How to build a long short portfolio with Hierarchical Risk Parity (HRP)

AI & Machine learning
1

I know how to build a long-only portfolio with HRP.

How can I select a few assets among the universe and get a solution that can short them and ultimately makes my portfolio Market Neutral?



The third phase of the HRP algortihm is to use the inverse volatilty approach recursively to the various clusters, this mathematically implies to solve a quadratic form with a diagonal covariance matrix and the contraint : sum(weights) = 1.

What should be the constraints for getting a market Neutral Portfolio?

If I use only: sum(weights) = 0 I will only get the obvious solution w=0 that does not mean anything from a practical point of view.



best,

R

2

Hello Raimondo, 

A portfolio is said to be market neutral when its beta is equal/close to zero. So, if you want to create a long-short portfolio that is market neutral, you should make sure its beta is close to zero. 

You can take a simple approach of creating two base portfolios, one long only and one short only. Following this, you can allocate capital to these two portfolios such that the combined beta is close to zero.



For example, let's create a long-short market-neutral portfolio of S&P 500 stocks by using momentum as a screener. 

  1. Rank the 500 stocks as per returns of the last 12 months
  2. Select the top 10 performers to create a long portfolio and the bottom 10 performers to create a short portfolio.
  3. Generate weights of stocks in the long portfolio and short portfolio separately using the Hierarchical Risk Parity (HRP) approach.
  4. Now you have two portfolios (long only and short only) and the weights of their stocks. 
  5. Calculate the beta of each portfolio. ( multiple the weightage of stock with its beta. Repeat this step for all stocks in the portfolio and take the sum to get the portfolio beta)
  6. As a last step, split the capital among the long portfolio and short portfolio such that the total beta is close to zero.

    For example, 

    If the beta of the long and short portfolios are 0.3 and 1.9 respectively, and the capital is $10000. 

    Then, the capital allocation would be the solution of the following equations.



    0.3x -1.9y = 0 

    x+y = 10000



    x =  8636.4 and y = 1363.6

    i.e. A capital of $8636.4 is allocated to the long portfolio and a capital of $1363.6 is allocated to the short portfolio to make a  long-short portfolio that is market neutral. The capital allocated to the long/short portfolio will be distributed across its stocks as per the HRP weights generated. 



    Hope this helps!

     
3

thank you for your detailed solution.  The only question I have is that my universe is composed of 40 currency pairs, 10 indices 7 commodities. What is the benchmark for evaluating the Beta? Is there a method for building a sinthetic bechmark based on the portfolio I have?



thanks



Raimondo

4

Hello Raimondo, 

Here are two approaches for creating the synthetic benchmark for your multi-asset portfolio of currency pairs, indices and commodities. 



1) Create an equal-weighted portfolio of assets and use it as your benchmark index.



Indices like S&P 500 are created by giving weightage to the constituents as per their float-adjusted market capitalization (FMC). (Methodology )

However, since you are dealing not just with equities but with multiple asset classes, you can create a synthetic index by giving equal weights to the asset classes involved. 



For example, in your case, you can create a synthetic index by giving 33.33% weightage to currency pairs, indices and commodities. In this case, 33.33% of weightage is equally split among the 40 currency pairs. So, each currency pair will have a weightage of 0.83%. 

Allocation of weightage for 10 indices and 7 commodities is done in the same way. So, each index and commodity has a weightage of 3.33% and 4.76% respectively.



Refer to this link to know more about the equal weightage index and its methodology 



2) Create a synthetic index using composite indices



You can create a synthetic index by giving equal weightage to the composite indices (or ETFs) that represent the asset classes in the portfolio. 



For example, in your case, you can create a synthetic index by giving equal weightage to 'MSCI Intl Emerging Market Currency index' (to represent multiple currencies in your portfolio),  'MSCI All-Country World Equity Index' (to represent the multiple equity indices your portfolio contains), 'S&P GSCI' (a benchmark for investment in the commodity markets, used to represent commodities in your portfolios). 



It should be noted that the synthetic index may not exactly represent the constituents of your portfolio and the results may change according to the asset benchmark used.

Please check the following references to know more about creating a benchmark for a multi-asset portfolio


  1. Investing in Currencies: The Problem with Benchmarks (link)
  2. How Do You Benchmark a Multi-Asset Fund? (link)
  3. Benchmarking Multi-Asset Portfolios: The Global Capital Stock (link)
  4. How to Select and Build a Benchmark to Measure Portfolio Performance (link)
  5. Benchmark (link)
  6. Benchmark Portfolio  (link)
  7. The Global Capital Stock. A Proxy for the Unobservable Global Market Portfolio (link)



    Hope this helps!

    Thanks 





     
5

wow!!!

That was a superb answer.

Many thanks for your help!