Performance of investment strategies in the absence of correct beliefs

Long-run heterogeneity in an exchange economy with fixed-mix traders

“…Together with Lemma 4.3, Proposition 4.3 implies the survival of the agent whose beliefs are such that the portfolio rule she uses is the 'closest', in terms of relative entropy, to the Generalized Kelly rules derived under correct beliefs. This extends the result of Bektur (2013) who shows that if a rule is the closest to x * coordinate-wise then it survives. Whether the agent also dominates, or both agents survive, it depends on his performance when he has most of the aggragte endowment.…”

“…Third, in an economy of fixed-mix traders it is already known that the generalized Kelly rule derived under correct belies dominates almost surely (Evstigneev et al, 2008). Moreover, when nobody plays the generalized Kelly rule with correct beliefs, if there is a rule properly "close" to it, then it survives almost surely (Bektur, 2013). 10 Finding that the rule with most accurate beliefs also dominates would indicate that the MSH should have asset pricing implications also in financial markets where portfolio rules rely neither on perfect foresight on future prices nor on the exact knowledge of the dividend process.…”

“…Bottazzi and Dindo (2014) investigate the same issue in an economy with short-lived assets, finding that the MSH does not generally hold Bektur (2013). shows that the agent whose rule is the "closest" to the generalized Kelly rule derived using correct beliefs survives almost surely.…”