불완전 정보 하에서 추가적인 제약조건들이 포트폴리오 선정 모형의 성과에 미치는 영향

박경찬(Kyungchan Park),정종빈(Jongbin Jung),김성문(Seongmoon Kim) 한국경영과학회 2015 經營 科學 Vol.32 No.1

Under complete information, introducing additional constraints to a portfolio will have a negative impact on performance. However, real-life investments inevitably involve use of error-prone estimations, such as expected stock returns. In addition to the reality of incomplete data, investments of most Korean domestic equity funds are regulated externally by the government, as well as internally, resulting in limited maximum investment allocation to single stocks and risk free assets. This paper presents an investment framework, which takes such real-life situations into account, based on a newly developed portfolio selection model considering realistic constraints under incomplete information. Additionally, we examined the effects of additional constraints on portfolio’s performance under incomplete information, taking the well-known Samsung and SK group stocks as performance benchmarks during the period beginning from the launch of each commercial fund, 2005 and 2007 respectively, up to 2013. The empirical study shows that an investment model, built under incomplete information with additional constraints, outperformed a model built without any constraints, and benchmarks, in terms of rate of return, standard deviation of returns, and Sharpe ratio.

외환 시장 포트폴리오 선정 모형과 투자 알고리즘 개발 및 성과평가

최재호(Jaeho Choi),정종빈(Jongbin Jung),김성문(Seongmoon Kim) 한국경영과학회 2014 한국경영과학회지 Vol.39 No.2

In this paper, we develop a portfolio selection model that can be used to invest in markets with margin requirements such as the foreign exchange market. An investment algorithm to implement the proposed portfolio selection model based on objective historical data is also presented. We further conduct empirical analysis on the performance of a hypothetical investment in the foreign exchange market, using the proposed portfolio selection model and investment algorithm. Using 7 currency pairs that recorded the highest trading volume in the foreign exchange market during the most recent 10 years, we compare the performance of 1) the Dollar Index, 2) a 1/N Portfolio which equally allocates capital to all N assets considered for investment, and 3) a hypothetical investment portfolio selected and managed according to the portfolio selection model and investment algorithm proposed in this paper. Performance is compared in terms of accumulated returns and Sharpe ratios for the 10-year period from January 2003 to December 2012. The results show that the hypothetical investment portfolio outperforms both benchmarks, with superior performance especially during the period following financial crisis. Overall, this paper suggests that a mathematical approach for selecting and managing an optimal investment portfolio based on objective data can achieve outstanding performance in the foreign exchange market.

지수가중이동평균법과 결합된 마코위츠 포트폴리오 선정 모형 기반 투자 프레임워크 개발

박경찬(Kyungchan Park),정종빈(Jongbin Jung),김성문(Seongmoon Kim) 한국경영과학회 2013 한국경영과학회지 Vol.38 No.2

In applying Markowitz’s portfolio selection model to the stock market, we developed a comprehensive investment decision-making framework including key inputs for portfolio theory (i.e.. individual stocks’ expected rate of return and covariance) and minimum required expected return. For estimating the key inputs of our decision-making framework, we utilized an exponentially weighted moving average (EWMA) which places more emphasis on recent data than the conventional simple moving average (SMA). We empirically analyzed the investment results of the decision-making framework with the same 15 stocks in Samsung Group Funds found in the Korean stock market between 2007 and 2011. This five-year investment horizon is marked by global financial crises including the U.S. subprime mortgage crisis, the collapse of Lehman Brothers, and the European sovereign-debt crisis. We measure portfolio performance in terms of rate of return, standard deviation of returns, and Sharpe ratio. Results are compared with the following benchmarks: 1) KOSPI, 2) Samsung Group Funds, 3) Talmudic portfolio based on the naive 1/N rule, and 4) Markowitz’s model with SMA. We performed sensitivity analyses on all the input parameters that are necessary for designing an investment decision-making framework : smoothing constant for EWMA, minimum required expected return for the portfolio, and portfolio rebalancing period. In conclusion, appropriate use of the comprehensive investment decision-making framework based on the Markowitz’s model integrated with EWMA proves to achieve outstanding performance compared to the benchmarks.

외환 시장에서 마코브 체인을 활용한 포트폴리오 선정 모형과 투자 알고리즘 개발 및 성과평가

최재호(Jaeho Choi),정종빈(Jongbin Jung),김성문(Seongmoon Kim) 한국경영과학회 2015 한국경영과학회지 Vol.40 No.2

In this paper, we propose a portfolio selection model utilizing a Markov chain for investing in the foreign exchange market based on market forecasts and exchange rate movement predictions. The proposed model is utilized to compute optimum investment portfolio weights for investing in margin-based markets such as the FX margin market. We further present an objective investment algorithm for applying the proposed model in real-life investments. Empirical performance of the proposed model and investment algorithm is evaluated by conducting an experiment in the FX market consisting of the 7 most traded currency pairs, for a period of 9 years, from the beginning of 2005 to the end of 2013. We compare performance with 1) the Dollar Index, 2) a 1/N Portfolio that invests the equal amount in the N target assets, and 3) the Barclay BTOP FX Index. Performance is compared in terms of cumulated returns and Sharpe ratios. The results suggest that the proposed model outperforms all benchmarks during the period of our experiment, for both performance measures. Even when compared in terms of pre- and post-financial crisis, the proposed model outperformed all other benchmarks, showing that the model based on objective data and mathematical optimization achieves superior performance empirically.

한국 주식시장에서 마코위츠 포트폴리오 선정 모형의 입력 변수의 정확도에 따른 투자 성과 연구

김홍선(Hongseon Kim),정종빈(Jongbin Jung),김성문(Seongmoon Kim) 한국경영과학회 2013 한국경영과학회지 Vol.38 No.4

Markowitz’s portfolio selection model is used to construct an optimal portfolio which has minimum variance, while satisfying a minimum required expected return. The model uses estimators based on analysis of historical data to estimate the returns, standard deviations, and correlation coefficients of individual stocks being considered for investment. However, due to the inaccuracies involved in estimations, the true optimality of a portfolio constructed using the model is questionable. To investigate the effect of estimation inaccuracy on actual portfolio performance, we study the changes in a portfolio’s realized return and standard deviation as the accuracy of the estimations for each stock’s return, standard deviation, and correlation coefficient is increased. Furthermore, we empirically analyze the portfolio’s performance by comparing it with the performance of active mutual funds that are being traded in the Korean stock market and the KOSPI benchmark index, in terms of portfolio returns, standard deviations of returns, and Sharpe ratios. Our results suggest that, among the three input parameters, the accuracy of the estimated returns of individual stocks has the largest effect on performance, while the accuracy of the estimates of the standard deviation of each stock’s returns and the correlation coefficient between different stocks have smaller effects. In addition, it is shown that even a small increase in the accuracy of the estimated return of individual stocks improves the portfolio’s performance substantially, suggesting that Markowitz’s model can be more effectively applied in real-life investments with just an incremental effort to increase estimation accuracy.

마코위츠 포트폴리오 선정 모형을 기반으로 한 투자 알고리즘 개발 및 성과평가

최재호(Jaeho Choi),정종빈(Jongbin Jung),김성문(Seongmoon Kim) 한국경영과학회 2013 經營 科學 Vol.30 No.1

This paper develops an investment algorithm based on Markowitz’s Portfolio Selection Theory, using historical stock return data, and empirically evaluates the performance of the proposed algorithm in the U.S. and the Hong Kong stock markets. The proposed investment algorithm is empirically tested with the 30 constituents of Dow Jones Industrial Average in the U.S. stock market, and the 30 constituents of Hang Seng Index in the Hong Kong stock market. During the 6-year investment period, starting on the first trading day of 2006 and ending on the last trading day of 2011, growth rates of 12.63% and 23.25% were observed for Dow Jones Industrial Average and Hang Seng Index, respectively, while the proposed investment algorithm achieved substantially higher cumulative returns of 35.7% in the U.S. stock market, and 150.62% in the Hong Kong stock market. When compared in terms of Sharpe ratio, Dow Jones Industrial Average and Hang Seng Index achieved 0.075 and 0.155 each, while the proposed investment algorithm showed superior performance, achieving 0.363 and 1.074 in the U.S. and Hong Kong stock markets, respectively. Further, performance in the U.S. stock market is shown to be less sensitive to an investor’s risk preference, while aggressive performance goals are shown to achieve relatively higher performance in the Hong Kong stock market. In conclusion, this paper empirically demonstrates that an investment based on a mathematical model using objective historical stock return data for constructing optimal portfolios achieves outstanding performance, in terms of both cumulative returns and Sharpe ratios.