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What about a short portfolio?   As usual, I take a world with two assets, cash bearing zero interest rate and a risky asset with price \(p\). At inception, investment is initiated with one dollar. The initial price is \(p_{0}=1\). The initial amount is leveraged to reach an exposure to Shares are sold until  the risky asset has a proportion  of \(-\pi \lt 0\). 0\) in the overall portfolio.  The position in cash is thus \(1+\pi \gt 1\). Assuming the portfolio is continuously rebalanced and the price trajectory is smooth, its value as a function of the price is given by:  \[V(p)=p^{-\pi},\]  and the number of shares held as a function of the price is: