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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.

EDIT

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.

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  • $\begingroup$ For those curious, Reschenhofer's paper can be found here www.jds-online.com/file_download/220/JDS-499.pdf $\endgroup$
    – nbbo2
    Commented Jul 21, 2015 at 16:12

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First. Use quotes around the quoted part of this question to make it clear what isn't your opinion.

Second. White noise is exactly what efficiency should generate. This para. neither makes sense nor is supported (if the support is elsewhere in the quoted article please post it). My questions in parentheses prefaced with "AC":

"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 (AC: explain. White noise is defined as mean-variance stationary IID). This super-whiteness can not just be the result of random fluctuations (AC: why not? White noise would appear to be defined as random fluctuations). Something more must be at work besides chance. (AC: ?)"

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  • $\begingroup$ White noise has constant amplitude (amplitude that varies with time has a corresponding frequency spectrum) and does not change amplitude, while in the article speaks about a permanent change in the amplitude as per after the 70s from that of pre 70s interpreted from the change of the level of significance in pre 70s close to rejection rates to post 70s well below the rejection of the white noise null hipothesis $\endgroup$
    – Barnaby
    Commented Jul 21, 2015 at 17:18
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    $\begingroup$ Institutional change (e.g. new hedging derivatives, freer capital flows, electronic trading) could account for this. Markets became more efficient and as a result the arbitrage opportunities (serial correlation) were eliminated from the data as the variance of returns was reduced. $\endgroup$
    – Andrew
    Commented Jul 21, 2015 at 18:49
  • $\begingroup$ @Barnaby Also, a lot of the tests pre 70s were done on stock indices or portfolios. Thin trading in the underlying components of the indices led to "spurious" autocorrelation in the index series itself. I think the classic paper on this is Dimson (1979) "Risk Measurement When Shares are Subject to Infrequent Trading" $\endgroup$
    – Colin T Bowers
    Commented Jul 22, 2015 at 0:59
  • $\begingroup$ The tests were done on S&P500 and other derived stock indexes, however not portfolios $\endgroup$
    – Barnaby
    Commented Jul 22, 2015 at 1:36
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    $\begingroup$ @Barnaby Understood. The problem I refer to can potentially apply to any portfolio of more than one asset, if one examines returns constructed from end-of-day prices. I think your question is an interesting one, by the way, and I might come back and have a crack at a second answer if I get some spare time over the next week or two. Cheers. $\endgroup$
    – Colin T Bowers
    Commented Jul 23, 2015 at 1:10

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