Chapter 3. Stochastic Growth and Discretionary Wealth

JARROD W. WILCOX, PhD, CFA

President, Wilcox Investment Inc.

Abstract: Stochastic growth models, which focus on logarithmic returns to produce better median compound returns, can deal with higher moments of return such as skewness and kurtosis. Applying growth optimal procedures to discretionary rather than total wealth overcomes old objections to growth optimality by allowing it to be used by conservative investors, with the bonus that it offers a criterion for setting the Markowitz risk-aversion parameter such that long-term median wealth is expected without intermediate shortfalls. Translating the discretionary wealth growth criterion to ordinary return moments through a Taylor series provides a direct link to Markowitz mean-variance optimization, offers a means of testing whether higher moments need to be considered, and provides insight into several problematic investment issues not well explained otherwise.

Keywords: growth-optimality, Kelly rule (or strategy), discretionary wealth, leverage, Markowitz, mean-variance optimization, skewness, kurtosis, risk management, gambling, fractional Kelly, nonlinearity, implied balance sheet, investor balance sheet, implied assets, implied liabilities, financial commitments, median return, geometric mean, Taylor series

Over 50 years after the publication of the work of Markowitz (1952, 1959) on better diversification through mean-variance optimization, his method is still far from universal ...

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