What is the reward for performing Hajj on behalf of a deceased person?

Some scholars hope that the proxy receives the reward for Hajj on behalf of the deceased, citing the hadith: "Whoever performs Hajj on behalf of a deceased person, the one who performed it for him will receive a reward similar to his." While others believe that the proxy does not receive the reward for Hajj itself, but rather receives the reward for the acts of obedience and proximity he performed during Hajj, while the reward for Hajj is exclusive to the one who commissioned it.