the problem is is analogous to the case of riskless lending and borrowing with short sales allowed. one portfolio is optimal. once again, it is the one that maximizes the slope of the line connecting the riskless asset and a risky portfolio. however, the set of portfolios that is available to combine with lending and borrowing is different because a new constraint has been added. investors cannot hold securities in negative amounts. more foemally, the problem can be stated as