For schizophrenia, we find that prediction accuracy increases in 20 of the 36 cohorts of the PGC2 data when using a wMT-SBLUP predictor as compared to a SBLUP predictor (Supplementary Fig. 5). However, the median correlation (0.300 with an SBLUP predictor, and 0.304 with a wMT-SBLUP predictor) and mean correlation (0.295 with a SBLUP predictor and 0.294 with a wMT-SBLUP predictor) across the 36 PGC2 cohorts did not improve with a wMT-BLUP predictor. For bipolar disorder, we find an improvement of the wMT-SBLUP predictor over the SBLUP predictor in 17 out of the 23 cohorts (Supplementary Fig. 6), with a mean correlation increase from 0.212 to 0.229 and a median correlation increase from 0.210 to 0.225. To evaluate whether this is because the weights we used for schizophrenia and bipolar disorder do not represent the mixing proportions that lead to the highest accuracy in this data set or whether other factors explain the variable results across cohorts, we created multi-trait predictors using not only weights calculated from Eq. (17) but also weights corresponding to any other mixing proportion of the two disorders (Supplementary Figs. 5, 6 and 7). This demonstrates (i) that our calculated weights are very close to the empirically optimal weights when averaged across cohorts (Supplementary Fig. 7), (ii) that there is substantial heterogeneity across cohorts as shown by the variable prediction accuracies of single-trait and cross-trait predictors across cohorts, which is supported by previous studies25, and (iii) that, for some test set cohorts, there is no mixing proportion that will lead to a multi-trait predictor which outperforms a single-trait predictor. The larger gain in accuracy that results from supplementing a bipolar disorder predictor with schizophrenia data compared to supplementing a schizophrenia predictor with bipolar disorder data is consistent with greater power of the schizophrenia discovery sample. We find that for both single-trait and multi-trait predictors the SBLUP predictors outperform the OLS predictors in almost all cohorts (Supplementary Figs. 5 and 6).