... which is superlinear in r. For small values of r this is not a big effect, just a small second-order correction but for large r the nonlinearity dominates and you go bankrupt very quickly unless you reduce the position size by buying back stock.
If you are short a stock with a fraction x of your account, and it’s price increases by r% then you now have a position with value x(1+r) and your account value is lower by xr, so the new weight in your portfolio is x(1+r)/(1-xr) which is bigger than before by an amount ...
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Now add in a term which links the size of the return r with the amount of stock bought back, y (with r’(y) > 0) and you can see that you can get into a positive reinforcement loop where r (and hence your losses) increase unboundedly.
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