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Why using mid price to compute mark-to-market P&L if it is less accurate than using bid/offer price? If spread is wide, mid is really not representative of what you would get by getting rid of your inventory. Using best bid/offer would be more accurate even if it does not include slippage. Why don't we use best bid/offer to compute MTM P&L?

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This is an excellent philosophical question.

Recall that the goal of mark to market is to predict the P&L if we unwound this position in an orderly market.

Suppose that you're in a very convinient world, where for every asset you know at all times the bid and offer (ask) prices, at which you can sell or buy these assets.

Suppose you're just long some assets and don't do anything more complicated. It makes sense to mark them at bid, which is a more realistic prediction of what you'd receive if you unwound the position than mid; as well as more "conservative", as accountants say. The most common reasons for using mid, rather than bid, in this scenario are:

  • it is sometimes harder to observe bid/offer than mid in real life. You may be less confident in the bid/offser spread than you are in the mid. The b/o spread may have very different dynamics (in particular, be less volatile) than the mid.

  • the people marking the assets just want to look better.

Next, suppose that you're short some assets. There are many ways to accomplish this. For example (naked short), you could borrow an asset, sell it to someone, and later buy the asset (or its "fungible" equivalent), and return it to the asset lender. How should you mark your short position? Since you need to buy the asset at offer price in order to flatten your short position, it seems reasonable to mark the short position at offer price, which is more conservative than mid. In contrast, the asset buyers can mark their side of the trade at bid, since they don't care that they bought an asset that you borrowed.

But suppose that instead you are long the asset and you sold a total return swap (TRS) on the asset. You agree that the TRS buyer can unwind at certain times, then you will sell your asset (at bid), and give the proceeds to the TRS buyer. It seems more reasonable to mark the short TRS at bid.

As you can see, even with very simple contracts there are a lot of subtly different use cases and a lot of room for different interpretations of simple principles. Once you get into more complicated derivatives, it just gets too hard to track.

Many methodologies for calculating fair price of derivatives assume that

  • bid = offer;

  • if we can replicate the payoffs of one portfolio with the payoffs of another portoflio, then the two portfolios have the same fair price. But keeping track of where the repicating portfolio uses which side can get confusing.

Practically, it is much easier to mark at mid and to add on a reserve for bid-offer under normal market conditions, as well as for liquidity, and other uncertainties. It is also more informative than lumping together mid-based mark and b/o spead.

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    $\begingroup$ I would add that, at a theoretical level, we usually are assuming that the fundamental value of traded assets lies somewhere in the bid-ask spread, with the existence of the spread reflecting things like transaction costs and asymmetric information. Many models create a symmetric bid-ask spread about the fundamental value, or something very close to it. So, there might simply be a cultural understanding, a sort of convention if you will, that the mid point is just 'fair value.' $\endgroup$ – Stéphane Dec 29 '20 at 16:13
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    $\begingroup$ Yes I get it, it's to get the "fair value". But practically it's used as an approximation to realized pnl, and for that you don't care about the "fair value", what you care about is what would be realized pnl at time t. Without getting into derivatives, even for spot FX you'll find that most methodologies use mid, while they could use best bid/offer of most liquid ECNs to derive mtm pnl. Why is it "easier to mark at mid"? If you stream live prices from the main ECNs it's easy to compute mtm pnl using best bid/offer. $\endgroup$ – AnastasiaShishkova Dec 29 '20 at 16:47
  • $\begingroup$ OK, simple FX. Suppose that we price in USD, and that we're long EUR 1 in one book, and also short EUR 1 in another book. To me, this picture looks much more clear if we mark both the long and short EUR exposures at the same mid, and further add on bid-offer reserves in each book, than if we simply marked at bid and offer - hiding theit composition. $\endgroup$ – Dimitri Vulis Dec 29 '20 at 17:02
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    $\begingroup$ Indeed, carried to an extreme one could create two offsetting portfolios long Eur1bn and short Eur1bn for the deliberate effect of manipulating pnl downwards inappropriately, if bid offers are applied automatically to all portfolios. $\endgroup$ – dm63 Dec 31 '20 at 11:53
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Most banks use mid market to compute daily MTM p/l whilst maintaining a reserve to account for liquidation costs. The latter is usually recalculated periodically and is indeed a function of market bid-offers.

Market participants may use different methods because the definition of MTM pnl may differ depending on jurisdiction, accounting standards etc.

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