Collateral Optimization
Collateral Optimization
Why Optimize
A particular item in inventory, such as holding of a specific stock, can be used in a wide range of ways. The revenue or cost savings varies greatly depending on how the stock is used.
Generally there are two categories of usage:
- Security specific uses. Borrows of specific securities for a range of purposes (shorting, fails, ...). Optimization can more effectively re-use available inventory to reduce the cost of borrowing
- Secured borrowing/collateralization where a range of acceptable collateral can be used. Both the most optimal collateral and the source of the collateral have to be determined
The two problems are related. If a specific item is used for one purpose, such as 100 shares of a specific stock is used for collateralization (which can use a wide range of securities), it cannot also be used to covers a short sale (which requires the specific stock).
Sources and Uses
A given item in inventory can be used in a vast number of different ways. For example, use for a short; lent out via stock loan; pledged as collateral to a wide range of OTC, Exchange Cleared and Exchange traded margin arrangements; pledged as Tri-party collateral (Derivatives trading); used for regulatory segregation; etc.
The same applies to sources, where inventory held at multiple repositories, rehypothecated collateral received from counter-parties; customer assets that can be rehypothecated (140% of the margin loan amount); fully paid borrowing; substitution (changing collateral that has already been pledged); etc.
Even with a partial integration of some of the sources and uses of collateral - there is an explosion of possible ways to use collateral. Optimization improves the overall use and can provide significant savings. Even the most simplistic optimization - where collateral is used, beats collateral sitting around in inventory and not being used.
Timing
If all the sources and uses of collateral were available in a single platform at a single point in time, then this is an interesting optimization problem. The problem is a combinatorial nightmare. It is not possible to brute force try all the possible ways to use collateral against all the possible uses. There are a range of waterfall and other heuristics that are employed to avoid the combinatorial explosion. However, linear programming, specifically linear optimization, is highly applicable to collateral optimization. Open source shareware through to commercial packages capable of handling 10s of millions of variables are available off the shelf. This is a large complex optimization that requires someone with extensive optimization experience.
Timing makes the problem more complicated. Decisions have to be made throughout the data (margin calls, tri-party pledges, ...) and not all at once. For an organization that operates in multiple regions, the same daily activities are shifted in time with respect to one another. Here information translates to better optimization and more cost savings. Real-time data, and fast optimization is important. Delaying the optimization, or rather not running the optimization too early, results in more available information and a better result. Models can also be used. You can project the later in the day tri-party pledging and incorporate it into optimization runs that take place during the day.
Optimization should also look at the T+1, T+2, ... future optimization requirements. It does not make sense that pledge out a security that will create a problem in the future. For example term repo a security, and not have enough available for a T+2 delivery.
Collateral substitution is performed periodically and one of the important optimizations. Collateral is pledged to exchanges and customers, and what is optimal will change over time. A stock, for example, could become a hard to borrow, and clearly should be substituted if it is pledged (and haircut) as collateral. Typically, a very small number of substitutions are done because of operational and settlement costs and risks to both parties.
Collateral Substitution
Over time, what collateral management choices that were made in the past are not necessarily the best choices at the moment. For example, a stock pledged to as collateral may now be a hard-to-borrow and be much more valuable to lend out via Stock Loan.
Done wrong, a substitution model will recommend a vast number of substitutions - way more than an operations team can handle and way more than counterparties will tolerate. Done right, the substitution model considers the cost of substitution, the capacity of an operations team to make substitutions, and the impact on counterparties. The model does not recommend tens of thousands of substitutions that save a few cents, it recommends the few substitutions that save thousands of dollars.
Substitution needs to be run periodically, normally on a daily basis. Substitution can also be used for specific security locates. Instead of borrowing a specific security a lower cost alternative can be identified through substitution. If a customer is holding the security, and also borrowing on margin, the security of interest may be seg'ed. Through segregation optimization, a different holding can be segregated and the security of interest freed up. Its not just segregation; its collateral pledged to exchanges or to other counterparties - that can be substituted.
Start Small
It is not necessary to do everything at once. Working on a small portion of the overall optimization, will result in an improvement and will save money. As examples, focus on a specific task, such as tri-party pledges or just the T+1 collateral.
Optimization Issues
Linear optimization is a powerful tool. There are websites that claim that the simplex method is one of the most useful and efficient algorithms ever invented, or even stronger claims on the importance of the methodology. Note that in practice two algorithm's developed in the 1980's outperform simplex for large problems.
There is no substitute for experience when developing a linear optimization model:
- If there is no feasible solution, the model just ends without any solution. This can be as simple as one stock, where 200 shares are needed, but only 100 shares are in inventory, resulting in no solution whatsoever for the rest of the optimization. There are modeling techniques that will result in a feasible mathematical solution even if there is no real-world solution to meet all the requirements
Importantly, modeling can optimize how fails are handled. For example, prioritize exchanges and important customer over other uses of collateral. - Not all problems can be represented with linear optimization. For example, a bond that must be delivered in multiples of $1,000. Here, mixed integer programming using branch and bound is used to model these constraints. Integer constraints are much slower to solve, and require proper judgement as to when and how to use such constraints
- There are countless tricks of the trade that have to be employed. Mixed integer can only specify integer bounds and not, for example, units of $1,000 for bonds. Yet, any experienced model developer will understand how to express the constraint
There is also no substitution for understanding the margin, seg, settlement and other processes that are being modeled:
Take, for example, a collateral substitution model that a large, and not named, broker dealer instituted. It identified 10s of thousands of substitutions that should be performed. The model failed to take into account:
- The capacity of the operations team, which was capable of doing at best, several hundred substitutions a day. The model can be set to identify, for example, the top 50 substitutions that are worth more than $100 a day
- The cost substituting collateral and the settlement risk. Both of which should be considered in the optimization
- The impact on the customer, which also experiences capacity and settlement risk issues. The model could, for example, limit the number of substitutions per month per customer
This is by far not an exhaustive list of how incomplete or poor modeling can result in less than optimal, and even more costly behavior