Risk Management with ClusteringHow to uncover structure bellow the surfaceCharles BrecqueBlockedUnblockFollowFollowingFeb 8Every portfolio manager is evaluated on their Sharpe ratio which measures the associated risk of their return on investment and is given by the following formula:Where:Rp is the return of the portfolioRf is the risk-free return (e.
g.
treasury bonds)Sigma p is the standard deviation of the portfolio’s excess return and acts as a proxy of the portfolio’s riskThe Sharpe ratio has often been criticised because it assumes that volatility is bad and because of its dimensionless ratio it can sometimes be difficult to interpret.
In this article, we are going to see how investing in “good” Sharpe ratios might be a lot riskier than expected.
To do this, we will uncover hidden structure using K-Means Clustering.
The DataWe are going to analyse the quarterly US holdings of ~50 institutional investors who have more than $100M in total assets under management.
This data is public as they need to file 13F Forms detailing their holdings, to the SEC every quarter.
I used Sentieo’s platform to download the data.
The form details the nature and value of their investments as well as their respective percentage of their portfolio.
For the purpose of simplicity, we are only going to consider their total assets under managements and the percentage sizes of their investments.
We are also going to extract the following features which can act as a proxy of their investment style:% of their largest holding% of their second, third, fourth and fith% of the remainder of the portfolioTotal Assets under managementWe chose these features to see if there was a relationship between the size of the fund and their allocation strategy.
An allocation strategy can also be used as a proxy of their aggressiveness.
If a manager places all their eggs in one basket they will be taking more risks than someone who uses multiple baskets.
However, the Sharpe ratio will not pick up on the diversification risk if all the eggs are of a good quality.
Data VisualisationAfter downloading and preparing the data for the 3rd quarter of 2018, I uploaded it to AuDaS.
AuDaS is developed by Mind Foundry and allows anyone to easily learn about Machine Learning and build models in minutes.
Once the data is uploaded, AuDaS scans it for anomalies and triggers advice to the user.
In this case it has identified that the Name column has no predictive value and that we can drop it.
The managers in the dataset are a combination of pension, proprietary, fundamental and quant funds.
The histogram view also allows us to see how the funds distribute across the features.
ClusteringWe are now going to ask AuDaS to identify clusters in our basket of fund managers and as a result it has automatically excluded the name column.
The associated model and performance results are given bellow and we can see that AuDaS has identified 4 fairly clear clusters.
To understand the properties of these clusters we can go back to the histogram view to see how the classes distribute across the other features.
Interpreting the ClustersClass 0: The small-medium funds that are fairly diversifiedThese funds’ top 5 holdings occupy between 10 and 20% of their total assets and as a result are considered fairly diversified.
An example fund in this class is Polar Capital which offers fundamentally driven investment products that deliver differentiated risk adjusted returns over the long term.
Class 1: The Medium- Large funds which are conservativeThese funds’ top 5 holdings occupy less than 10% of their total assets which means they are very diversified.
This also highlights that larger funds seem to be more risk averse.
Intuitively this can be explained by the fact that they have more to lose and as a result need to place their eggs in more baskets.
Examples in this class include AQR Capital Management, Prudential and Millennium Management.
Class 2: The small aggressive fundsThese funds’ top 5 holdings occupy at least 20% of their portfolio and in some cases up to 50%.
These funds have to be a bit more tactical to generate returns from their investments because of their size.
Examples in this class are Lansdowne Partners, Odey Asset Management and Egerton Capital who are known to make big bets.
Lansdowne’s Glencore bet backfired in 2017 and cost them $100M.
Odey bet against the UK government’s debt equivalent to 147.
4 percent of the fund’s net asset value in June 2018.
Class 3: The small very aggressive fundsThese funds are even more aggressive than the previous class as the majority’s top 5 holdings occupy at least 40% of the portfolio.
Examples in this class are Wolverine Trading and Jump Trading which are both proprietary funds.
This means that they are trading their own capital (as opposed to investor capital) which gives them more freedom and control over how they invest.
As a result, they can be as aggressive as they wish.
Conclusions and ExtensionsIn this brief study we were able to extract some clear structure within our basket of investment managers who could have potentially been hiding behind similar Sharpe ratios.
This structure highlighted the aggressiveness of the funds depending on their size, type and nature.
Moreover, we only considered some basic features and there are many potential extensions to this study:The Liquidity of the funds considers whether they are able to sell when they want to (i.
e.
will there be buyers of the assets they are offloading).
Including Liquidity as a feature could have revealed which funds are stuck in lobster pot investments.
Permanent capital loss: this can happen when a stock crashes to 0 or when you make losses on money you have borrowed.
Using leverage as a feature could highlight some additional structure.
The type/category of the investments: in this study we only considered the size of the top 5 investments but we could have considered their categories (Tech, Industrial, …).
Certain funds might be holding the same portfolios albeit in different proportions so an investor should avoid investing simultaneously in all of them.
Other Management features such as fees, number of employees, average years spent at the firm, bonus pool, etc.
could help uncover additional layers of structure that can be beneficial to our risk analysis.
If you are interested in finding out how our Quant and Fundamental Hedge Fund customers use AuDaS for their Risk analysis and Investment Management please don’t hesitate to reach out to me by email or LinkedIn.
You can also read some more case studies bellow:Value Investing with Machine LearningYour favourite holding period doesn’t have to be forever…towardsdatascience.
comAugmenting Investment Analysts with Data ScienceHow fundamental investing can benefit from Machine Learningtowardsdatascience.
comTeam and ResourcesMind Foundry is an Oxford University spin-out founded by Professors Stephen Roberts and Michael Osborne who have 35 person years in data analytics.
The Mind Foundry team is composed of over 30 world class Machine Learning researchers and elite software engineers, many former post-docs from the University of Oxford.
Moreover, Mind Foundry has a privileged access to over 30 Oxford University Machine Learning PhDs through its spin-out status.
Mind Foundry is a portfolio company of the University of Oxford and its investors include Oxford Sciences Innovation, the Oxford Technology and Innovations Fund, the University of Oxford Innovation Fund and Parkwalk Advisors.
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