Bridgewater was the one that popularized risk parity, and they use it in their hedge fund which is the largest in the world. Here's their white paper on it
https://drive.google.com/open?id=0BzyyTlvGE-T2WnRndjhnUGpwLW8&authuser=0They use it in a multi-asset portfolio, so they'll take domestic and int'l stocks, domestic and int'l bonds, real estate and commodities. Let's just call it 4 asset classes to keep it simple. Instead of weighting the portfolio by market cap or by equal weighting or by the efficient frontier in modern portfolio theory, they weight the portfolio based on how volatile each asset class is. More volatile assets get a lower weighting, and less volatile assets get a higher weighting. What they want is for each asset class to get an equal risk weight to each other.
If I take VTSMX, VGTSX, VBMFX, VGSIX and DBC as stocks, bonds, REITs and commodities; and I weight them according to their volatility (std deviation) of the past month, this is what my portfolio would look like on Monday:
VTSMX - 21.07%
VGTSX - 16.10%
VBMFX - 36.70%
VGSIX - 15.47%
DBC - 10.66%
Bonds get most of the portfolio because they are the least volatile. Commodities get the least amount of the portfolio because they've been the most volatile the past month. Volatility changes all the time so you need to rebalance this on probably a quarterly or monthly basis. I've made a quick and dirty spreadsheet so you can calculate the weights yourself. Just put in the volatility for each fund and it'll give you how much you should have in the portfolio. It's really easy, just do 1/volatility.
https://drive.google.com/file/d/0BzyyTlvGE-T2VzVUcUFvcmxmYTA/view?usp=sharingHistorically at least, the portfolio has performed about as good or a little bit less than a standard 60/40 or 100% stock portfolio on a total return basis. However, the volatility has been very low. If you brought the risk parity portfolio up to the same level of volatility as a 100% stock portfolio, it handily beat the market with (theoretically) the same amount of risk. They are obviously using leverage here. The 'risk' in risk parity, at least how it is implemented in the Risk Parity funds out there, is that most of the portfolio is held in bonds. So what happens if bonds start a 30 year bear market after a 30 year bull market? What would that do to the portfolio? Tough to say, and it's one of the main reasons I haven't jumped on the bandwagon for my personal portfolio.
In any case, I haven't seen someone post a backtest to an index fund/individual stock risk parity portfolio, and I thought the results were interesting.
To do this yourself, I would think a spreadsheet/google doc that automatically updates each day would be easiest. I don't know how to do that so, for a little more manual process, go to this link
http://www.barchart.com/stocks/sp500.php?view=technicalBarchart at least gives you a nice list of the S&P 500 companies, and they are even nice enough to calculate the 20 day (1 month) volatility for you. Sign up for a free account...this might be a problem for you forummm... :) and you can dump the list to a spreadsheet. Then you need to calculate the weights for each stock based on the inverse of their volatility. It's late and I'm doing this quickly, I don't know if the math is 100% correct but I'm pretty sure this is how you'd do it here:
https://drive.google.com/file/d/0BzyyTlvGE-T2SEhtRkczV3FVN1k/view?usp=sharingSo then you'd have to go out and buy each stock in the index in the 'Portfolio Weight' column. Even with a $1 million portfolio, it looks like you'd only be buying 2 shares of NFLX and 1 share of PCLN, because the price of the shares are so expensive. Then you'd have to recalculate everything on a monthly or quarterly basis and adjust the holdings. Better have a low cost broker...
Perhaps this would still work well on the DJIA. That would be only 30 stocks and be a much more manageable universe.
Edit: here's a test of a more complex form of risk parity on the ASX50 index
https://drive.google.com/file/d/0BzyyTlvGE-T2LUJmU3lqYVFvUjA/view?usp=sharingEdit: and for the Bombay stock exchange
http://www.tandfonline.com/doi/pdf/10.1080/23322039.2014.890060Edit: I can't seem to find this pdf but the summary here says they tested it on the DJIA and the returns were almost 3x as much from 2002 to 2012
https://researchbank.rmit.edu.au/view/rmit:28057