Why Noncash Collateral Can Produce a Negative ColVA

Summary

The document addresses why a collateral valuation adjustment can become more negative when a counterparty posts more collateral. The displayed expression weights expected collateral by a reinvestment spread and discounts the result, while the questioner's sign convention treats collateral received as positive. The apparent contradiction arises from assuming that received collateral is cash available to invest.

The answer explains that ColVA in this context concerns nonstandard collateral, such as corporate bonds. The recipient does not receive cash by holding those securities and may need to pledge them in the repo market to borrow cash. If that borrowing carries a spread over the reference rate, more expected noncash collateral can increase the associated funding cost and make the adjustment more negative. The answer contrasts this with cash collateral, for which the recipient pays the poster the reference rate. This is a concise explanation of the stated setup; it does not develop the full valuation framework or cover other collateral agreements and conventions.

Key ideas

• The sign intuition depends on distinguishing cash collateral from noncash collateral.
• Holding corporate bonds as collateral does not itself provide cash to reinvest.
• The recipient may pledge noncash collateral in repo to borrow cash at a spread over the reference rate.
• Greater expected noncash collateral can increase this funding cost and make ColVA more negative.
• The explanation is limited to the collateral setup described in the document.

Tags

# Why is ColVA a negative XVA adjustment?


# Why is ColVA a negative XVA adjustment?












The expression for ColVA is usually written as something similar to this:

$ColVA= -\int_{t}^{T} D(t,u) E_{t}\Big[ s_{X}(u)X(u)\Big]du$

Where D is the discount, $s_{x}$ the spread at which the collateral can be reinvested and X the collateral posted. X has a positive sign when the counterparty posts collateral and negative when we are posting it.

If we increase the amount of collateral that the counterparty is posting, X will increase and the ColVA will become more negative (i.e we would be losing more money). Why does it work like this? If the counterparty is posting more collateral we should be able to re-invest it at $s_{x}$ and make profits not losses.

Could anybody explain what am I missing here? Thanks!

## Answer by dm63 (score 3)

https://quant.stackexchange.com/a/79885

There is a misconception here. CollVA is a concept that applies only when the counterparty posts non standard collateral (ie bonds, not cash). When a counterparty posts collateral in the form of (say) corporate bonds, you do not have any cash to invest. In fact, you have to pledge these bonds into the repo market in order to borrow cash. This is where the spread comes in, because the repo rate for corporates is SOFR + a spread S. This situation would not occur if the counterparty posted you cash on which you pay them SOFR flat. Hence the collVA adjustment which is negative and grows if there is more expected non standard collatsral.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.