Funding Value Adjustments

• Author: LEIF ANDERSEN,YANG SONG,DARRELL DUFFIE
• Published date: 01 February 2019
• DOI: http://doi.org/10.1111/jofi.12739
• Date: 01 February 2019

THE JOURNAL OF FINANCE •VOL. LXXIV, NO. 1 •FEBRUARY 2019

Funding Value Adjustments

LEIF ANDERSEN, DARRELL DUFFIE, and YANG SONG∗

ABSTRACT

In this paper, we demonstrate that the funding value adjustments (FVAs) of major

dealers are debt overhang costs to their shareholders. Tomaximize shareholder value,

dealer quotations therefore adjust for FVAs. Our case studies include interest-rate

swap FVAs and violations of covered interest parity. Contrary to current valuation

practice, FVAs are not themselves components of the market values of the positions

being financed. Current dealer practice does, however, align incentives between trad-

ing desks and shareholders. We also establish a pecking order for preferred asset

financing strategies and provide a new interpretation of the standard debit value

adjustment.

IN THIS PAPER,WE CALCULATE THE DEBT overhang costs to dealer-bank sharehold-

ers associated with financing new balance sheet positions. For debt-financed

swap positions, we show that these shareholder costs are equal to the funding

value adjustments (FVAs) that dealers make to the reported market values of

their swap books. Contrary to this dealer practice, however, FVAs are not actu-

ally components of the market values of the positions being financed. Instead,

they are debt-overhang transfers from shareholders to creditors.

We show that dealer bid and ask quotes, if aligned with shareholder interests,

must incorporate the debt overhang costs that FVAs represent. That is, to

maximize their shareholders’ equity value, dealers must quote so as to extract

enough trading profit from their counterparties to overcome the FVA costs to

their shareholders. This wedge represents a significant friction in over-the-

counter (OTC) markets.

To see this, consider following a simple example. A dealer purchases $100

face value of one-year T-bills and commits to hold them to maturity. Risk-

free interest rates are assumed to be zero. The dealer purchases the T-bills at

∗Leif Andersen is with Bank of America Merrill Lynch.Darrell Duffie is with Stanford University

Graduate School of Business and NBER. Yang Song is with the University of Washington. We

are grateful for comments from the referees, the Associate Editor, and the Editor, as well as

Claudio Albanese, Shalom Benaim, Damiano Brigo, Rupert Brotherton-Ratcliffe, YannCoatanlem,

St´

ephane Cr´

epey,Yuanchu Dang, YoussefElouerkhaoui, Marco Francischello, Jon Gregory, Lincoln

Hannah, Burton Hollifield, John Hull, David Lando, Wujiang Lou, Alexander Marini, Martin

Oehmke, Andrea Pallavicini, Stephen Ryan, Steven Shreve, Taylor Spears, and Hongjun Yan.

Andersen is a Managing Director at Bank of America Merrill Lynch (BAML). Like all major banks,

BAML incorporates funding value adjustments in its financial statements. The opinions stated in

the article are his own and do not necessarily reflect those of BAML. Duffie and Song have no

conflicts of interest to disclose.

DOI: 10.1111/jofi.12739

145

146 The Journal of Finance R

their mid-market value, $100. The purchase is funded by issuing unsecured

debt, which could be motivated by a desire to increase the dealer’s regulatory

measure of High Quality Liquid Assets (HQLA). The dealer has an unsecured

one-year credit spread of 50 basis points. At the end of the year, the T-bills pay

$100 and the dealer repays $100.50 on its financing. The dealer’s shareholders

therefore suffer a net loss in one year, after financing costs, of $0.50. This loss

is borne by the dealer’s shareholders only if the dealer survives. Assuming that

the dealer’s one-year risk-neutral survival probability p∗is 0.99, shareholders’

equity value is thus reduced by p∗×0.50 =0.495. This cost to shareholders is

the FVA of this trade. The FVA is a transfer in value to legacy creditors, who

now have access to an additional safe asset in the event of default.

If the dealer were to apply FVA-based valuation to the T-bills following the

same method currently used for swaps,1the dealer would assign the T-bills a

market value equal to the mid-market value of $100 less an FVA of $0.495, for

a net market value of only $99.505. By assumption, however, the T-bills have

an actual market value of $100, implying an inconsistency.

Were it not for the HQLA requirement in this example, the dealer would not

conduct this trade at the given pricing terms. The dealer’s shareholders benefit

from this trade only if the T-bills can be purchased at a price below $99.505.

More generally,to align its market-making function with shareholder interests,

a dealer’s price quotations must reflect FVAs. Thus, even though the current

FVA practice of dealers is not correct from the perspective of market valuation,

it does achieve this alignment of incentives. Being forced to mark down the

value of the T-bills by the FVA implies that traders will not be credited with

a trading profit unless they can purchase the T-bills at a price that is below

the true market value by at least the FVA. As we discuss below, there are

other ways to obtain this shareholder alignment that do not involve valuation

inconsistencies.

Funding costs have long been informally considered an input to dealer trad-

ing decisions. Beginning in 2011, major dealer banks started to formally show

FVAs on their balance sheets, as described by Cameron (2014b) and Becker

(2015), and as reported in Table I. Details on how these adjustments have been

made are provided by Albanese, Andersen, and Iabichino (2015).

The move by dealers to formally introduce FVAs likely has several causes.

First, beginning in 2008, severe deviations of dealers’ borrowing rates from

risk-free rates resulted in funding costs that were so large that excluding them

from financial statements might have been considered imprudent. (Indeed, we

provide assumptions under which large FVAs should be made, although not

to the asset side of the balance sheet). Second, the finance departments of

many dealers now feel confident that funding cost adjustments are reflected in

market transaction terms. (Our model explains why this should be the case.)

Third, despite the absence of published financial accounting standards that

support the practice of making FVAs, large accounting firms have signaled a

1In current practice, dealers do not typically apply FVAs to their bond positions.

Funding Value Adjustments 147

Tabl e I

Funding Value Adjustments of Major Dealers (Millions)

The $1.5 billion 2013 FVA of JP Morgan includes an FVA of about $1.1 billion for derivatives and

about $400 million for structured notes.

Amount Date Disclosed

Bank of America Merrill Lynch $497 Q4 2014

Morgan Stanley $468 Q4 2014

Citi $474 Q4 2014

HSBC $263 Q4 2014

Royal Bank of Canada C$105 Q4 2014

UBS Fr267 Q3 2014

Cr´

edit Suisse Fr279 Q3 2014

BNP Paribas €166 Q2 2014

Cr´

edit Agricole €167 Q2 2014

J.P.Morgan Chase $1,500 Q4 2013

Nomura $98 Q1 2014

ANZ AUD61 Q4 2013

Bank of Ireland €36 Q4 2013

Deutsche Bank €364 Q42012

Royal Bank of Scotland $475 Q4 2012

Barclays £101 Q4 2012

Lloyds Banking Group €143 Q4 2012

Goldman Sachs Unknown Q4 2011

Source: Supplementary notes of quarterly or annual financial disclosures.

willingness to accept FVA disclosures in dealers’ financial statements. See, for

example, Ernst and Young (2012) and KPMG (2013).

Current practice also implies that FVAs generate tax savings for dealers,

because their taxable incomes are lowered whenever swap values are reduced

by FVAs. However, as we show below, in economic terms, FVAs do not actually

involve a reduction in income.

Missing from the controversy over FVA, thus far, is a model that is consis-

tent with accepted theories of asset pricing and corporate finance and that

accounts for the effect of funding strategies on the market valuation of claims

on a dealer’s assets, most importantly, equity and debt. We provide such a

model, along with a number of implications for dealer quotations, trading desk

incentives, and preferred financing strategies.

We show, both theoretically and in calibrated numerical examples, that FVAs

are also an important determinant of dealer bid-ask spreads. Because the fi-

nancing of collateral or cash up-front payments can cause a change in capital

structure that is costly to dealer shareholders, dealers maximize shareholder

value by using quoting strategies that overcome this cost to their shareholders

with a sufficient widening of bid-ask spreads.

As an empirical example, Wang et al. (2016, p. 10) estimate the impact of

the 2009 “big-bang” introduction of up-front payments for credit default swaps

(CDS) on bid-ask spreads. They note that, “Intuitively, the up-front payment

is an impediment to trading, and so reduces the market liquidity, leading to