Improvement of Optimal Portfolio using Correlation Matrix

Cheoljun Eom

doi:10.23842/jif.2020.31.3.006

Journal of Insurance and Finance

2020, 31(3), pp.171-210
DOI :10.23842/jif.2020.31.3.006
Publisher : Korea Insurance Research Institute
Research Area : Business Management

Cheoljun Eom ¹

¹ 부산대학교

ABSTRACT

This study empirically investigates the practical applicability of Markowitz (1952) optimization function through correlation matrixes among stocks in the Korean stock market. The proposed method is a correlation matrix that removes the property of a market factor included in the sample correlation matrix, that is, the non-market correlation matrix. For comparison with the previous studies, the correlation matrixes that is known in the optimal portfolio are utilized, along with equal-weighted and value-weighted portfolios. According to the results, the optimal portfolio from the non-market correlation matrix may construct better diversified portfolio, and then, achieve lower risk and higher performance compared to other correlation matrixes. In comparison by the perspective of prediction error from expected return and standard deviation of returns, moreover, the optimal portfolio from the non-market correlation matrix has much lower magnitude of sensitivity from prediction error of input variables than those from the other correlation matrixes. These results show the evidence supporting that the non-market correlation matrix has a comparative benefit for improving the practical applicability of the optimal function as well as for effectively reducing the influence of prediction error from input variables.
KEYWORDS

Optimization , Optimal Portfolio , Correlation Matrix , Certainty Condition , Uncertainty Conditions , Sensitivity Test
REFERENCES (38)

[journal] 김인수 / 2008 / Equity Premium Puzzle in Korean Stock Market / 재무연구 / 한국재무학회 21 (1) : 1~32

[journal] 엄철준 / 2012 / Re-Examination on Cross-Section of Expected Stock Returns under Up/Down Market Conditions / 재무연구 / 한국재무학회 25 (4) : 599~639

[journal] Best, M. / 1991 / On the Sensitivity of the Mean-Variance Efficient Portfolio to Changes in Asset Means : Son Analytical and Computational Results / Review of Financial Studies 4 (2) : 315~342

[journal] Brinson, G. / 1986 / Determinants of portfolio Performance / Financial Analysts Journal 42 (4) : 133~138

[journal] Brinson, G. / 1991 / Determinants of portfolio Performance Ⅱ : An Update / Financial Analysts Journal 47 (3) : 40~48

[journal] Brown, S. / 1989 / The Number of Factors in Security Returns / Journal of Finance 44 (5) : 1247~1262

[journal] Chan, L. / 1999 / On Portfolio Optimization : Forecasting Covariances and Choosing the Risk Model / Review of Financial Studies 12 (5) : 937~974

[journal] Connor, G. / 1993 / A Test for the Number of Factors in an Approximate Factor Model / Journal of Finance 48 (4) : 1263~1291

[journal] DeMiguel V. / 2009 / Optimal versus Naive Diversification : How Inefficient is the 1/N Portfolio Strategy? / Review of Financial Studies 22 : 1915~1953

[journal] Duchin, R. / 2009 / Markowitz Versus the Talmudic Portfolio Diversification Strategies / Journal of Portfolio Management : 71~74

[journal] Elton, E. / 1973 / Estimating the Dependence Structure of Share Prices : Implications for Portfolio Selection / Journal of Finance 28 : 1203~1232

[journal] Elton, E. / 1979 / Are betas best? / Journal of Finance 23 : 1375~1384

[journal] Elton, E. M. / 2006 / Improved Estimates of Correlation Coefficients and Their Impact on Optimum Portfolios / European Financial Management 12 (3) : 303~318

[journal] Eom, C. / 2017 / Two-faced Property of a Market Factor in Asset Pricing and Diversification Effect / Physica A: Statistical Mechanics and its Applications 471 : 190~199

[journal] Eom, C. / 2009 / Effect of Changing Data Size on Eigenvalues in the Korean and Japanese Stock Markets / Physica A : Statistical Mechanics and its Applications 388 : 4780~4786

[journal] Eom, C. / 2015 / Effects of the Market Factor on portfolio Diversification : the case of Market Crashes / Investment Analysts Journal 44 (1) : 71~83

[journal] Eom, C. / 2017 / Effects of Common Factors on Stock Correlation Networks and Portfolio Diversification / International Review of Financial Analysis 49 : 1~11

[journal] Eom, C. / 2018 / A New Method for Better Portfolio Investment : A Case of the Korean Stock market / Pacific-Basin Finance Journal 49 : 213~231

[book] Fabozzi, F. / 2007 / Robust Portfolio Optimization and Management / John Wiley & Sons

[journal] Fama, E. / 1970 / Efficient Capital Markets : A Review of Theory and Empirical Work / Journal of Finance 25 (2) : 383~417

[journal] Fama, E. / 1991 / Efficient Capital Markets : II / Journal of Finance 46 (5) : 1575~1617

[journal] Fama, E. / 1993 / Common Risk Factors in the Returns on Stocks and Bonds / Journal of Financial Economics 33 : 3~56

[journal] Kleibergen, F. / 2006 / Generalized reduced rank tests using the singular value decomposition / Journal of Econometrics 133 : 97~126

[journal] King, B. / 1966 / Market and Industry Factors in Stock Price Behavior / Journal of Business 39 (1) : 139~190

[journal] Ledoit, O. / 2003 / Improved estimation of the covariance matrix of stock returns with an application to portfolio selection / Journal of Empirical Finance 10 : 603~621

[journal] Ledoit, O. / 2004 / Honey, I shrunk the sample covariance matrix / Journal of Portfolio Management 31 : 110~119

[journal] Markowitz H. / 1952 / Portfolio Selection / Journal of Finance 7 (1) : 77~91

[journal] Markowitz H. / 1991 / Foundations of Portfolio Theory / Journal of Finance 46 (2) : 469~477

[journal] Markowitz H. / 1999 / The Early History of Portfolio Theory : 1600-1960 / Financial Analysts Journal 55 (4) : 5~16

[journal] Merton, R. / 1972 / An Analytic Derivation of the Efficient Portfolio Frontier / Journal of Financial and Quantitative Analysis 7 (4) : 1851~1872

[journal] Michaud, R. / 1989 / The Markowitz Optimization Enigma : Is ’Optimized’Optimal? / Financial Analysts Journal 45 (1) : 31~42

[journal] Plerou / 2002 / Random matrix approach to cross correlations in financial data / Physical Review, E 65 : 066126~

[journal] Roll, R. / 1980 / An Empirical Investigation of the Arbitrage Pricing Theory / Journal of Finance 35 (5) : 1073~1103

[journal] Rubinstein, M. / 2002 / Markowitz’s “Portfolio Selection”: A Fifty-Year Retrospective / Journal of Finance 57 (3) : 1041~1045

[journal] Sengupta, A. / 1999 / Distributions of singular values for some random matrices / Physical Review, E 60 : 3389~

[journal] Sharpe, W. / 1963 / A simplified model for portfolio analysis / Management Science 9 : 277~293

[journal] Trzcinka, C. / 1986 / On the Number of Factors in the Arbitrage Pricing Model / Journal of Finance 41 (2) : 347~368

[journal] Tu, J. / 2011 / Markowitz Meets Talmud : A Combination of Sophisticated and Naive Diversification Strategies / Journal of Financial Economics 99 : 204~2015
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