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You have linear price exposure (constant number of shares). But your aum falls at the same time as dollar value of your position grows, which introduces nonlinearity into your returns.
eg if you are 100% long and the stock goes up 20% then another 20%, you make 20% return on each move. If you are 100% short, you lose 20% on the first move and 30% on the second move.
Any position 0 < x < 1 is “positive gamma” in this sense (they become larger as a proportion of your aum when they make money) and any position x < 0 or x > 1 is “negative gamma” (become larger as a proportion of your aum when you lose money)
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