# Concentration risk in Rates

What are some good ways to assess the concentration risk for a rates curve or by currency when volumes traded by instrument are not easily available? For ex, if for some currencies, the PV01 at certain tenors is very high or the sum of absolute risks for a curve is very high, how can we quantify on whether we can exit the positions in a given number of days?

• It would seem you would need the advice of someone who has traded in these markets every day for a while and therefore has a "feel" for how much is traded, and what size of orders it is possible to put through. In other words at least a approximate/informal knowledge of volumes traded is essential. – noob2 Mar 7 at 22:01
• I see there are some volumes as of last day for the major currencies on LCH, but not sure how to get historical data. If I take some kind of average for a few days and assume that to be true for most days, is there a way to quantify what amount of PV01 at each tenor is too high or too low if one were to exit a position in x days? (Assuming I can find the avg. notional for IR swaps trades for my bank) – access_nash Mar 7 at 22:07

## Market Impact

I was asked this question numerous times, often by clearing houses as a measure to gauge their initial margins and concentration fees.

As a market maker you may have limited information about the volumes traded, i.e. you know your own volumes. Our strategy was to first infer expectations about the market as a whole, and ask brokers to corroborate this view or provide some generic, non-sensitive information that would be useful.

Once you have a range of tradeable volumes you can consider market impact of various sizes. Numerous empirical studies often find there is a square root relationship between market impact and volume of order (sorry I dont have time to look up some references right now (perhaps someone can edit them to my answer)). I.e. consider the hypothetical market impact of various notionals of 30Y IRS:

10mm     0.08bps
100mm    0.25bps
1000mm   0.80bps
5000mm   1.79bps
10000mm  2.53bps


Market impact is inevitably related to execution time provided, for example if you are asked to 100mm in 5days as opposed to 1 second the cost due to market impact will be different: in one second you would obviously have to lift all available prices at that time, regardless of what they are.

When it comes to considering the volumes of instruments such as 10Y/30Y spread, where the information might be mixed with data on outright 10Y or outright 30Y trades. The recommendation is to build a model with some sensible parameters.

## Liquidation

If your concern is solely risk then you will inevitably have to make the decision about how much residual risk you will tolerate upon liquidation:

• Will you be content being delta neutral measured over any tenors?
• Will you be content if major macros buckets are allocate to zero, eg 2Y 5Y 10Y or 30Y?
• Will you only be content if every yearly bucket is hedged, i.e. 15Y 16Y 17Y cannot be +1mm, -2mm, +1mm pv01 for example.
• Will you only be content if every position is exited with every counterparty, so you book is essentially closed?

The levels of tolerance also greatly impact the answer. Practically it is probably only worth considering upto about the second level of the above bullet points if you are talking about an execution timeframe of days.

• @ Attack68 - Thanks. "Numerous empirical studies...."- I'll look for those. As for what you said on liquidation, I did a quick check for the first two points and there's no consistency and usually it doesn't hold. We do use a concentration charge above a certain limit for PV01, but how that number came up has no justification and the regulators are asking. Whoever came up with those numbers have probably left. So we probably need to think up something new. – access_nash Mar 9 at 16:16
• just one example of a paper I have in my drive is "Market Impact: A systematic study of limit order". Going back 4 or 5years ago LCH applied their maintenance margin concentration charge according to bullet 2: macro buckets. Not sure if they adopt a different approach these days. – Attack68 Mar 9 at 17:13