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I think risk parity means something like allocation based on absolute [eg., dollar] value with a measure of risk &/or volatility &/or correlation to other asset classes factored in...

The general notion is to weight things based on the inverse of their recent price volatility.
You have big weightings in things that have steady prices lately and small weightings of things that have shown price volatility.
The goal is to have each position contribute a relatively constant amount of price volatility to the overall portfolio.
Ignoring correlations, of course.
Sometimes the strategy includes a cash or fixed income component, so equity allocations may be reduced when the whole market gets volatile.
There are fancier weighting formulas and sundry extensions, but that's the general idea.

The deep problem with this is that risk is best defined as the answer to the questions: How likely are you to have permanent capital loss on this position, and how big might that be?
Price volatility isn't in that definition, which is why price volatility is not a useful proxy for risk in the real world.
It does however make math easy, so it is very popular among academics, which makes it popular among sales pitches by investment managers.
And many investors prefer smooth portfolio valuations to safe portfolios.
This is the main reason funds are so popular, since averaging across positions gives smoothness.
Most investors would be aghast to see what the prices of their actual holdings are doing, but it's hidden behind the screen of the fund's reporting.
There are far more equity funds than equities these days.

On a much more pragmatic level, past price volatility is not always a good predictor of future price volatility.
Sometimes something goes bump in the night. With a sudden lurch in prices, usually down, the measured volatility spikes on lots of things.
The formulas they use can trigger big selloff when there is a dip in the market, selling at the new lower price, and all those funds (bazillions worth) are in the same positions.
As they sell, they trigger each other's rules to sell more and more.

The amount of money tracking risk parity these days certainly dwarfs, say, the amount of money using "portfolio protection" strategies in 1987.
When a whole lot of money follows the same formula, and that formula is based on recent prices, sometimes things get interesting.

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