While conducting Confirmatory factor analysis, the Convergent reliability for a factor A has been found to be 0.787 but the value of AVE has been obtained to be 0.483. Can this value of AVE be reported as Acceptable value?????
Guidelines abound, but, let's parse what AVE suggests. In the usual situation, the squared variable-factor loading represents the proportion of shared variance. So, if a variable had a factor loading of .65 (which most folks would judge as satisfactory to assert that the variable is indeed affiliated with the factor, or "salient"), the shared variance would be .65 * .65 = .4225 (42.25%). Is that poor, mediocre, good, or fantastic? I think that context matters.
What does an AVE threshold of .50 imply? A "typical" variable-factor loading of about .71. Again, whether that is marvelous, meritorious, middling, mediocre, or miserable is, to a considerable extent, in the eye of the beholder.
So, take any guidelines with a grain of salt; they are for guidance, and are not commandments.