This paper derives no arbitrage moment bounds from Fama and French 25 portfolios(FF25) and tests stochastic discount factor models through them. We compare the result of moment diagnosis test with that of generalized method of moment(GMM) test and Hansen and Jagannathan(1997)'s minimum distance(H-J distance) test. The result is the following. The greatest lower bound of moment for FF25 is marginally increasing with the order of moment. This phenomenon is inferred to be occurred from fat-tail property in security market data including FF25. But most of constant parameter models in our research do not satisfy these moment conditions from the second to the fourth and therefore cannot be among no arbitrage stochastic discount factor set for FF25. But some of time-varying parameter models in our research satisfy these conditions and some of them are not rejected at given significance level in H-J distance test. This implies that instrumental variables in conjunction with models are effective to price FF25.