Arbitrage Pricing Theory: The returns in an economy with an infinite number of assets are given by: 7 = 1, 11 10 + n-11 n 22. Here, the first asset is risk-free, with (normalized) returns equal to 1, whereas the other assets are risky, and en are i.i.d. random variables such that en 2-1, P (en 0, Elen] = 0, and Var(en) = . Consider the sequence of portfolios {w}N, N=1,..., where w contains N assets: n = 1, 2 n N n > N. -N, 1, 0 1. Is there a portfolio, w, for some specific N that constitutes a (pure) arbitrage opportunity? 2. Show that the sequence w, N 1,..., does not constitute an asymptotic arbitrage oppor- tunity. 3. Construct a modified sequence of portfolios, v YNw, where (7N)N is a sequence of positive numbers, such that (NN does constitute an asymptotic arbitrage opportunity.