People are saying I am not posting enough finance content. FINE. Once you have decent alphas a lot of the skill in running a systematic strategy is reducing turnover. Alpha is unknown but trading costs are certain. Keep trading to the minimum needed to monetise your alpha.
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Nice thing about knowing the derivation is that it’s straightforward to extend it eg other t-cost forms (3/2 or quadratic), multiple assets (sigma becomes a covariance matrix) or introduce constraints on position size or turnover. Most extensions need to be solved numerically.
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I think Magill, M. J. and Constantinides, G. M. Portfolio selection with transactions costs. Journal of economic theory, 13(2):245–263, 1976 is the orginal reference for no trade regions.
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The assumptions might be slightly different than yours.
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you have beautiful handwriting
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I concur.
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Excellent!
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Can I just say that I'm a huge fan of this posting format? Crystal clear snapshots of interesting pen-n-paper derivations that can fit on a page or two, with just enough context and immaculate hand script -- truly this is the content I'm here for. It's the anti-meme!
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Particularly when the derivation is the footnote/justification to a nice, memorable maxim like: "Alpha is unknown but trading costs are certain. Keep trading to the minimum needed to monetise your alpha." Love it.
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@alvinjamur you need to know this dude
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I use it regularly so nice to have it on paper. Only place I’ve seen is Mei-DeMiguel-Nogales for n-assets. (Don’t mind the “multiperiod” - it’s just bluster) https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2295345 ….
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Other paper which is basically the same is by Ding Liu https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3075547 …
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