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geometric mean/Kelly:
https://www.google.com/search?q=kelly+portfolio+optimization
http://www.bjmath.com/bjmath/thorp/paper.htm THE KELLY CRITERION IN BLACKJACK, SPORTS BETTING, AND THE STOCK MARKET by Edward O. Thorp
note: for an asset, is basically (expected return)/((standard dev of expected return)^2)
note: basically suggests a leverage of 2 for stock market indices
http://www.fma.org/NY/Papers/Estrada-GMM.pdf Geometric Mean Maximization: An Overlooked Portfolio Approach? or, according to Estrada below,
note: the quantity to optiize according to Estrada is not mean/variance, but ln(mean) + variance/2*mean. this would solve the problem that i noticed in straight mean/var where an asset with zero variance is infinitely preferred. mb still have the problem with geometric mean optimization in general that scenarios of losing all your money cannot be considered?
the second part (page 10) of the methodology section of the Estrada article cites various approaches to actually doing this maximization
note: i am hoping for a simplified approximation that does not require linear (or quadratic etc) programming. also, shouldn't we incorporate correlation too? i guess one could always start with the obvious oversimplification (compute Kelly factor for each asset individually, normalize, multiply by square of reciprocal of correlation (1/(http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient)^2) to portfolio, iterate that, then calculate Kelly portfolio-wide leverage at the end by return/variance for a bet on the portfolio vs. a riskfree, returnfree asset) no actually portfolio Kelly only cares about square of correlation to entire portfolio, individual asset Kelly doesn't matter at all note that if no assets have any return (or in fact whenever all assets have the same return), and all are uncorrelated, then this will invest proportionately to the recipriocal of the square of portfolio correlation of each assett
but maybe the formula on page 10 of the Estrada paper, which seems similar but different to the 'utility function' mentioned on page 5 of Chapter 7 of the Thorp paper ( http://www.bjmath.com/bjmath/thorp/ch7.pdf )
other articles which may or may not be worth reading:
http://www.iijournals.com/doi/abs/10.3905/joi.2013.22.2.106?journalCode=joi#sthash.RXyBBRA8.dpbs
http://www.hindawi.com/journals/ijsa/2012/498050/
http://www.albany.edu/faculty/faugere/PhDcourse/GeomeanReturn.pdf
http://mpra.ub.uni-muenchen.de/50240/
papers.ssrn.com/sol3/papers.cfm?abstract_id=2259133
"every investor holding the portfolio with the lowest possible return variance consistent with that investor's chosen level of expected return (called a minimum-variance portfolio),"
http://www.efficientfrontier.com/ef/497/mvo.htm
(note these criticism apply to many of the other models too)
" Mincorr: this method normalizes both the correlation matri x, and the rank-weighted average normalized correlations and proportionately weights (re-levera ging to 1) by the lowest average correlations. This first step forms the base weight. A risk-parity multiplier is applied- each is asset is sized according to invers e of their individual standard deviations. The final allocatio n is derived by re-leveraging these fractions to su m to 1. " -- http://cssanalytics.com/doc/MCA%20Paper.pdf
comparisons used in the MCA paper
shrinkage regularization of a correlation matrix: http://en.wikipedia.org/wiki/Estimation_of_covariance_matrices#Shrinkage_estimation e.g. "One considers a convex combination of the empirical estimator (A) with some suitable chosen target (B), e.g., the diagonal matrix. "
http://cssanalytics.wordpress.com/2013/10/31/shrinkage-a-simple-composite-model-performs-the-best/
" The best performing shrinkage model can be implemented by virtually anyone with a minimum of excel skills: it is the simple average of the sample correlation matrix, the anchored correlation matrix (all history), and the average correlation shrinkage model. "
"Average Correlation Shrinkage Model (ACS): the correlation between each asset versus all other assets" is the target off-diagonal constant, i think
