7 votes

How to construct a Risk-Parity portfolio?

I am very happy with the following equivalent formulation for the risk budgeting problem (as presented in Bruder, Roncalli, 2012, Managing Risk Exposures using the Risk Budgeting Apporach): Let $b_i$,...
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  • 2,874
6 votes
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 ...
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  • 496
5 votes

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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  • 26.7k
4 votes

How to construct a Risk-Parity portfolio?

Another approach to construct a risk parity portfolio would be to use the formulation proposed by Spinu [1]: $$\begin{array}{ll} \underset{\mathbf{w}}{\textsf{minimize}} & \frac{1}{2}\mathbf{w}^{T}...
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4 votes
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Risk Parity / Equal Risk Contribution with Tail Risk Measures

For question 1), lets add the topic of positive homogeneity to the discussion: Whenever a risk measure is positively homogeneous, we can calculate risk contributions. A risk measure is positively ...
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  • 2,874
3 votes
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Implementing leveraged Risk Parity Portfolio using Direxion 3X ETF

Apologies in advance for being hyper-critical. I have somewhat strong feelings about this =P The purpose of risk parity is to improve portfolio efficiency via achieving better diversification. (We ...
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  • 10.9k
3 votes
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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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  • 9,077
2 votes

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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  • 5,291
2 votes

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 ...
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2 votes

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 ...
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2 votes
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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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  • 10.9k
1 vote
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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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  • 5,533
1 vote

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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  • 4,896
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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  • 609
1 vote

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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  • 13
1 vote
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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; ...
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  • 8,007
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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  • 413
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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