I have this older post on what convexity is and isn't. https://moontowermeta.com/where-does-convexity-come-from/ … I think of it as the size of your position changing. As the exposure changes, the slope of your p/l changes for a given move. So your p/l for a 1% move varies with exposure. ...
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Replying to @KrisAbdelmessih
I think shorting stock is an interesting case where it's technically linear, but some L/S hedgies have described it to me as "feeling" like negative convexity, since the dollar position size increases as the market moves against you.
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Replying to @robertmartin88
When you are losing your position size increases as your aum falls. Double whammy, that's why.
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Replying to @KrisAbdelmessih
Right – so I guess I'm trying to reconcile the "negative gamma" with the fact that you have linear exposure.
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Replying to @robertmartin88 @KrisAbdelmessih
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.
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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.
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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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