An index fund is a collective investment scheme that aims to replicate the movements of an index of a specific financial market regardless of market conditions. An index fund is a popular investment alternative because it is much cheaper to run than an active fund and it performs better than actively managed funds. This paper illustrates the usefulness of wavelet analysis in constructing an index fund. The wavelet analysis can decompose the time series data in frequency domain as well as in time domain. The major findings of this paper are as follows. First, the beta coefficient that represents the systematic risk has the scale dependent property. This result can provide important information to the investors with various investment time frequency. Investors can use the betas corresponding to their investment frequencies among the various scale betas estimated by wavelet analysis. Second, we can find the usefulness of wavelet analysis in constructing index fund because the wavelet technique gives less tracking error(difference between the index performance and the index fund performance) than the traditional constructing techniques. The result of this study implies that the wavelet techniques can be an important analytic method to the other financial markets such as option market, futures market, bond markets and currency market.