I am comparing the results of broad bond market to equity market for a hypothetical portfolio.

The hypothetical portfolio consists of 60% large cap; 20% mid cap; 20% small cap equities.

The correlation for the large, mid, & small cap to the broad bond market are -0.09, -0.05, -0.11 respectively.

Would taking the weighted average of the correlation of the large, med, & small cap be the right approach to get the correlation for the bond market to the equity market?