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A very broad question but nevertheless a important and difficult one.

Within private markets (Private Equity funds, infrastructure funds and private credit funds) how should one do a risk-based PCA analysis in order to identify the uncorrelated factors? Within Private Credit should you take some liquid index as a reference or can you use quarterly indices with the very low volatility in mind.

Appreciate any feedback

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  • $\begingroup$ Can't directly answer your question (not involved in private markets) but there was a recent paper on Alpha Architect that might be relevant: alphaarchitect.com/2021/06/22/…. Might provide some ideas for factors that are observable. HTH. $\endgroup$
    – user42108
    Commented Oct 5, 2021 at 21:43

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The PCA approach on listed equities is based on the time series of returns of all the considered stocks. You generally do not have such time series for private equities (since they do not have a market price).

One way is to have a beta-driven approach: you look for characteristics of the companies (see Pukthuanthong, Kuntara, Richard Roll, and Avanidhar Subrahmanyam "A protocol for factor identification" The Review of Financial Studies 32, no. 4 (2019): 1573-1607 for an exhaustive definition of characteristics in this context), like their sectors/industries, their suppliers and providers, some of their KPIs you can observe, etc. Alternative data can be a way to get some of these characteristics (see the Part "A better connection with the real Economy" of Capponi, Agostino, and C-A L, eds. Machine Learning and Data Sciences for Financial Markets: A Guide to Contemporary Practices Cambridge University Press, 2023.

Thanks to this you can have common factors, that you can then link to listed equities to map some market risks on them. A PCA on the returns of this synthetic characteristics (obtained via the mapping of listed equities on them), should do the job.

Of course (as mentioned by Si Chen) there is an illiquidity factor specific to PE (Private Equities). If you want it you should do an ad hoc studies on PE you have data on. You can have a look at Kooli, Maher, Mohamed Kortas, and Jean-François L'her "A new examination of the private company discount: The acquisition approach" The Journal of Private Equity (2003): 48-55 with this respect.

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Yes, indeed an important and difficult question! It's really like asking what happens in a forest where nobody is around to see it?

You would have to start with a fundamental analysis of the assets to calculate its key risk factors, and then find one or more liquid indices as a reference. For example, if you have a portfolio private credit instruments, you should calculate their duration, convexity, etc., but also their sectors and implied ratings based on some basic credit metrics. Then you can match it to benchmark bonds with similar credit risk.

Then you should consider that there is an added liquid risk. If you're buying them at +100 bp to liquid assets, just be careful that in a bad market, there could be no bids for the illiquid assets, or it could be +500 or +1000 bp to liquid benchmark assets. (Yes, seriously, that much worse.)

This doesn't mean that they should be marked down as much, but you should have enough liquidity cushion to ride out those markets.

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