Dynamic optimal capital growth of diversified investment

Abstract

We investigate the problem of dynamic optimal capital growth of diversified investment. A general framework that the trader maximize the expected log utility of long-term growth rate of initial wealth was developed. We show that the trader's fortune will exceed any fixed bound when the fraction is chosen less than critical value. But, if the fraction is larger than that value, ruin is almost sure. In order to maximize wealth, we should choose the optimal fraction at each trade. Empirical results with real financial data show the feasible allocation. The larger the fraction and hence the larger the chance of falling below the desired wealth growth path.

Keywords:

• capital growth
• asset allocation
• portfolio optimization
• diversification
• reinvestment

Acknowledgements

This work was supported by The National Natural Science Foundation of China (project 71103146). I appreciate Liang Zhang, Yong Tang for discussions and many stimulating comments from professor Zhang.

Notes

1. The pool portfolio include 50 assets from USA market: CSCO, AMZN, AAPL, YHOO, MSFT, C, ADS, BRK.A, BAC, AFL, KO, SBUX, JNJ, KFT, PFE, CBS, TWX, DIS, TRI, AOL, DUK, RIO, XOM, AEP, COP, CL, GE, PG, AA, DD, DIA, XLE, XLV, USO, FXI, CPHI, SNP, BIDU, PTR, CHL, AES, ORCL, QCOM, EBAY, GOOG, GS, MA, WMT, FDX, RTN