Using genetic algorithm (GA), this study proposes a portfolio optimization scheme for index fund management. Index fund is one of popular strategies in portfolio management that aims at matching the performance of the benchmark index such as the S&P 500 in New York and the FTSE 100 in London as closely as possible. This strategy is taken by fund managers particularly when they are not sure about outperforming the market and adjust themselves to average performance. Recently, it is noticed that the performances of index funds are better than those of many other actively managed mutual funds [Elton et al., 1996, Gruber, 1996 and Malkiel, 1995]. The main objective of this paper is to report that index fund could improve its performance greatly with the proposed GA portfolio scheme, which will be demonstrated for index fund designed to track Korea Stock Price Index (KOSPI) 200.
Index funds are popular investment tools being used in modern portfolio management. Index funds are designed to mimic the behavior of the given benchmark market indices (e.g. the S&P 500 in New York, the FTSE 100 in London, the KOSPI 200 in Seoul, etc.). Thus, index funds are generally regarded as relatively stable and efficient investment tool compared with other mutual funds (Jensen, 1968 and Sharpe, 1966).
The index fund strategy is based on the concept of the passive investment management. There are several interesting papers reporting the superior performance of the index funds compared with other actively managed portfolios (Elton et al., 1996, Gruber, 1996 and Malkiel, 1995). In addition to the performances of index funds in terms of risk and return, index funds are also considered cost effective investment tool in the capital market (Hogan, 1994).
Index funds are composed of relatively small number of stocks. If we want to set up a perfect index fund, we need put every company included in the index into the index fund portfolio (e.g. 500 companies for S&P 500, 100 companies for FTSE 100, and 200 companies for KOPSI 200). However, it is costly and not practical to include every company in the index fund portfolio. Thus, index funds try to replicate the movement of the indices with a relatively small number of stocks.
This article proposes a genetic algorithm (GA) portfolio scheme for the index fund optimization. The scheme exploits GA and provides the optimal selection of stocks utilizing fundamental variables—standard error of portfolio beta given by formula (1), average trading amount, and average market capitalization. These fundamental variables are well-known core factors frequently used in analyzing and forecasting the stock market. Roughly speaking, the GA portfolio scheme consists of two steps. First, the stocks for the index fund are selected through working with the fundamental variables in each industry sector of the benchmark index. Second, the relative weights of the selected stocks are optimized through the GA process. It will be shown that the portfolio scheme efficiently replicates the benchmark index with a relatively small number of stocks. Notice that the business of the efficient index fund management relies on the technique of replicating the benchmark index.
The proposed GA scheme is applied to Korea stock price index (KOSPI) 200 from Jan 1999 to Dec 2001. KOSPI 200 includes 200 major companies in 22 industry sectors, which are currently listed on the Korean Stock Exchange. The 200 companies cover general spectrum on the Korea Stock Exchange and KOSPI 200 is also the base index of KOSPI 200 futures contract, which is the most active futures contract on the Korea Stock Exchange.
This paper consists of five sections. Following this section, Section 2 provides a brief survey about portfolio theory, index funds, and GA. Section 3 discusses the detailed procedure of the proposed scheme and Section 4 reports empirical experiment results. Finally, Section 5 is devoted to the concluding remarks.
