This problem 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
7This only works for the standard definition of short sales. The Lintner definition of short sales assumes riskless lending and borrowing at a particular rate for each point on the original (curved) efficient frontier.
Figure 6.3 Tangency portfolios for different riskless rates.
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 formally, the problem can be stated as
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