In the paper Super-Whiteness of Returns Spectra from Erhard Reschenhofer of University of Vienna it is commented the following
"Until the late 70’s the spectral densities of stock returns and stock index returns exhibited a type of non-constancy that could be detected by standard tests for white noise. Since then these tests have been unable to find any substantial deviations from whiteness in stocks returns and index returns.
Actually, there is a striking power deficiency, which implies that these series exhibit even fewer patterns than white noise. A typical frequency domain test for white noise rejects the null hypothesis whenever the time series contains sinusoidal components with too large amplitudes.
Under the null hypothesis of white noise, all amplitudes are roughly of the same size, no amplitudes can be systematically larger than others. There is a perfect uniformity. Amazingly, the amplitudes obtained from the S&P 500 returns appear even more uniform. This super-whiteness can not just be the result of random fluctuations. Something more must be at work besides chance.
All in all, it seems that active traders contribute to market efficiency only up to a certain point. Beyond that point, their activities may lead to super-efficiency, which must on no account be misinterpreted as perfect efficiency but rather implies some special form of predictability."
This paper seems to imply that a portfolio should be taken as just white noise or better super white noise so basically there is no signal or if there is must be microcopic in power and that this super white noise must be a mix of superpossitioned different distribution white noises with additional noise components as to lead to this greater uniformity in amplitude than white noise.
If you have any additional information on what processes could create this superwhite noise kindly let me know.
Power deficiency of significance of tests on the frequency domain for rolling windons of 5 years found after the 70s (data analyzed from the 50s). This significance results of tests with much lower rates than the rejection level of the null hipothesis implies that any deviation from the null hypothesis reveals that the spectrum should be greater at some frequencies and lower at others.