The purpose of this paper is to use APT framework to investigate both the existing and pricing questions. The _rst test in the paper shows that equity returns seem to depend on several common factor, perhaps as many as four. Table 3 explains this statement.
When _0 is assumed to be 6%, 88:1% of the groups had at least one signi_cant factor risk premium, 57:1% had at least two signi_cant factor risk premium and 33:3% of the groups at least three risk premia were signi_cant. However, this results are far from the case in which _0 = 0. So, part 1 of table 3 shows that at least three factors are important for pricing but it is unlikely that more than four are present.
In the second part of table 3, _0 is not assumed to be a constant, on the contrary it is estimated. However, this does not change the result much, similar statistics are obtained.
47:6% of the groups had at least two signi_cant factor risk premium while only 7:1% of the groups had three or more signi_cant factor risk premium. The three signi_cant fac- tors which is obtained when _0 = 6% may be an overestimate because of the incorrect choice of the zero beta return _0.
The second test is about one particular variable, the total variance of individual returns or the \own" variance. When APT is valid, total variance would not a_ect expected returns since its diversi_able component would be eliminated by portfolio formation and its non-diversi_able part would depend only on the factor loading and factor variances.
However, this test is less e_ective for detecting the \priced" factors. Table 4 give the results of own standard deviation, sj , for both t-statistics and F-statistics over the 42 groups of securities. t-statistics for sj , is 2.17 for 45:2% of the 42 groups with the 95% level of signi_cance while F-statistics for sj , is 2.21 for 28:6% of the 42 groups with the
95% level of