Assume a scalper/market maker who is operating on an exchange with $N$ stocks with different characteristics such as current market value, average bid-ask spread, average daily volume and historical volatility.
Due to constraints imposed on this market maker he can only engage in $n$ of the $N$ stocks on the exchange, where $n << N$ ($n$ is much smaller than $N$).
Thus the market maker needs to choose which $n$ stocks to engage in. Obviously he wants to choose those $n$ stocks so that he maximizes his risk reward ratio.
What procedure/algorithm should the market maker follow to choose which stocks to make a market in? What trade-offs does he face in his choice?