1. DVA, Own Credit and Funding cost: The unresolved issues Tanguy DEHAPIOT

2. Accounting and regulatory rules for Own Credit
Basel III paragraph 75 (following the 25th July 2012 amendment)
“Derecognise in the calculation of Common Equity Tier 1 all unrealised gains and losses that have resulted from changes in the fair value of liabilities that are due to changes in the bank’s own credit risk.
In addition, with regards to derivative liabilities, derecognise all accounting valuation adjustments arising from the bank’s own credit risk. The offsetting between valuation adjustments arising from the bank’s own credit risk and those arising from its counterparties’ credit risk is not allowed”
Derecognise variation for debts
Derecognise full stock for derivatives
Intensive debate between regulators and the financial industry following Basel Committee consultative document “Application of own credit risk adjustments to derivatives”, December 2011

3. Accounting and regulatory rules for Own Credit
CRR Article 30 – prudential filter for liabilities
Institutions shall not include the following items in any of own funds:
(b) Gains or losses on liabilities of the institutions that are valued at fair value that result from changes in the own credit standing of the institution.
(c) All fair value gains or losses arising from the institution’s own credit risks related to derivative liabilities. Institutions shall not offset the fair value gains and losses arising from the institution’s own credit risk (e.g. DVA) with those arising from its counterparty credit risk (e.g. CVA)
Modification compared to Basel III article 75 that required to derecognise the full DVA amount (not the variation)

4. Accounting and regulatory rules for Own Credit
IFRS 9 paragraph (a)
“The amount of change of fair value of the financial liability that is attributable to the change of credit risk of that liability shall be presented in other comprehensive income”
Realised gain on repurchases not recycled into P&L
Fair value option debts only  not applicable to derivatives
IFRS 9 paragraph B5.7.16
“The amount of change of fair value attributable to changes in credit risk of a liability can be determined as the amount of change in its fair value that is not attributable to changes in market condition that give rise to market risk; or using an alternative method…”
IFRS 9 paragraph B5.7.17
“Changes in market conditions that give rise to market risk include changes in a benchmark interest rate, the price of another entity’s financial instrument, a commodity price, a foreign exchange rate”

5. Accounting literature on Own Credit
IASB Staff paper: “Credit Risk in Liability Measurement”, June Discussion paper DP/2009/2
Questions from discussion paper:
When a liability is first recognised, should its measurement incorporate the price of credit risk inherent in the liability?
Should current measurement following initial recognition incorporate the price of credit risk inherent in the liability?
Project Principal for staff paper: Wayne S. Upton Jr.
Arguments for incorporating credit risk:
Consistency at initial recognition, Wealth transfer, Account. mismatch
Arguments against incorporating credit risk:
Counter-intuitive results, Accounting mismatch, Realisation
Alternatives to consider
1. Risk free debt + loss to income, 2.Risk free debt + charge to equity, 3. Freeze credit spread

6. The paradox: which company is stronger?
“Strong corporation” invests in low risk assets
“Weak corporation” invests in high risk assets
 “Strong corporation” seems to have more leverage, so more risky
 The higher the asset risk, the higher the equity, the stronger it appears
Debt
100 proba 90%
0 proba 10%
Fair value 90
Fair value
100
Low risk asset
111 proba 90%
0 proba 10%
Leverage 9
Equity
Fair value 10
Debt
100 proba 80%
0 proba 20%
Fair value 80
Fair value
100
High risk asset
125 proba 80%
0 proba 20%
Leverage 4
Equity
Fair value 20

7. Realisability: Debt repurchase
Initial investment:
Sell all assets then repurchase debt with cash raised:
 We do not manage to realise the own credit gain
Debt
100 proba 80%
0 proba 20%
Fair value 80
Fair value
100
Risky asset
125 proba 80%
0 proba 20%
Equity
Fair value 20
Debt
100
Risk free
Fair value
100
Fair value
100
Cash
100
Equity
Fair value

8. Counterintuitive effect of change of credit risk
Initial investment:
Switch to new investment at no cost:
 Did the COMPANY make a gain?
 Should it pay tax, dividends, bonus on this gain?
Debt
100 proba 90%
0 proba 10%
Fair value 90
Fair value
100
Low risk asset
111 proba 90%
0 proba 10%
Equity
Fair value 10
Debt
100 proba 80%
0 proba 20%
Fair value 80
Fair value
100
High risk asset
125 proba 80%
0 proba 20%
Equity
Fair value 20

9. FASB Arguments for incorporating Credit risk
FASB paper: “Credit Standing in Liability Measurement” (G. Michael Crooch, Wayne S. Upton), June 2001
Should credit standing affect the measurement on initial recognition?
PRINCIPLE: “The simple act of borrowing money at prevailing interest rates is not an event that gives rise to a gain or a loss”
CONCLUSION: “Any measurement that reports a loss from the simple act of borrowing at the market rate must be rejected”
Should credit standing affect subsequent fresh start measurement?
PRINCIPLE: “The fair value measurement system should not attach different measurements to assets and liabilities that are economically the same”
CONCLUSION: “Excluding changes in credit standing leads inevitably to measuring two identical liabilities at different amounts. That must surely provide an ‘inaccurate’ reading”

10. FASB Arguments for incorporating Credit risk
At inception, if the debt is valued as default free rather than with its current credit risk, we would need to record a loss
If credit changes and we issue a new debt, the old debt must have the same value as the new debt
ASSETS
Debt
100 proba 80%
0 proba 20%
Fair value 80
Cash received 80
Bond value 80
Risky asset
125 proba 80%
0 proba 20%
Fair value
100
Fair value 20
Cash received 20
Share value 80
Equity
Old Debt
100 proba 80%
50 proba 20%
Risky asset 1
125 proba 80%
0 proba 20%
Fair value 90
Fair value
= 200
New debt
100 proba 80%
50 proba 20%
Fair value 90
Safe asset 2
100 proba 100%
Fair value 20
Equity

11. Limited liability vs unlimited liability
Initial investment from limited liability company
Conversion to an infinite liability company
Creditors pay 20 to shareholders to make the change fair
The transformation is equivalent to bondholders buying a credit protection from the shareholder  What is the P&L?
Debt
100 proba 80%
0 proba 20%
Fair value 80
Fair value
100
Risky asset
125 proba 80%
0 proba 20%
Fair value 20
Equity
Debt
100
Guaranteed by shareholders
Fair value
100
Fair value
100
Risky asset
125 proba 80%
0 proba 20%
Fair value
Equity

12. The shareholder insolvency put
Limited liability company
Infinite liability company + shareholder insolvency put
The two representation are economically equivalent for creditors and shareholders  is the company’s equity the same?
Debt
100 proba 80%
0 proba 20%
Fair value 80
Creditors
Fair value
100
Risky asset
125 proba 80%
0 proba 20%
Fair value 20
Equity
Shareholders
Put option
Debt
100
Guaranteed by shareholders
Fair value
100
Fair value
-20
Creditors
Fair value
100
Risky asset
125 proba 80%
0 proba 20%
Fair value
+20
Fair value
Equity
Shareholders

13. The third party guarantee representation
IFRS 13 paragraph 44
“The issuer of a liability issued with an inseparable third party credit enhancement that is accounted for separately from the liability shall not include the effect of the credit enhancement (e.g. a third party guarantee on debt) in the fair value measurement of the liability”
i.e.: the third party guarantee is outside the balance sheet of the issuer
Does it make a difference if we guarantee the assets rather than the liabilities?
Does it make a difference if the guarantee is provided by the parent company (i.e.: the shareholders)?

14. Merton & Perold analysis
Theory of Risk capital in financial firms, R. Merton & A. Perold, 1993
They compare 3 situations:
Guarantee on assets of the company by third party
Guarantee on liabilities of the company by the parent company
Defaultable liabilities with no guarantee
Conclusion: Risky debt = Default free debt – Debt insurance by creditors
A limited liability company is equivalent to an asset insurance purchased by the company from the creditors
Risky asset
125 proba 80%
0 proba 20%
Default free debt
100
Fair value
100
Fair value
100
Asset insurance
0 proba 80%
100 proba 20%
Fair value 20
Equity
Fair value 20

15. Francis, Heckman, Mango analysis
Credit Standing and the Fair Value of Liabilities: A Critique, Philip E. Heckman, 2003 (published 2004)
Insolvency Put: Whose Assets, Louise A. Francis, Philip E. Heckman, Donald F. Mango, 2005 (FHM)
They start with the analysis of the firm value: The Franchise value needs to be added to the Tangible asset value
They consider like Merton & Perold that the risky debt must be decomposed as a default free debt plus an insolvency put
The differ from Merton & Perold because they consider that the insolvency put is not an asset of the company as it provides benefits only to its owners
The creditors have not sold the insurance to the company but to the owners (limited liability shareholders)
The insolvency put is not an asset distributable to creditors
The difference between default free debt value and risk debt value is a borrowing penalty charged to earning

16. Different balance sheets
Accounting view Market view
Economic
Public balance sheet (FHM) value
Risky debt
including
own credit
Risky debt
including
own credit
Tangible assets
at market
Bonds FV
Tangible
assets
at market
Equity
Franchise
value
Shares FV
Owner value
- Insolvency put
Bonds FV
Debt at default free value
Debt at default free value
Tangible assets
at market
Tangible
assets
at market
Entreprise
net worth
Franchise
value
Entreprise net value
Shares FV
+ Insolvency put

17. Chasteen & Ransom analysis
Including Credit Standing in Measuring the Fair Value of liabilities – Let’s pass This One To the Shareholders, Lanny G. Chasteen & Charles R. Ransom, June 2007 (C&R)
The liability is measured as if it is default free: entities with identical obligations should report liabilities of identical amounts
The difference between default free value and the risky value is the put option, which is an asset of the shareholders
This difference is recorded as a distribution to shareholder (decrease in equity)
Interest expenses in P&L are based on the current borrowing rate (risky). The difference between interest rate expense and default free value variation is accounted as an increase in shareholder’s equity
Change of the entities credit risk has not direct P&L impact but change in the default free rate has a P&L impact

18. The two views in debt measurement
FASB Approach: Asset and Liability symmetry
“For a liability, fair value should reflect the amount that would be paid by the reporting entity to transfer the liability to a willing third party of comparable credit standing (lay off amount)”
“When estimating fair value, we must be sure that the estimate is for the liability that is recognised in the financial statement, and not some other item”
Liability seen as an asset of a creditor
The alternative approach: Asset and liability differences
“The different entities with the same promised stream of cashflows should report the same obligation regardless of the proceeds received in exchange of the promise”
“A liability should be valued solely on the basis of the contractual terms under the assumption that the contract will be performed”
Liability seen as the performance of an obligation from the debtor

19. Example D (Assets – Debts) = D Equity = P&L + OCI + Var. Capital
100 proba 80%
0 proba 20%
Risky asset
125 proba 80%
0 proba 20%
Fair value
100
Equity
T0: Start of company (no asset, no debt, no equity)
T1: Raise 20 Capital from shareholders  Invest in risky assets
T2: Raise 80 Debt with redemption 100  Invest in risk assets
T3: Assets perform: sell assets for 125, pay back debt
We show the cash movements as well as P&L and capital movements

20. Chasteem & Ransom analysis (1)
T1: Capital investment 20 20
Assets I S
Shareholders
Purchase assets
Capital increase
Value = 20
Net Worth =20
T0 T1: P&L = 0, Var. Capital = +20
T2: New Debt
New debt
(Default free)
Bondholders B
Value = = 80 80
Assets I
Sell Put
100 20
Purchase assets
Buy Put
Entity 20 S
Shareholders
Net Worth = 0
Capital
distribution
Value = 20
Put = 20, Intrinsic Value = 0
T1 T2: P&L = 0, Var. Capital = -20

21. Chasteem & Ransom analysis (2)
T3: Debt redemption (no default)
Redemption B
Bondholders
100
Value = 100, P&L = +20
125
Assets I
Sell assets
Entity
Shareholders S
Net Worth = 25
Value = 25, P&L = +5
T2 T3: P&L = +25 – 20 = +5, Var. Capital = +20
Recycle 20 from capital account into P&L
Differences FASB, Heckman, Chasteem & Ranson
FASB: T2 no impact on equity, P&L = 0, T3 P&L +5
Heckman: T2 borrowing penalty in P&L -20, T3 P&L +25
Chasteem & Ranson: T2 Capital decrease, T3 recycle to P&L

22. Does Funding spread exist without credit risk?
Example of investments with no credit risk
Investment 1: rolling overnight loan  pays EONIA
Investment 2: Fixed term loan  pays EONIA + spread
Why do investor require a strictly positive spread ?
Non arbitrage argument
Term loan + rolling overnight borrowing = profit with certainty
Strong assumptions:
No bid-offer
We can always borrow overnight at EONIA
Permanent borrowing at EONIA is not guaranteed
Bid-offer cost + capital charge
If we borrow continuously, we may be charged more than those who alternate borrowing and lending, event with no default risk
EONIA is an average: some pay more than others

23. FVA: Separating Credit and Funding cost
A debt is issued at a spread over “Risk-free” rate. This is an “all-in” financing cost that is observable. This spreads includes:
The issuer credit risk
A “pure” cost of term funding (locking financing for a term)
A measure of the attractiveness of the paper (supply and demand)
Ignoring the last component, there are two ways to split between credit and funding
Assume credit risk spread is measured by CDS and consider the pure funding spread as the residue  The basis
Assume “pure” funding cost is measured with secured debt (covered bonds) and consider the credit spread as the residue
The two methods lead to totally different splits
The first method lead to volatile credit spread and often negative funding spread (if we borrow below CDS spread)

24. Discounting assets at cost of funding (incl. credit)
Debt
200 proba 80%
100 proba 20%
Risky asset
125 proba 80%
0 proba 20%
Expected value
180
Equity
25 proba 80%
0 proba 20%
Safe asset
100 proba 100%
Valuation of assets with Funding Cost Adjustments:
Debt discount rate = 11.1% = cost of funding
Risky asset value: 100 x 0.9 = 90
Safe asset value: 100 x 0.9 =90
Net equity value: 180 – 180 = 0
 Same effect as removing Own credit effect from debt

25. Equity impact of new derivative
Initial situation
Debt
100 proba 80%
0 proba 20%
Fair value 80
Fair value
100
Risky asset
125 proba 80%
0 proba 20%
Equity
25 proba 80%
0 proba 20%
Fair value 20
Simple derivative
80%
+10 C does not default
Market up
Pu = 50%
20%
0 C defaults
80%
-10 I does not default
Market down
Pd = 50%
20%
0 I defaults

26. Scenarios with debt and derivatives
Asset Ctpy Market Proba Debt Deriv. Equity Put S
OK OK Up 32%
OK OK Down 32%
OK Default Up 8%
OK Default Down 8%
Default OK Up 8%
Default OK Down 8%
Default Default Up 2%
Default Default Down %
100%
A: Asset value L: Contractual debt D: contractual derivative pay-off
Put S = Max(L-A-D,0) = (L-A-D). 1L-A-D>0 = 20.2
Put S = (L-A-Max(D,0)). 1L-A-D>0 + Max(-D,0). 1L-A-D>0
Put B = Put C = DVA = 1

27. Derivative counterparty
Initial payment flow
Before trading derivative
New debt
(Default free)
Bondholders B
Value = = 80
Entity I
100 20
Sell Put
Buy Put 20
Net Worth = 0
Capital
distribution
Shareholders S
Put So = Put Bo = 20,
After trading derivative
Derivative counterparty C
Value = = 80
Entity I 1 1 B
Bondholders
Put C
Var Value = 80.8 – 80 = 0.8
Net Worth = -1
0.8? 1
Shareholders
Capital
distribution S
Put S1 = Put C + Put B1 = 20.2

28. DVA analysis with external shareholder put
DFV: Default free value DFV(I) = - DFV(C) = 0
CRV: Counterparty risk value CRV = DFV –CVA
DVA(I) = Put(SI) = 1 SI SC
DVA(C) = Put(SC) = 1
Buy Put
Buy Put 1 1
Capital decrease
Capital decrease 1 1 I C
Default free derivative
CRV(I) = DFV(I) –CVA(I) = -1
CRV(C) = DFV(C) –CVA(C) = -1
Total Value I + SI = 0
Total Value C + SC = 0

29. Conclusion We have detailed the alternative valuation of liabilities.
DVA does not belong to the entity but is an asset of the shareholders (the limited liability guarantee is a put option).
The entity is compensated for the CVA cost at deal inception, so initial P&L is zero and both counterparties agree the price.
The entity has implicitly made a capital distribution (decrease) to the shareholder and share intrinsic value decrease but time value increases. DVA is like a dividend in kind.
Basel III paragraph 75 seems correct: the new derivative generates a decrease of CET1 capital. Stock vs. variation.
The new derivative affects the value of other debts without proper compensation between shareholders and creditors.
New subject: do we need a valuation adjustment for the cost of capital that we can call KVA?