How are we underestimating liquidity risk?

Question

Malz explains that marking to model can underestimate liquidity risk. From his example, I don't see it. I can see us underestimating market risk because we are using an incorrect price.

Why does a divergence between the market and model prices cause liquidity risk ?

Another example is convertible bond trading. Convertible bonds can be mapped to a set of risk factors including implied volatilities, interest rates, and credit spreads. Such mappings are based on the theoretical price of a convertible bond, which is arrived at using its replicating portfolio. However, theoretical and market prices of converts can diverge dramatically. These divergences are liquidity risk events that are hard to capture with market data, so VaR based on the replicating portfolio alone can drastically understate risk. Stress testing can mitigate the problem.

I'm not familiar with Malz, is this the book you're reading? — Bob Jansen, Oct 15 '15 at 14:55

Sergey Bushmanov · Accepted Answer · 2015-10-15T10:20:58.487

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In order for the risks of a presumably "correct" model to realize in practice, there should be enough liquidity in the market. This is what he is referring to when saying

[...] liquidity risk events that are hard to capture with market data, so VaR based on the replicating portfolio alone can drastically understate risk

The problem with many models is the fact that when your model raises red flag, there are thousands of similar models at others' traders, that raise red flags too. Too many people rushing to the exit at the same time, no liquidity at all. This is called Liquidity risk (or lack thereof): [in]ability to quickly liquidate your position without significant loss (or at preconceived price, if you wish).

I believe Taleb in his "Fooled by Randomness" discussed this issue (and issues with VaR) in detail.

edited Oct 15 '15 at 10:20

answered Oct 15 '15 at 10:06

Sergey Bushmanov

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Hi Bushmanov, thanks for your reply, but it doesn't seem to fit the text. The text I quoted is saying that by mapping positions to common risk factors we are underestimating the liquidity risk. Your answers seems to suggest that the use of models in general can lead to a systemic liquidity crisis. – AfterWorkGuinness Oct 15 '15 at 16:39
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Maybe it is a little but like the "peso problem" in foreign exchange. The Mexican peso had not been devalued in many years, so an econometric study would conclude that there is no devaluation risk. In reality the risk did materialize one day in (I think) 1982. So risks that only occur occasionally can be underestimated via econometric models applied to a finite time sample. https://en.wikipedia.org/wiki/Peso_problem_%28finance%29 – nbbo2 Oct 15 '15 at 19:36
Of course if your time interval is 2007 to 2008 you are probably ^overestimating^ liquidity risk LOL – nbbo2 Oct 15 '15 at 19:40
@AfterWorkGuinness My answer is just restating the text saying that apart from "volatilities, interest rates, and credit spreads" in real life there are other risks, e.g. liquidity risk. Where does it seem to not fit the excerpt you provided? Can you be more specific? My answer does not imply "systemic liquidity crisis" either – Sergey Bushmanov Oct 15 '15 at 22:17
[1/2] Hi bushmanov, I've edited my question to be a bit clearer (after many re-readings of the quoted text). As I understand the first part of your answer - "In order for the risks of a presumably "correct" model to realize in practice, there should be enough liquidity in the market" - You are saying that a sufficient amount of liquidity needs to exist in the market for a model to accurately quantify other risks. I don't see from here why marking to model vs marking-to-market would underestimate liquidity. – AfterWorkGuinness Oct 16 '15 at 00:32
[2/3] As I understand the second part of your answer, - "The problem with many models is the fact that when your model raises red flag, there are thousands of similar models at others' traders, that raise red flags too. Too many people rushing to the exit at the same time, no liquidity at all." - you are saying that similar models in use by many traders will "raise red flags" which lead to lots of sales, drying up of liquidity and endogenous liquidity risk, but not how a divergence between market & model price underestimate liquidity. – AfterWorkGuinness Oct 16 '15 at 00:37
[3/3] I'm not criticizing your answer, I'm just trying to understand it by digging deeper. – AfterWorkGuinness Oct 16 '15 at 00:38
Hi noob2, good example. Your comment made me think a bit deeper about the problem and led me to clarify my question. My confusion is centred around why does this divergence in price between the model and the market underestimate liquidity risk. I don't see how it tells us anything about liquidity risk. I thought liquidity risk (exogenous) is a function of the bid-ask spread and (endogenious) the size of the position. – AfterWorkGuinness Oct 16 '15 at 00:42
@AfterWorkGuinness It is not that divergence causes liquidity risks, it is the other way around: [sometimes] lack of liquidity causes divergence. And examples are abound: LTCM, Lehman Brothers, Flash Crash to name a few. – Sergey Bushmanov Oct 16 '15 at 05:34
@bushmanov, I think I get it now after reading your last comment. By marking to model we are making liquidity assumptions that may not hold. As a result, if the model assumes a liquid market, it may spit out a better price than we can get in a market where liquidity is scarce. Is my understanding right? – AfterWorkGuinness Oct 16 '15 at 14:20
That's right. Liquidity is just another dimension in a real world that may be overlooked by a model. Anyways, "all models are wrong, but some are useful" © – Sergey Bushmanov Oct 16 '15 at 14:54

score 2 · Answer 2 · answered Oct 17 '15 at 06:55

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I agree with @bushmanov about "running for exit", but I would like to underline an important point. In the question you stated "marking to model can underestimate liquidity risk." It is not true since you will need a model to estimate liquidity risk.

You have two kinds of models that for:

usual market impact models. If there is not that much people running for exit, square root based models will be good enough. You may nevertheless need another model to compute the time needed to get rid pf your position, like stopping time computations.
models fitted on extreme events.

answered Oct 17 '15 at 06:55

lehalle

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Concerning your "it's not true.....". One does NOT need a model for liquidity risk to "under-estimate" it. Simply not having liquidity dimension in a model is enough. – Sergey Bushmanov Oct 17 '15 at 13:56
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Fully agreed @bushmanov, I wanted to make sure there is not in the discussion an implicit view like "liquidity cannot be modelled". It is not true at all. Of course (as usual with models) you have stationarity issues. – lehalle Oct 18 '15 at 11:06

How are we underestimating liquidity risk?

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