Questions tagged [risk-parity]

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13 votes
4 answers
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How to construct a Risk-Parity portfolio?

If I would like to construct a fully invested long-only portfolio with two asset classes (Bonds $B$ and Stocks $S$) based on the concept of risk-parity. The weights $W$ of my portfolio would then be ...
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5 votes
2 answers
915 views

Risk Parity / Equal Risk Contribution with Tail Risk Measures

Risk Parity or (synonymous) Equal Risk Contribution is an approach to portfolio construction which could work in theory with a broad class of risk measures. Yet, all references I have found so far ...
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4 votes
1 answer
449 views

Ledoit/Wolf covariance shrinkage in risk-parity optimisation

This is more of a theoretical question. I have been working on some mean-variance / Black-Litterman models and played around with Ledoit/Wolf's covariance shrinkage method (sklearn function in Python)....
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  • 95
3 votes
3 answers
716 views

How were Dalio's All Weather weights determined?

Somewhere along the lines, Ray Dalio's all weather became known to be a portfolio with the following weights: 30% Equities 40% Long Term Treasuries 15% Intermediate Term Treasuries 7.5% Gold 7.5% ...
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  • 133
3 votes
0 answers
75 views

Fixed Income portfolio type

Could someone kindly point me toward a primer that would cover the various type of fixed income portfolio strategies under modern portfolio theory ? In a nutshell, I would like to know what kind of ...
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2 votes
4 answers
840 views

Are smart beta and risk-parity the same?

From what I have been reading online, smart beta ETFs aim to use a different type of weighting (instead of by market cap as traditional ETFs like SPY do to track an index) to achieve positive ...
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  • 41
2 votes
2 answers
3k views

Implementing leveraged Risk Parity Portfolio using Direxion 3X ETF

The "common man" version of a leveraged Risk Parity portolio (40% stocks and 60% long term bond, Quarterly Rebalanced) can now be easily implemented using the 3X leveraged ETF's (UPRO=stocks, TMF=...
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2 votes
1 answer
1k views

How to understand this Risk Parity Algorithm?

I am trying to understand an optimization algorithm to achieve risk parity in a portfolio. I need some help figuring out the notation in the following formula: I found this on THIS paper. I ...
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2 votes
1 answer
191 views

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

I would like to get the weights of a risk parity portfolio (equal risk contribution). Therefore I use following formulas: $\sigma(w)=\sqrt{w' \Sigma w}$ $\sigma_i(w)= w_i \times \partial_{w_i} \...
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2 votes
0 answers
133 views

How to optimize a non-linear least squares problem with cvxpy/cvxopt

I know how to minimize a linear function $f : \mathbb{R}^{n} \rightarrow \mathbb{R}$ with CVXPY but in my problem the function $f$ is quadratic and hence the problem is now in the form : $$\lVert AW-...
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  • 45
2 votes
2 answers
162 views

Can the dependent samples t test be used for this problem?

Short story: I have 2 sets of data: Set 1: Vector with daily data of stock market returns (eg. [1%, 1.2%, -2%]) Set 2: That vector of stock market returns, multiplied by another vector (eg. [2%, 0....
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1 vote
0 answers
38 views

Equivalent constructions of risk budgeted portfolios?

When building an ERC portfolio given covariance $S$, I am familiar with the approach in optimalPortfolio. It takes the risks of a given weight vector $(w_i * (S w)_i)$, divides it by total risk to get ...
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  • 1,327
0 votes
2 answers
1k views

Equal Risk Contribution portfolio scipy optimization not working

I'm trying to create a tool for an equal risk contribution portfolio,essentially following this article (https://quantdare.com/risk-parity-in-python/) but it is failing at the last step (def ...
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  • 13
0 votes
1 answer
79 views

Express the covariance in terms of the standard deviations and correlations

I really need help on this problem. Any suggestion is greatly appreciated! Suppose there are $n$ assets with $n\times n $ covariance matrix $C=SRS$, where $S$ is a matrix with standard deviations $\...
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  • 3
0 votes
1 answer
127 views

Looking for non-GAUSS Code for Thiery Roncalli's book on Risk Parity and Budgeting

I am going through the book 'Introduction to Risk Parity and Budgeting' by Thierry Roncalli (2013). The author provides software for the various concepts illustrated in the book, but it is all done in ...
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