Hi, there!
Anyone can explain intuitively why “Risk Parity Portfolio(unleveraged)” is close enough to efficient portfolio(tangency portfolio) ?
This is because ,for example, large cap stocks tend to have lower volatility, indicating higher allocation weight? (I assume that weights are determined in terms of inverse of volatility…)
Thanks in advance! 
If all portfolio assets have the same Sharpe ratio, then the risk parity portfolio *IS* the tangency portfolio. To the extent that that assumption doesn’t hold, the tangency portfolio and the risk parity portfolio will differ. Over the long term, it is reasonable to think that liquid assets will have similar Sharpe ratios, since differentials among liquid assets should attract investments in such a way as to reduce the difference. In practice, the risk tolerances and time horizons of the investing public will affect the total demand for certain investments and thus the Sharpe ratio. In the short term, fads and fashion will affect differentials. This also depends a bit on how you define risk. I’ve assumed that you are measuring risk using variances and covariances. But you said “close enough” in your question. I’m confused about: “close enough for what, exactly?”
bchad,i’m amazed you can remember all this, but doyou find this stuff practical?
I remember that one because I find it very practical.
It is true that stocks with high volatility (assuming away correlations) will tend to have lower weights in risk parity than a comparable low volatility security. However, it is also possible to draw a mean-riskparity frontier where one trades off return versus how close you are to the risk parity ideal. In this sense, it would be possible to hold a portfolio on this frontier that has a higher weight in high volatility stocks if that’s the only way to get the stronger return (assuming there’s no risk-free asset in the optimization). Hence, the real advantage of the risk parity framework is not necessarily that the contribution to risk of each asset is equal or minimized, it’s that the resulting portfolios are less sensitive to estimation risk than a mean-variance portfolio. This is because they will likely be less concentrated in a few assets than the mean-variance portfolio will be. Also, since the portfolios tend to be more spread out among assets, it also means that you won’t get the transaction costs of constantly switching between assets that you would get in a simple mean-variance optimization.
Can you elaborate on the meaning of your comment? Sorry for my poor understanding… >If all portfolio assets have the same Sharpe ratio, then the risk parity portfolio *IS* the tangency portfolio. To the extent that that assumption doesn’t hold, the tangency portfolio and the risk parity portfolio will differ. >But you said “close enough” in your question. I’m confused about: “close enough for what, exactly?” Samuel Kunz(2011) “At Par with Risk Parity?” says, “Risk parity proponents believe that unleveraged portfolios are “close enough” to the efficient portfolio, but that belief suggests another trade-offs.”
OK, so “close enough” means “close enough for the proponents of risk parity.” That presumably means that they’ve decided that they can’t generate good enough estimates to justify doing a regular optimization, and that risk parity gets you close enough in their judgement. In practice, that means that the proponents don’t believe that they can estimate differences in Sharpe ratios (forward looking) accurately enough to gain any benefit from the difference between risk parity and full mean-variance optimization (or other robust optimizations). They are effectively asserting that their best estimate of asset Sharpe ratios is that they are all equal. This makes sense if you think markets are more-or-less efficient. I thought that you might have your own judgement about what was close enough or not. As for part one, if you have a bunch of assets that all have the same Sharpe ratio, and then you perform a mean-variance optimization on it, and then select the highest Sharpe-ratio portfolio on the efficient frontier, you will get the same portfolio weights that you would if you just took the those assets and stuck them in a risk-parity (risk measured as variance) portfolio. It’s only when the forward-looking Sharpe ratios of assets are different that an optimized portfolio and a risk-parity portfolio will look different. …at least for the long only case. In long-short portfolios, optimized portfolios tend to have assets balanced against each other to neutralize each others’ risk, and that may not line up with the risk-parity portfolio (there are also multiple risk parity portfolios in the long-short case).
Many thanks, bchadwick!! very helpful. Thanks again!