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Problem: correlation between realized returns per trade and ex ante payoff is relatively low. Given that, it's possible that small (large) bets should be larger (smaller) than recommended by Kelly.

I have seen shrinkage estimators for Kelly which aim to take into account uncertainty about win rate and payoff but these all reduce the position sizes.

Is there any literature on adjusting position sizes up or down as mentioned in my problem statement above?

Thanks in advance.

EDIT: there are some relevant comments here https://mobile.twitter.com/macrocephalopod/status/1461456567522537473. In particular: "On trade sizing I think sizes should be proportional to confidence and inversely proportional to risk. That assumes you can meaningfully distinguish confidence levels! If not then equal weight or risk-parity weight is better than overthinking it"

user42108
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  • As far as I know, kelly doesn't really apply to individual trades because the "pool of money" available is undefined. How do you handle that ? There are some new papers that try to handle this. These methods are computationally intense but maybe you're using them ? – mark leeds Mar 04 '21 at 01:06
  • I define the "pool of money" or bankroll as the capital allocation to the strategy. The Kelly fraction is then the % of your capital you risk on a given bet. – user42108 Mar 04 '21 at 14:11
  • Hi: okay. but if you're bets overlap, ( in time ), that's going to be problematic. in fact, it seems problematic regardless of the overlapping issue because the position sizes ( atleast to me ), would seem like they'd be biased upward ? A kelly fraction of 0.5 would allocate half of the portfolio to one position. – mark leeds Mar 05 '21 at 16:53
  • Hi @markleeds - I was using fractional Kelly for the strategy; even a fairly conservative fraction results in high leverage (and high volatility of returns) which is difficult to implement in an institutional environment due to investor preferences (they're solving for Sharpe, not terminal wealth). Leverage is possible but only at a relatively low level for a single strategy. – user42108 Mar 05 '21 at 17:34
  • @markleeds - you are correct that bets overlapped in time. Obviously you have to adjust for the correlation which is not trivial as corr is volatile, regime-dependent, etc. – user42108 Mar 05 '21 at 17:36
  • Hi: but the thing I don't get and would appreciate your comments on, is that if bets overlap in time, then how to decide on the "pool of money" that you use. if you want a more recent paper on using kelly in trading, email me off-list and I can track it down. Don't know if its useful but it might be. email is name with a 2 on the end at gmail. thanks. – mark leeds Mar 06 '21 at 18:42
  • @markleeds - I'll send you an email, thank you. The bankroll changes each day. In theory this should mean the position sizes change each day, but in practice, I only change the position sizes when new trades are added. Could amend that to have some threshold to reduce TC, e.g. only re-size if change in size is >= |10%|. – user42108 Mar 08 '21 at 16:45
  • Okay. I'm not totally clear on what you're doing but hopefully something I send you can help ? Of course, there's a chance it won't help too :). – mark leeds Mar 09 '21 at 10:50
  • Also, put something good in the subject line because I get a lot of spam and could miss it if it goes to spam. thanks. – mark leeds Mar 09 '21 at 10:51
  • Will do, thanks – user42108 Mar 09 '21 at 17:59
  • @markleeds could you please share the reference (its DOI or authors+year would suffice) that you have discussed in the comments? I think it would be interesting to a bunch of us happening on this question. Many thanks in advance! – jarm May 03 '21 at 11:59
  • Mark has kindly shared with me the following references: https://arxiv.org/abs/1806.05293 , https://www.mdpi.com/2227-9091/7/3/86 , https://arxiv.org/abs/1710.00431 . Hope this will be useful for other people interested in the question :) – jarm May 04 '21 at 13:03

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