Abstract-In this article we introduce a new strategy for optimal diversification which combines elements of Diversified Risk Parity [1], [2] and Diversification Ratio [3], with emphasis on positive risk premiums. The Uncorrelated Positive Bets strategy involves the identification of reliable, independent sources of randomness and the quantification of their positive risk premium. We use principal component analysis to identify the most significant sources of randomness contributing to the market and then apply the Randomness Deficiency Coefficient metric [4] and principal portfolio positivity to identify a set of reliable uncorrelated positive bets. Portfolios are then optimized by maximizing their diversified positive risk premium. We contrast the performance of a range of diversification strategies for a portfolio held for a two-year out-of-sample period with a 30 stock constraint. In particular, we introduce the notion of diversification inefficiency to explain why diversification strategies might outperform the market.

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An idealised decentralised exchange (DEX) provides a medium in which players wishing to exchange one token for another can interact with other such players and liquidity providers at a price which reflects the true exchange rate, without the need for a trusted third-party. Unfortunately, extractable value is an inherent flaw in existing blockchain-based DEX implementations. This extractable value takes the form of monetizable opportunities that allow blockchain participants to extract money from a DEX without adding demand or liquidity to the DEX, the two functions for which DEXs are intended. This money is taken directly from the intended DEX participants. As a result, the cost of participation in existing DEXs is much larger than the upfront fees required to post a transaction on a blockchain and/or into a smart contract.We present FairTraDEX, a decentralised variant of a frequent batch auction (FBA), a DEX protocol which provides formal game-theoretic guarantees against extractable value. FBAs when run by a trusted third-party provide unique game-theoretic optimal strategies which ensure players are shown prices equal to the liquidity provider's fair price, excluding explicit, pre-determined fees. FairTraDEX replicates the key features of an FBA that provide these game-theoretic guarantees using a combination of setmembership in zero-knowledge protocols and an escrow-enforced commit-reveal protocol. We extend the results of FBAs to handle monopolistic and/or malicious liquidity providers, and provide a detailed pseudo-code implementation of FairTraDEX based on existing mainstream blockchain protocols.