1. Following the previous question, for an arbitrageur, such as an hedge fund manager, suppose she achieves her goal to construct an arbitrage portfolio with the following return in each period t

   alpha+e_p,t

   That means on average over time, her expected return is pure alpha, i.e., E(alpha+e_p,t)=alpha. This is so called pure play in the hedge fund industry.

   However, every period, her actual return is not exactly alpha. It is alpha+e_p,t.

   How can a manager eliminate the idiosyncratic risk as much as possible in every period t?

   		Try N arbitrage strategies with the same return structure and correlated idiosyncratic risk. In other words, if one strategy is the value strategy; another strategy can be some variations of the value strategy. For example, one value strategy is based on the book-to-market signal; another value strategy is based on the P/E signal.
   		Try N arbitrage strategies with the same return structure but correlated idiosyncratic risk. That is, for each strategy i, its return is alpha+e_i,t, where e_i,t of each strategy is not related to each other. For example, one strategy can be the value strategy; another strategy can be a strategy completely unrelated to value investing. As long as there are many of these strategies (i.e., N is big), the idiosyncratic risk e_i,t can be diversified towards zero. In other words, the average e_i,t across N strategies is close to zero.
   		Invest in an arbitrage strategy that many other hedge funds also are trading on. In other words, if there are many funds trading on the same strategy, there maybe some diversification across funds. For example, if in the last five years, the momentum strategy is a strategy used by many fund mangers, then the arbitrageur should get into that strategy too.