Treatment of Coefficients from Regression Using Lagged Independent Variables

I'm running a regression on two time series of financial returns, one dependent and one explanatory/independent. For the explanatory time series, I'm creating several lagged versions and using all of them as independent variables in in a multiple linear regression.

My question is, how do I think about the coefficients obtained for each of the various lags, in terms of how well does the explanatory time series explain the dependent time series?

I've seen a similar analysis done in a paper, where the author sums up all of the coefficients from the regression to arrive at a single beta parameter, but this does not make intuitive sense to me, can we just add up regression coefficients for lagged versions of the same time series like this? Are there any multicollinearity or autocorrelation concerns with doing this? Thanks in advance