Hi John,
If I agreed with your assumptions then your math would hold. Those assumptions: a) People can buy the 'Market' portfolio, and b) that every active manager holds a subset of the Market portfolio as their portfolios.
Regarding your first assumption, how can an investor invest in a single passive product that includes claims on the performance of, yes, the S&P 500, but also silver, molybdenum, lumber, art, every option, a 2020 maturity bond from Slovenia, et. al.? Not only that, but the 'Market' portfolio is not just the public assets. For if it is to lay claim to 'Market' (with your capital 'M,' not small 'm') then it must include every private asset, too. So my collection of mid-century modern furniture needs to be in there, too. How does an individual investor get to buy a claim on my coffee table in a single product?
Regarding your second assumption, since I am guessing your answer to the first question is that there is no such investible Market, then all an active manager has to do is to hold assets not in your proxy for the Market. That is, she just needs to have assets different than the market, little 'm.' One way of doing this, that is quite obvious is to hold the S&P 500 plus one other asset.
Yours, in service,
Jason