The study, by Wintergreen Advisers, a money management firm, looked at two hits that shareholders absorb from executive stock awards. The first hit is well known. When a company issues shares under an executive-pay agreement, the increase in the number of shares outstanding dilutes the value of existing shareholders’ stakes. The second blow, involving share buybacks, is less obvious. Buybacks, in which management reduces the number of publicly held shares by repurchasing the company’s stock, are often pitched as a way to boost a company’s earnings per share. But the study points out that buybacks are aimed not necessarily at benefiting shareholders, but rather at offsetting the dilution that results from awarding stock to executives.