If I were managing all the investment capital in the world the best I could manage to gain would be market return. My return would be market return. As long as I only manage part on that capital I can get above market return if the other capital in the world gets below market return. The higher the percentage of all capital I do not manage is the easier it is to stray significantly from market return. Large amounts can be moved more easily if you use more than one basket and keep more than one egg in the baskets you use.
Transaction fees tend to be bigger problems for small accounts that large ones.
Many systems fail in the real world because the designers do not use realistic assumptions when they design their systems. You can look at crossings on a smoothed graph and say that if I buy at one crossing and sell at the other I will have a profitable system. If one is designing a system for end of day fund trading one must take into account that one can not trade at the crossing. That crossing will not be spotted until after you know the NAV for the day of the crossing. That means you not only do not get part of the gain on the day of the crossing but can't effectively get in or out of the fund until the end of the next day.