Finance for Legal Funders 201: Duration & Convexity


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In Part 1, I introduced how important it is for legal funders to effectively communicate with capital providers and how the goal of this series is to show how legal funding companies can use established financial concepts to help bridge the communication gap between themselves and financiers.

From here on out, we will look at how financial concepts that are commonplace in capital markets can be applied to legal funding in order to help you bridge the gap, improve your business, and pitch your business more effectively the next time you are in the market for capital.

This Week: Duration and Convexity

There are two questions I inevitably get when I talk to hedge funds interested in investing in litigation finance:

#1 “What are the characteristics of the typical litigation fund’s portfolio?”

#2 “What do duration, diversification, and convexity look like in the portfolio?”

To answer those questions, we will take a deep look at duration and convexity, and how those concepts can be applied to litigation finance.

For starters, duration and convexity are commonly used metrics to evaluate risk in a portfolio. While they don’t measure risk themselves, they are directly related to risk under potential future scenarios, such as changes in market rates. Mathematically, the duration of a financial asset is just the weighted average of the time until the fixed cash flows of the asset are received. Convexity is the change in asset value when another variable, like interest rates, changes. Understanding how duration and convexity affect a litigation finance portfolio is key to credibly establishing its value.

By the end of this article, you will

  1. Have a better understanding of duration and convexity.
  2. Understand exactly how they apply to legal funding.
  3. Know how you can use them in your discussions with capital providers.

Duration Explained

Duration

In the broader financial field, duration is used by portfolio managers to measure the exposure of their portfolio to refinancing risk and interest rate risk. On the one hand, if a portfolio’s duration is too long, the risk that interest rates will rise and hurt valuation is a serious concern. On the other, if a portfolio’s duration is too short, there is a risk that new investment opportunities will not be available with sufficient returns as the securities mature. Portfolio managers balance duration to meet the needs of investors. Some investors are looking for long duration portfolios, while others are looking for short duration portfolios.

The immediate counter argument that legal funders raise about using duration is that lawsuits have an uncertain time to maturity, and that’s fair. However, while any single lawsuit may have an uncertain life, a pool of lawsuits as a whole should have a stable and well-established average time to conclusion. In other words, duration as a metric needs to be modified by litigation finance firms, not discarded.

All of this still might seem unimportant in the context of legal funding. After all, if the multiple on invested capital, or MOIC, is 2-3X and we feel good about the litigation, then who cares about a 25 basis point hike in rates? The reality is that interest rates play an important role in litigation finance investments whether participants understand it or not. The fact that returns are high is immaterial.  Returns are high in the risky peer-to-peer lending space, but interest rates still matter.

Litigation finance investments are most often structured as a form of non-recourse debt. (In certain jurisdictions, you can get backend equity exposure through a partial ownership in the law firm itself, but that’s quite rare.) Pricing in is complex with consumer litigation finance and commercial litigation finance handling the matters differently.

Pricing in commercial litigation finance is often done through multiples – a firm might say that they want a 2X return on their capital, plus their capital back. That metric is imprecise from a financial point of view since it says nothing about the time frame for that return. 2X capital in one year is outstanding. 2X capital in 50 years is not.

On the consumer legal funding side, the pricing is based on a preferred rate of return on the invested capital. The latter is a more sophisticated approach, but once we add a timeframe to the equation, the multiple approach is just another way of expressing an interest rate. On both sides of the business, parties make assumptions about the relative likelihood of success in cases, and recoveries in the event that the cases themselves are successful. The commercial side is built around a more ad hoc methodology on the whole than the consumer litigation finance space is.

In essence then, legal funding is simply composed of a series of risky fixed-rate debt obligations with an expected recovery rate of 0 in the event of a default. The risk premiums on that debt need to change as factors like interest rates change.

Independent of concerns about interest rate risk, it’s useful to understand average duration in a portfolio, because litigation finance investors want to ladder the maturities on their portfolio just as they ladder maturities on bonds.

Convexity Explained

convexity

Convexity is similarly useful in establishing how much exposure a portfolio of assets has to risks like interest rate changes, increases in default rates, etc.

Convexity is traditionally thought of as being the change in price of a debt security with respect to a one unit change in interest rates. That concept has clear applications in mainstream finance, and it’s useful in litigation finance as well. But the concept has broader applications than that.

In particular, convexity paves the way for potential measures of risk in a portfolio that can be reported to investors. Rather than measuring risk based on the number of successful cases or rates of return – metrics which do not sit well with most institutional investors for technical reasons – a modified form of convexity can be used to quantitatively measure how the value of a portfolio of litigation claims changes when success rates rise one percent, or when average portfolio duration rises one month, or even when expected award levels rise one percent.

To frame it another way, convexity is really a form of scenario analysis. Convexity measures the effect of a 1% move, but by extension, it could also be extrapolated to the effect of a 100% move  – just like you can look at the impact of a 10% hike in rates vs. 1% hike. Here are 3 examples of “100%” moves that could affect your portfolio of cases:

Here are 3 examples of “100%” moves that could affect your portfolio of cases:

  1. Attorney Joe gets disbarred and none of his clients were transferred to another attorney.
  2. One of the mass torts you’ve invested in rules in favor of the pharma company.
  3. You find out that all of the plaintiffs you funded from a broker are actually the names of famous TV cats and the broker has fled the country.

In each of those examples, knowing quantitatively how much each of those situations affects your portfolio’s success rate, and thus value, would be a boon not only for running your business effectively but being able to communicate with capital providers.

Summary

Calculating duration and convexity and other financial measures we’ll talk about in future articles might not seem like core concerns in the legal funding space, but they are important as part of running a solid business.

Understanding and using these metrics can help lower cost of capital by giving investors more confidence in the fund manager, but just as importantly, they can also help a manager to understand the risks in their own portfolio and then take action to offset those risks.

In the next article in our series, we will talk more about risk metrics in finance, risk tools like Monte Carlo simulations, and how litigation finance measures risk.

For deeper reading on duration and convexity, check out these resources:

  1. TheStreet – Bond Convexity: The Relationship Between Price and Yield
  2. Vanguard – Distinguishing duration from convexity
  3. BlackRock – What is bond duration and why does it matter?
  4. TheStreet – Bond Duration and Convexity: Practical Application
  5. Pimco – Understanding Duration

If you have more questions on duration and convexity, don’t hesitate to shoot me an email: m.mcdonald@morninginvestmentsct.com


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About Michael McDonald

Michael McDonald is a PhD in finance, former Wall Street trader, and hedge fund quant. Currently, he is a university professor of finance and partner at the investment consulting firm Morning Investments. His firm provides services for hedge funds, asset managers, and litigation finance firms. He is also a periodic columnist for AboveTheLaw.com and the Litigation Finance Journal. He can be reached at: m.mcdonald@morninginvestmentsct.com

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