub.2], [U.sup.D.sub.3]).
The inference here is that there is no FDSD between the two returns and futures are preferred to spot for upside returns, while spot is preferred to futures for downside returns.
It shows that, for the full sample, 28% (22%) of [T.sup.D.sub.1] is significantly positive (negative), from which we can infer no dominance in FDSD. Because there is no FDSD, we examine the [T.sup.D.sub.j] for the second and third orders.
Here, FASD, SASD, and TASD (FDSD, SDSD, and TDSD) refer to first-, second-, and third-order ASD (DSD) for risk averters (risk seekers) defined in Definition 1 (2).
Because the analysis of the FDSD is the same as that for the FASD, we skip the discussion of the FDSD analysis.
Table 6 shows that 20% (38%) of [T.sup.D.sub.1] is significantly positive (negative), from which we can infer no dominance in FDSD. We also find that 53% (88%) of [T.sup.A.sub.2] ([T.sup.A.sub.3]) is significantly positive and no [T.sup.A.sub.2] ([T.sup.A.sub.3]) is significantly negative at the 5% level.
This is one of two data sets used in BFT .(6) Using the same data allows for direct comparison to the partial orderings using FDSD and SDSD found in BFT .
Comparison of Table I with the stochastic dominance rankings in BFT  confirms that all FDSD and SDSD ranked pairs are consistent with the ranking provided by the generalized welfare measure.