As simple as possible;
but no simpler

The Volcker metric known as inventory aging… and thoughts of Whisky

Inventory Aging is a rather innocuous looking member of the band of (now) seven metrics that, under the Volcker rule, banking entities with significant trading assets and liabilities are required to calculate daily and report monthly.

As written, the metric description seems straightforward enough:

Inventory Aging generally describes a schedule of the trading desk’s aggregate assets and liabilities and the amount of time that those assets and liabilities have been held. [It] should measure the age profile of the trading desk’s assets and liabilities and must include two schedules, an asset- aging schedule and a liability-aging schedule.

The graphic below broadly outlines the processes of asset/liability tagging, matching, sorting and netting of trades involved in generating an inventory aging schedule.


P&L Attribution – Judging the weathermen

“The storm starts, when the drops start dropping
When the drops stop dropping then the storm starts stopping.”
― Dr. Seuss, Oh Say Can You Say?

“Pray don’t talk to me about the weather, Mr. Worthing. Whenever people talk to me about the weather, I always feel quite certain that they mean something else. And that makes me so nervous.”
– Oscar Wilde, The Importance of Being Earnest, Act 1

We will talk about weathermen and the predictions they make. And we will mean something entirely different. By weathermen, we will mean the models in a bank and the predictions they make or the hypotheses they form. And for the realism of Dr. Seuss’ drops dropping, we will substitute the realism of P&L..  More specifically, we will talk about P&L attribution (PLA) and the role it plays in helping us use the realism of P&L to test the hypotheses posed by our various risk models – which actually is its primary purpose in life.

We will focus specifically on 3 hypotheses formulated by a bank’s risk models, its VAR model and its CVA/EPE model respectively. Namely, for a given bank:

I.         Change in the mark-to-market value of its positions are materially determined by changes to a specified set of variables and parameters (i.e. risk factors) and the expected change is quantified by the sensitivities obtained to these risk factors from its models;

II.         There is a specified % probability that the value of its positions will lose more than its VAR number over any given interval equal to the VAR holding period;

III.         The cost of insuring its aggregate positions against the risk of counterparty Z defaulting is not expected to exceed the cumulative sum of the CVA fees charged to its trading desks for originating exposure to counterparty Z.


A Practical Example of Classification

Of herding 1 million hissing cats onto a carousel somewhere a few blocks north of Bryant Park in New York. It must be said though that the music on this particular carousel had stopped (and Edith Piaf had most definitely left the building).

As part of the unwind of Lehman Brothers’ derivatives portfolio for the post-bankruptcy Estate (a portfolio of over 1 million derivatives trades); the team conducted a classification exercise of the products in the portfolio (with underlying covering all major asset classes; and instruments running the gamut of complexity from vanilla single factor single asset class flow products to highly exotic structured multi-factor hybrid products).

The context and objective was valuing them in the shortest possible time, in the most efficient manner possible (given limited to no infrastructure), in the most defensible manner possible (given their eventual day in Bankruptcy court) over the days in September/October 2008 when they were unwound.

This classification exercise was essential to developing and driving the valuation strategy for the portfolio, covering:

  • Team selection;
  • Valuation platform, model and method selection;
  • Computational resource provisioning;
  • Market data requirements definition;
  • Developing the netting and hedging assumptions needed to take a view on reasonable bid/offer and transaction costs;
  • And conducting self-consistency checks of the valuations.

A complex and gargantuan valuation exercise that could only be accomplished by intelligent abstraction of product commonality through classification.

Classifying Derivatives (or herding cats onto a carousel)

It is always easy to find fault with a classification. There are a hundred ways of arranging any set of objects, and something may almost always be said against the best, and in favour of the worst of them. But the merits of a classification depend on the purposes to which it is instrumental.

John Stuart Mill
Auguste Comte and Positivism

Classification as used here attempts to arrange traded financial derivatives into product classes or groups based on similar or related properties; properties as identified within a defined scheme of taxonomies; and similarity of properties as meaningful within some context.

The motivation for classification here is not much different to classification in biology in that the focus is not so much on the naming of things but on coming up with the best possible ordering of our knowledge base about the properties of the objects being classified such that the ordering gives us the greatest contextual command of the knowledge already acquired about the objects, and also leads us in the most direct way to the acquisition of more.

In plain English and as an example, within the context of classification for risk based P&L attribution policy as an example, we want to think of how to order the properties of financial derivative contracts in such a way that we can group them around the types of risk sensitive behavior they are likely to exhibit and thus how their P&L behavior may be best explained. Additionally, a fundamentally intuitive grouping helps shed light on more risk-sensitive properties that may be applicable within groups.


The contract before the chicken and the egg

To the perennial question “Which comes first; the music or the words”? Ira Gershwin responded, “What usually comes first is the contract”.

And so it is with financial instruments like derivatives, which after all are contracts – whether standardized or bespoke.

The structure of the contract – unsurprisingly – influences its behavior.

Structure would be the terms of the contract (as found in the confirm or term sheet).  This would detail: the commitments required and resources committed under the contract (e.g. the payouts or payments to be made, the instruments to be referenced or delivered, the notices or services required etc.); the parties involved in these commitments (e.g. the counterparties to the trade, payment or calculation agents etc.); and the events that both govern and unfold from the realization of these commitments (e.g. time, an embedded choice, a default or downgrade etc.). The sharp-eyed will notice the (deliberate) borrowing of terminology from the REA accounting model – more of which to come.

Behavior can be thought of both as the remaining state space of possibilities that the contract embodies and the actual realization of paths through that state space. The state space is bounded (and so influenced) by the contract terms – e.g.

  • The specified parties bound actors that can be involved in the execution of the contract,
  • The contract’s maturity time-bounds its existence,
  • A knock-out barrier in a barrier option state-bounds the contract’s existence.

Behavior in turn influences (future) structure in that the realization of certain states within the state space can alter the (future) state space of possibilities

– think how an option exercise constrains the state space of the un-exercised option, or how the default of a reference entity within the index constrains the state space of an index default swap, or the touching of a knock-in barrier expands the state space of a barrier option, or just the passage of time on the state space of an option (all else being equal).

Much of the management of a financial derivative contract (or indeed any financial contract) involves an ongoing analysis of that bounded state space of possibilities

– whether in forming an expectation/probabilistic view and thus valuation of some or all of the states (in MTM, risk or collateral calculations say), or in determining the set of events embodied in one or more states (e.g. in determining payments for settlement or funding requirements).

We will use this structure and behavior axes often in our thinking about derivative contracts, their management processes and systems as it offers a very useful and intuitive way of thinking of similar sets of derivatives and financial instruments in general and also in thinking of how to dimension the complexity of products and their associated processes.