All the news and information can have diverse effects on the financial market dynamics at different time horizons. The effects can be determined in the form of the frequency which is the cycle of the data. In this thesis, I apply spectral analysis to quantify the return of each sector index across different time horizons. By using the Discrete-Time Fourier Transform, I can decompose return, variances, covariances, and expected return into the frequency domain. In the frequency domain, I can see how correlated of the different investment strategies and asset return at different time horizons. For the portfolio management, we can construct the mean-variance-frequency optimal portfolios by choosing the band spectrum of the asset return which the traditional mean-variance optimal portfolios can’t. The performance depends on how you choose the band spectrum, estimation window and period of rebalancing.
