ENCUESTA REALIZADA A COMERCIANTES DEL MERCADO DE ABASTOS DE LA CIUDAD DE CHONE

FVAs are well suited to be used as aprofitability analysis tool by trading desks intended in entering into an OTC derivative trade. The reason can be find in Andersen et al. (2017) who claim that, despite funding costs do not affect derivative valuation, they are rather responsible of some widening in the bid- ask spread19_{. In these regards, my contribution aims at shedding light on the}

mechanism leading to the widening in a straightforward way.

In the case of selling the derivative to its counterpart, the dealer’s P&L at inception equals to:

P&LSell =UAsk−Vˆ −F V AAsk (2.38) so that the minimum upfront orentry price, at which the trading desk would be willing to sell (i.e. ask price), would be:

UAsk= ˆV +F V AAsk (2.39)

This occurs because the trading desk aims at least to be compensated for the sum of expected cash outflows correspondent to the liability ˆV and incremental funding costs deriving from the entrance into the trade.

On the other hand, if the dealer would be intended to hold a long position into the trade, its P&L at inception would equal to:

P&LBuy=−UBid+ ˆV −F V ABid (2.40) so that the maximum upfront at which the trader would be willing to buy (i.e. the bid price) is:

UBid= ˆV −F V ABid (2.41)

This occurs because the trading desk sees the value which it gets by holding the derivative security ˆV, decreased by the additional funding cost.

I here stress that the funding costs faced by the dealer in case of going long rather than short in the OTC derivative trade are in general different, i.e. F V ABid6=F V AAsk. Therefore, the overallwidening of the bid-ask spread caused by funding costs is:

UAsk−UBid=F V AAsk+F V ABid (2.42) In the next step, I quantify more precisely the amount by which the bid-ask spread widens when funding costs are incorporated within the analysis. Following my approach, under a symmetric funding strategy the impact would reflect the specular view of the moneyness of the contract relatively to the cases of assuming a long rather then short position in the derivative trade:

19_{In fact, the belief which FVA had driven bid-ask spreads during the past years of financial}

F V AAsk+F V ABid= Z τ¯ t EQ h sB_s Vˆ_s+−Vˆ_s−| Gt i ds + Z τ¯ t EQ h sB_s Vˆ_s−−Vˆ_s+| Gt i ds (2.43)

By simple rearrangements of equation 2.43 it can be intuitively obtained:

F V AAsk+F V ABid= Z τ¯ t EQ h sB_s −Vˆ_s++ ˆV_s+−Vˆ_s−−Vˆ_s−| Gt i ds= 0 (2.44) In other words, under the cited assumptions it holdsF V ABid=−F V AAsk. In presence of symmetry between borrowing and lending spreads, the impact of funding on the bid-ask spread disappears via an offsetting effect due to specular view of the moneyness when selling rather than buying. The present result extends the one of Burgard and Kjaer (2011b) who postulated that the FVA, interpreted as an additive correction on the fair price, expires when the funding spread is null. My argument is that the bid-ask spread widening expires not only in the case of no funding spread, being sufficient that borrowing and funding spreads are symmetric as in the Balance-Sheet Shrinkage funding policy. Moreover, such policy would be particularly appealing in the current market landscape for dealers with a sufficiently liquid own bond market. To my knowledge, it misses in previous literature a comparative analysis regarding the efficiency of Balance-Sheet Shrinkage with respect to other funding policies based on equity repurchasing or on a combination of equity and bond repurchasing. Such analysis would configure as the extension of the pecking order of preferences of firms’ shareholders of Andersen et al. (2017) to the investing side of funding cash flows. I point out that the present analysis applies to the impact of funding costs on bid-ask spreads and not to the P&L from the perspective of theshareholders utility maximization20_.

Conversely, bid-ask spreads widening is definitely not null when symmetric funding policies cannot be attained. For instance, suppose that the bank does not cope with a sufficiently liquid own bond market, meaning that it cannot invest available liquidity in repurchasing back its own debt at any point in time. In that scenario, negative rates would represent an extra cost for risk-free investing, configuring as the price of third party custodial service.

20 _{In fact as explained by Andersen et al. (2017), the shareholders marginal utility from}

entering in a new trade amounts to:

V∗= ˆV −DV A−F V A (2.45)

This occurs since, despite the DVA is nowadays well recognized by accounting principles in order to allow for symmetric trade prices, it does not involve any real benefit for the equity side of the firm upon default.

The overall widening of the Bid-Ask spread caused by the cost faced by the dealer for financing the hedges under an asymmetric funding policy amounts to:

UAsk−UBid=F V AAsk+F V ABid

= Z τ¯ t EQ h sB_s Vˆ_s++ ˆV_s−| Gt i ds (2.46)

My line of reasoning can then be summarized in the following remark.

Remark 1 (Bid-Ask spread widening). When the dealer faces an illiquid own bond market and decides to invest available liquidity at the risk-free rate, it incurs in instantaneous funding costs widening the bid-ask spread in the amount of its CDS spread. In the current negative rates environment, risk-free investing configures as an extra cost for the trading desk, interpretable as a custodial service price. Nevertheless funding can be used as a tool to evaluate the economic convenience of entering in derivative trades. In many cases, the optimal entry

price is expected to be different from the fair value.

In current market conditions, BSS funding might be assumed to be partic- ularly appealing for dealers coping with sufficiently liquid own bond markets. Without loss of generality, the existence of a liquid own bond market can be supposed to be common knowledge among market participants. Because of that, clients are eased in making conjectures about dealers funding requirements. That might increase clients awareness when bargaining with the counterpart on the trade price. Charging funding costs to clients is never be fair from a valuation point of view and, especially in presence of a liquid own bond market, the dealer is not legitimate to quote an oversized bid-ask spread. Nevertheless, because of the scarce transparency and high searching costs observed OTC markets, corporations might be willing to give priority to their economic purposes to book the trade and pay an unfair bid-ask spread. Therefore as explained in Castagna (2014), the actual price at which the OTC trades are closed is influenced by the bargaining power of the two counterparts. As a consequence, upfronts do not necessary reflect fair prices, which in turn deviate from dealers’ overall valuations, i.e. those affected by funding costs.