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I am looking at bonds where some are more liquid than others, in that some bonds have a much higher volume than others. If I am holding a bond X with more liquidity than bond Y, but X and Y receive the same return, I would like a way of showing the “risk” of holding bond Y was higher.

Currently the way I would like to do this is incorporate into the bond volatility somehow. Are there any books or literature on this, or has this been done elsewhere?

This would allow me to say something about the risk adjusted return for the bonds which are illiquid - which is what I am looking to do.

It seems like theirs is a lot of talk about liquidity risk but not a lot of literature in how to take it into account quantitatively when analysing a portfolio systematically.

A basic metric I can think of is using some sort of normalized measure of the bid ask spread, and penalising the volatility by an additional term to account for the bid ask spread width.

Thanks in advance for your suggestions!

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The term liquidity risk is used to mean two different things. There are many books and web pages about liquidity risk in the sense of asset liability management, over-simplifying - the fear that while solvent, you have assets that you can't sell or repo fast enough to pay the bills.

I think you should be looking for "prudent valuation" (PruVal) for bonds, i.e. the difference between the fair yield that you'd get selling your bonds under normal market conditions versus the prudent yield, higher than fair, that you'd get selling your bonds in the secondary market under "fire sale" conditions. A good paper is https://pages.stern.nyu.edu/~adamodar/pdfiles/papers/liquidity.pdf . Also there is some EU regulatory and supervisory guidance, e.g. https://www.eba.europa.eu/sites/default/files/document_library/Publications/Draft%20Technical%20Standards/2020/RTS/882753/EBA-RTS-2020-04%20Amending%20RTS%20on%20Prudent%20Valuation.pdf

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  • $\begingroup$ Thanks - this seems a step in the right direction, but it seems like a lot of papers say “add a premium” but not how to calculate it. But maybe I’m asking for too much! I also would rather this premium was in the volatility somehow… so we see true yields, but altered risk metrics $\endgroup$ Commented Nov 19, 2024 at 19:06
  • $\begingroup$ I think EU has technical standards on how to estimate prudent valuations. I'm not sure how to plug them into volatility... You might consider a limit or constraint on the difference between portfolio level fair value minus prudent value. $\endgroup$ Commented Nov 19, 2024 at 19:18

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