Portfolio allocation using wavelet transform

To apply the mean-variance portfolio theory in real life, an investor needs to estimate a set of statistical characteristics from the underlying securities in the portfolio of interest, as well as the weight assigned to each portfolio; however, the noise present in the underlying securities may distort the estimated statistical characteristics of securities and in turn the resulting portfolio allocation strategy. In this dissertation, I investigate the effect of such noise on the statistical characteristics of financial series and on the portfolio allocation decision. I rely on the wavelet transform to minimize the effect of noise in the financial series. Different combination of smooth and non smooth series are employed to estimated the optimal portfolio weights, where each combination leads to different risk and return for investor. From these estimations, I observed that the allocation decision with highly smoothed variance matrix and non smoothed mean provides the highest Sharpe ratio. Overall, the obtained results show that the wavelet transform is an effective tool for smoothing the financial series and can lead to an improved investor allocation strategy.