This paper assumes transparent traders are ambiguous about the standard deviation ( variance，or investment risk) of the returns of the extra investment opportunities． This ambiguity restraints transparent trad-ers’investment decisions，and may lead to a higher equity premium and a loss of social welfare． Due to ambi-guity aversion，transparent traders make decisions by adopting smooth ambiguity aversion model． Their de-mand function manifests continuous and smooth features． While，opaque traders having information advantage after paying information acquisition cost are standard risk averse investors． From the Ｒational Expectation E-quilibrium ( ＲEE) ，our analysis shows that: opaque traders appear to generate strictly positive excess returns if only their net wealth is strictly positive; increasing information acquisition cost is not a good policy since it decreases the fraction of sophisticated traders，increases equity premium，and decreases welfare; regulation policy aiming to reduce ambiguity by improving the market transparency always increases the welfare．