The old method is not necessarily the best. Investment firms traditionally stress test their assets by calculating how much of a portfolio can be liquidated within a given time frame – two days or a week, for example.
But a new approach overturns orthodoxy. It sets the desired amount of the portfolio to sell, then aims to find the optimal liquidation moment.
Bastien Baldacci, Advisor in the Equity Derivatives team at HSBC Paris and co-author of the research, says this is more informative and useful in practice. “This paper aims to provide a fairly general framework to answer the fundamental question ‘how long does it take me to liquidate X percent of my portfolio, given a timeline, and what are the costs associated with that liquidation?’ “, he says. .
A schedule is a predefined set of orders that spans a fixed period of time and may include instructions to process, for example, an equal number of trades each day or a decreasing number of trades over time.
The research applies to relatively illiquid assets such as corporate bonds, and was originally designed for optimal execution at a UK-hedge fund based. Baldacci conducted the research with co-authors Mike Weber, Chief Risk Officer of UK quantitative asset manager BlueCove, and Iuliia Manziuk, quantitative researcher at Engineers Gate, a WE investment firm.
To build their framework, the authors assume that some or all of the assets in the portfolio follow the so-called locally linear order book (LLOB). The notion of LLOB arises from the assumed configuration of the shape of trading volume around small deviations from the average price. The pattern introduces the notion of latent volume, which is not directly observable. “Latent volumes around the best ticks are linear in price deviation from the best price,” the document notes.
The authors calculate the density of book trades in a closed formula. The idea is to reverse this formula and derive the volume traded in the market based on the price change. “Based on this, one can solve a standard convex optimization problem and derive the optimal liquidation time,” Baldacci explains.
Baldacci, who, together with Manziuk, received the prize Risk.net rising star in quantitative finance in 2021 for research on optimal execution across different venues, argues that the latent volume assumption is necessary for the model because it would be unrealistic to assume that liquidity is fully observable for markets in little by little.
In corporate bond markets, liquidity is fragmented. Some bonds can go several days without being traded, while there are single transactions that can represent 10 or 20 times the average daily volume.
And for corporate bonds, it’s not just the lack of liquidity, but also the lack of a fair price. In equity markets, the price and the bid/ask spread are observable, whereas the corporate bond market works on the principle of the request for quotation and the answers may differ from one to another .
“On OTC markets with fragmented liquidity, that’s a good use case,” says Baldacci.
The long and the short
The authors illustrate their method with two stylized examples, one with a long/short portfolio of two bonds of different liquidity and opposite directionality, the other with a long/short portfolio of 20 bonds chosen at random.
In the first case, the authors note that in case of zero correlation between the two bonds, the liquidation times depend only on their individual liquidity. But as their correlation increases, the liquidation time of the two bonds increases and tends to converge.
The portfolio of 20 bonds has a similar result, where the liquidation time tends to be longer for higher correlation levels.
Conversely, in both cases, the liquidation cost decreases with the increase in the correlation between the securities, under the effect of the longer liquidation time.
Once the methodology is established, using it for stress testing is relatively straightforward. The values of all relevant parameters – average daily volume of all assets, volatility and bid/ask spread – are multiplied by given stress coefficients. Recalculating the portfolio liquidation cost under these conditions provides the liquidation time in a stressed scenario.
The loss of the scenario, the impact of the stressed condition on the liquidation, is the difference between the liquidation cost of the stressed scenario and the liquidation cost of the unstressed scenario.
The approach does not apply to derivatives because it does not consider the cross-asset impact, Baldacci says, but he and other co-authors worked on a different method to solve optimal trading problems. while allowing a general cross-impact. matrices, and the results are coming in Risk.net soon.