## Thursday, 3 March 2016

### Liquidity in context - II

Last time I was thinking about funding liquidity and had in my head the multi-strategy hedge fund.  The two primary demands for cash come from prime brokers, who might offer less favourable leverage terms to the hedge fund, which would manifest itself as a demand for more cash to be deposited with them for a given set of holdings on the hedge fund's book at that PB.  The fund would then stump up more cash or gross down their set of holdings.  The second demand is if a significant number and weight of investors in the fund decided, subject to their gates, to redeem their investment.  Th.is is either going to be funded out of the hedge fund's cash (or cash equivalents) bucket or it will make them sell some of their assets and liabilities.  Which brings me on to ...

Asset Liquidity. (Or more strictly speaking, bottom up asset liquidity).
A firm owns a number of units of some security.  The 'asset liquidity' question arises about that holding.  The form of the question is always one of T|CF, C|TF or F|C,T and the source of the answer comes from (1) two facts about the firm and (2) a set of facts about the market for that security.

The primary firm fact is the position size.  The secondary fact is which collection of constraints are apposite for the liquidation of that asset.  The constraints impose costs (financial, time, fraction) on the unwind.

The market facts are more numerous.  Measuring a market's liquidity is a large subject and the set of data to come to an opinion about its current liquidity is probably asset type and market-specific.  But in general they are statistical reads on the market.

The final piece of the puzzle is how to codify the various statistical reads on the market to produce a liquidity response curve for that market at that time.  Actually, it is not a 2D curve but a 3D surface, with the primary independent variable being F*E, the fraction of the fund's holding of this security being targeted in the liquidity scenario at hand, multiplied by the exposure, E this firm  has to the asset (in simple cases, its quantity).  The surface exists for every exposure point.  In the most general case, the set of curves would extend into negative exposure values for F*E, allowing for asymmetric markets.  The slightly  simpler case is to assume the market is symmetrical and the sign of the exposure is not important.

Whilst in theory all those response curves exist, for any given day, you may only be interested in a single one of them, namely the curve associated with the F*E value in play on that day in your firm.

Usually, either the cost threshold is a parameter of the liquidity run, or the time threshold is given.  In this case, the surface becomes a curve.  E.g. Time(F*E|F=100%, C<1%)  - a safe and compete wind down curve / asset liquidity estimate.  Cost(F*E|F=50%,T=3d) - a drop dead target of 3d to reduce the holding size by half.  Both of these are asset liquidity estimates.

Think of the cost and time curves both in terms of the absolute cost (EUR) or time (days) for a position of size F*E to be unwound, in which case this is an upward sloping convex curve of some sort or another; or think of the cost as a cost per unit, in which case its convexity is fully explained by the expect saturation cost associated with bringing a larger and larger fraction to market.  Very liquid markets have a flat per-unit response curve both for time and cost.

I will call these per-unit response curves lower case $t_m(F_s \times E_f|F_s,C_s,n_s)$ where $m$ stands for a market object, $s$ being a liquidity scenario parameter and $f$ being a fact of the firm and $n_f$ being the collection of firm unwind constraints.  Likewise the second of the possible asset liquidity measures is $c_m(F_s \times E_f|F_s,T_s,n_s)$.