A trader finds shares of company A and B are out of their expected relative pricing pattern. Shares of A are under-priced while shares of B are over priced. The trader decided to use futures on A and B to set up a pair trading position:

II = NV-NV +N,V, A ? ? –
NA, NB, Ni are the number of future contracts on A, B and market index, VA, VB, Vi are the value of the future contracts. Nj is chosen to hedge out the residual beta of the long- short position so that II is market neutral. Currently VA = 100, VB = 50, Vi= 1250. The trader longs 1000 future contracts on A while shorting 2000 futures on B. BA= 0.8, BB = 1.1. What should the trader’s position in Ni be? ? =

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