The global financial crisis led to a lot of turmoil in derivative markets and large players introduced a number of changes in their valuation models. Acronyms like CVA (Credit Value Adjustment), DVA (Debit Value Adjustment) and FVA (Funding Value Adjustment) became quite commonplace. Of these, CVA and DVA have strong theoretical foundations and have gained wide ranging acceptance. But FVA remains controversial as it contradicts long standing financial theories. Hull and White wrote an incisive article The FVA Debate explaining why it is a mistake to use FVA either for valuing derivative positions on the balance sheet or for trading decisions. But four years later, FVA shows no signs of just going away.
Three months back, Andersen, Duffie and Song wrote a more nuanced piece on Funding Value Adjustments arguing that FVA will influence traded prices, but not balance sheet valuations. I have written a simplified note explaining the Andersen-Duffie-Song model, but at bottom it is a capital structure (debt overhang) issue than a derivative valuation issue.
Consider therefore a very simple capital structure problem of borrowing a small amount (say 1 unit) to invest in the risk free asset. The qualifier “small” is used to ensure that this borrowing itself does not change the company’s (risk neutral) Probability of Default (PD), Loss Given Default (LGD) or credit spread (s). From standard finance theory we get s=DL/(1-DL) where the expected Default Loss (DL) is given by DL=PD×LGD. For simplicity, we assume that the interest rate is zero (which is probably not too far from the median interest rate in the world today).
At default (which happens with probability PD), the pre-existing creditors pay only (1-LGD)(1+s) to the new lender and receive 1 from the risk free asset for a net gain of LGD-s+s×LGD. The expected gain to the unsecured creditors is therefore: PD(LGD-s+s×LGD) which after some tedious algebra reduces to (1-PD)s
If there is no default (which happens with probability 1-PD), the shareholders pay 1+s to the new lender but collect only 1 from the risk free asset. The expected loss to them is (1-PD)s which is the same as the expected gain to the pre-existing creditors.
The transaction does not change the value of the firm, but there would be a transfer of wealth from shareholders to pre-existing creditors. Somebody who owns a vertical slice of the company (say 10% of the equity and 10% of the pre-existing debt) would be quite happy to buy the risk free asset at its fair value of 1, but if the shareholders are running the company, they would refuse to do so. (This is of course the standard corporate finance result that a debt overhang causes the firm to reject low-risk low-return positive NPV projects because they transfer wealth to creditors). The shareholders would be ready to buy the risk free asset only if it is available at a price of 1/(1+s). At this price, the shareholders are indifferent, the pre-existing creditors gain a benefit and the counterparty (seller of the risk free asset) suffers a loss equal to s/(1+s). The price of 1/(1+s) includes a FVA because it is obtained by discounting the cash flows of the risk free asset not at the risk free rate of 0, but at the company’s funding cost of s.
Now consider a derivative dealer doing a trade with a risk free counterparty in which it has to make an upfront payment (for example, a prepaid forward contract or an off-market forward contract at a price lower than the market forward price). If the derivative is fairly valued, the counterparty would be expected to make a payment to the dealer at maturity. From the perspective of the dealer, the situation is very much like investing in a risk free asset (note that we assume that the counterparty is risk free). The shareholders of the derivative dealer would not agree to this deal unless there were a funding value adjustment so that the expected payment from the counterparty were discounted at s instead of 0.
Now consider the opposite scenario where the dealer receives an upfront payment and is expected to have to make payments to the counterparty at maturity. This is very much like the dealer taking a new loan to repay existing borrowing (Andersen-Duffie-Song assume that the dealer uses all cash inflows to retire existing debt and finances all outflows with fresh borrowings). There is no transfer of wealth between shareholders and creditors and no funding value adjustment.
The result is the standard FVA model: all expected future inflows from the derivative are discounted at the funding cost and all expected outflows are discounted at the risk free rate. This is because the future inflows require an upfront payment by the dealer (which requires FVA) and future outflows require upfront receipts by the dealer (which do not require FVA).
Andersen, Duffie and Song correctly argue that (unlike CVA and DVA) the FVA is purely a transfer of wealth from shareholders to pre-existing creditors and is not an adjustment that should be made to the carrying value of the derivative in the books of the firm. This part of their paper therefore agrees with Hull and White. However, Andersen, Duffie and Song argue that in the real world where shareholders are running the company, the FVA would be reflected in traded prices. Dealers would buy only at fair value less FVA. They argue that this is quite similar to a bid-ask spread in market making. The market maker buys assets only below their fair value (bid price is usually below fair value). Just as for liquidity or other reasons, counterparties are willing to pay the bid ask spread, they would be willing to pay the FVA also as a transaction cost for doing the trade.
I wonder whether this provides an alternative explanation for the declining liquidity in many markets post crisis. Much of this has been attributed to enhanced regulatory costs (Basel 3, Dodd-Frank, Volcker Rule and so on). Perhaps some of it is due to (a) the higher post crisis credit spread s and (b) greater adoption of FVA. The increasing market share of HFT and other alternative liquidity providers may also be due to their lower leverage and therefore lower debt overhang costs.