# FVA: off the mark

## With adjustments to increase, Darrell Duffie says dealers should improve weak valuation practices

Darrell Duffie is the Dean Witter distinguished professor of finance at Stanford University's Graduate School of Business

An intense controversy has been brewing among quants, accountants and academics over the recent practice known as FVA, or funding valuation adjustment. An FVA is a purported adjustment to the fair market value of a dealer's swaps book, designed to capture the cost of financing the cash necessary to enter and maintain certain swap positions.

The margin valuation adjustment (MVA) is an analogous adjustment for initial swap margins. In concept, MVA and FVA are essentially the same. Here, I will lump them together. My goal is to explain what these adjustments actually are, and what may motivate them.

As a warm-up, I will illustrate how FVA accounting would be applied to the purchase of one-year US Treasury bills that are held to maturity. Dealers would never actually apply an FVA to this sort of position, for reasons that will become obvious, but the example is instructive.

Suppose for simplicity that risk-free interest rates are zero, and that $100 million face value of the Treasuries are purchased by a dealer in a liquid market at par, funded by$100 million of new unsecured debt. The dealer has a one-year unsecured credit spread of 25 basis points. In one year, the Treasuries will pay off $100 million, and the dealer will repay$100.25 million on its financing, for a net loss L of $250,000. The loss will be borne by the dealer's shareholders only if the dealer survives. So, the dealer's shareholders suffer a loss in the initial market value of their equity of pL, where p is the dealer's risk-neutral one-year survival probability. For example, taking1 p = 0.995, the net cost to shareholder equity value is pL =$248,750.

If the dealer were to apply FVA accounting methods, the Treasuries would be marked-to-market at their entry value of $100 million, net of an FVA of$248,750 (computed by the same formula pL), for a net fair market value of only $99,751,250. Something just went wrong: the Treasuries clearly have an actual fair value of$100 million. Well, some might argue the Treasuries' position should be marked down a bit for liquidity by a bid/ask correction, but that would still leave a fair market value well above the purported FVA-adjusted fair value.

Although FVA practice aligns market-making incentives with shareholder interests, it fails some compelling tests of coherence with the principles of market valuation

As I said, dealers would not adopt FVA accounting in this situation. Yet current swap valuation practice follows exactly the same principles, as explained in some recent research I did with Leif Andersen of Bank of America Merrill Lynch and Yang Song of Stanford University.

The intricacies of swap valuation are too complex to go through here. But most major dealers do indeed arrive at their disclosed swap market values by subtracting an adjustment that is equal to the impact on equity market valuation of financing the required cashflows, using the same approach that I just explained in this simple example.

Why do dealers make these strange adjustments to their swap books? There is actually a good motive. Going back to the Treasuries example, the dealer's chief financial officer would not want shareholders to suffer a net loss in equity market value of 248,750. By adopting a practice of marking any position at its incremental value to shareholders in light of financing costs, rather than its actual market value, the chief financial officer properly aligns the incentives of the dealer's trading desks with those of shareholders. Traders would then conduct only those trades whose mark-to-market profit, net of FVA costs to shareholders, is positive. Although FVA practice aligns market-making incentives with shareholder interests, it fails some compelling tests of coherence with the principles of market valuation because it is simply not true that the market value of an asset or derivative position is equal to the market value of only that component of the net cashflows that go to equity shareholders. So, FVA accounting leads to inconsistencies, some of which have been pointed out by Hull and White (2014) and Albanese and Andersen (2014). So far, the cumulative total FVA of major dealers is under10 billion. The largest known instance occurred in 2014 when JP Morgan made a \$1 billion FVA to its swap book. These adjustments (including MVAs) will now get much bigger because dealers have begun to be forced by regulation to provide initial margin on a much greater fraction of their swap positions.

The major dealers or their external accounting auditors should straighten up these weak valuation practices before they get out of hand. Incentives can be aligned with other approaches.

1 The risk-neutral default probability 1–p can be approximated as the dealer’s credit spread divided by an estimate of LGD, the mean fractional loss to creditors on unsecured debt in the event of default. So, this example works with LGD = 0.5.