16.5 Smallest fund holdings consistent with portfolio return history. A fund consists of a portfolio with n assets, characterized by the weight 7-vector w, which satisfies 1?w = 1. (Negative entries correspond to short positions.) The fund manager publishes the return of the portfolio on T days, given by r=Rw, where Ris the T'x n matrix of asset returns, but does not divulge her holdings w. (We do, however, know R.) We consider the case where T is smaller than n, i.e., we are given fewer portfolio returns than there are assets. We will guess w by finding , the smallest weight vector 40 (measured by norm squared) that is consistent with the reported portfolio returns (and satisfies iTw=1). Give a formula for (in terms of R, r, and the dimensions n and T). Your formula can involve the usual matrix and vector operations, including matrix addition, transpose, multiplication, in- verse, pseudo-inverse, and so on. (If you use inverse or pseudo-inverse, you can assume that the appropriate condition, such as linear independence of columns or rows, holds.) 16.5 Smallest fund holdings consistent with portfolio return history. A fund consists of a portfolio with n assets, characterized by the weight 7-vector w, which satisfies 1?w = 1. (Negative entries correspond to short positions.) The fund manager publishes the return of the portfolio on T days, given by r=Rw, where Ris the T'x n matrix of asset returns, but does not divulge her holdings w. (We do, however, know R.) We consider the case where T is smaller than n, i.e., we are given fewer portfolio returns than there are assets. We will guess w by finding , the smallest weight vector 40 (measured by norm squared) that is consistent with the reported portfolio returns (and satisfies iTw=1). Give a formula for (in terms of R, r, and the dimensions n and T). Your formula can involve the usual matrix and vector operations, including matrix addition, transpose, multiplication, in- verse, pseudo-inverse, and so on. (If you use inverse or pseudo-inverse, you can assume that the appropriate condition, such as linear independence of columns or rows, holds.)