# Tag Info

Accepted

### Ledoit/Wolf covariance shrinkage in risk-parity optimisation

The Risk Parity portfolio will be equal weighted if the assets have uniform correlation and equal variance. This would be the case for the shrunk covariance matrix if the shrinkage coefficient used ...
• 516

### Are smart beta and risk-parity the same?

This is a very good question. It can be argued that risk parity is one example of a smart beta strategy. Yet it is important to understand that both are coming from two different directions: risk ...
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• 1,757
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### How to understand this Risk Parity Algorithm?

Your question seems very simple. The $\rho_{ij}$ are the correlations between asset i and asset j, in other words these are the elements of the correlation matrix. This notation is very standard in ...
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### Implementing leveraged Risk Parity Portfolio using Direxion 3X ETF

Here is my take on trying to answer this question. My backtest goes as far as December 1979 (just before the great bond bull run). I used daily total return index for Wilshire 5000 and 10-year ...
Accepted

### How to understand this convex optimization method to find risk budget portfolio

I believe the problem should be solved in two steps: the optimization without the condition that the sum equals 1, followed by a normalization step which divides w by sum(w) to produce the desired ...
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### How to construct a Risk-Parity portfolio?

Let us intuitively understand the risk parity algorithm. In this algorithm, the important point to consider is it allocates more capital for the assets which has lower risk and less capital to the ...

### Risk Parity / Equal Risk Contribution with Tail Risk Measures

I had tried something similar to this in the past. It's much easier when there's an analytical formula for CVaR than when using simulations because it's much easier to calculate the derivatives you ...
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### How were Dalio's All Weather weights determined?

As mentioned in the short comment above, this particular allocation comes from an interview documented in the book Money: Master the Game. Dalio explained that "in his All Weather strategy, they use ...
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1 vote
Accepted

### Express the covariance in terms of the standard deviations and correlations

Let $\mathbb{1}$ denote a vector of ones. With the definition of risk parity in the question, we have $$Sw=c\mathbb{1}$$ with $c$ some constant, thus $$w=cS^{-1}\mathbb{1}$$ As $\mathbb{1}^Tw=1$, ...
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### How were Dalio's All Weather weights determined?

What horizon are you using to calculate your "equal risk contribution" weights? I am guessing it's 1 year, maybe 5 year... versus Dalio looking over decades. Plus, where are TIPS? When the Taper ...
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1 vote

### How to construct a risk parity Portfolio by fixing the portfolio volatility on a desired level?

your goal is to find the weight vector, $w$, which minimized your "utility" function $\sum_{i}^{N} [\frac{\sqrt{w^{T}\Sigma w}}{N} - w_i\cdot c(w_i))] ^{2}$. A general approach is to use gradient ...
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### Equal Risk Contribution portfolio scipy optimization not working

I figured out the issue, in the risk_budget_objective_error(weights,*args) function, I used pre-defined variables to figure calculate portfolio_stdev and ...
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1 vote
Accepted

### Equal Risk Contribution portfolio scipy optimization not working

Further to my comment is it because your functions are returning matrix's which are deprecated? Why not re-write your functions using ndarrays; ...
• 10.2k
1 vote

### Are smart beta and risk-parity the same?

I think this paper gives a really good overview about risk parity link. As it points out, risk parity is a alternative to traditional mean variance portfolio construction.
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1 vote

### Are smart beta and risk-parity the same?

Smart Beta refers a trend in making well known quantitative strategies more accessible to investors. Simple examples for equities include Value, Momentum, Quality, and Low Volatility. Fixed income ...
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1 vote

### Are smart beta and risk-parity the same?

They are not the same as in they are equal, but risk parity can be considered a smart beta strategy. Smart beta is this opaque term that covers anything that can be put into a factor, regressed ...

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