How to suffer loss

A friend, who has started his own litigation finance platform, https://www.axiafunder.com/ has asked me to write something about litigation finance.  He’s not paying me – but maybe he’ll buy me a pint in The White Hart at Barnes Bridge on the River Thames. 

The idea of litigation finance is simple, legal cases cost money and sometimes a claimant is unable to afford to fight a case; so in exchange for money up front, they share the return of any settlement winnings paid out in the future.  Burford Capital does this very successfully – but Cormac is trying to allow retail investors to fund smaller cases.

Moscovy Company

I find the idea appealing, and not just because it should make money.  Partly because litigation finance reminds me of the original adventurous spirit of the City of London and the first Joint Stock Companies which were formed to trade with countries overseas from the 1550s.  Its members did not trade on their own account, but pooled their risk and contributed money to a joint “stock”.  Control and ownership was separated, and the capital was divided into shares which were freely transferable. Or as Richard Hakluyt puts it “lest any man should be too much oppressed or charged a course was taken, that every man willing to be of the society, should disburse the portion of twenty and five pounds a piece: so that in a short time, by this means a sum of six thousand pounds being gathered, three ships were bought.”  Hakluyt, who was rector of Wetheringsett, Suffolk later published Principal Navigations, Voyages and Discoveries of the English Nation, which became required reading for merchants planning new companies and overseas ventures.  On 10th May  1553 3 ships captained by Sir Hugh Willoughby, Cornelius Durfoorth and Richard Chancellor set sail down the Thames with 18 months of provisions, aiming to sail north of Norway and Russia to discover a north east route to China.  We will return to their fate later.

St Petersburg Paradox

But also litigation finance reminds me of the St Petersburg Paradox, discussed by Daniel and Nicolaus Bernoulli in 1738. It’s called the St Petersburg Paradox because that’s where Daniel Bernoulli was when he proposed a resolution to his cousin’s stated conundrum. The latter starts off with a discussion about lottery tickets, before discussing merchants protecting themselves from ships sinking.  Hopefully I can explain the connection, but let’s start with Bernoulli’s lottery ticket example.

“Somehow a very poor fellow obtains a lottery ticket that will yield with equal probability either nothing or twenty thousand ducats. Will this man evaluate his chance of winning at ten thousand ducats? Would he not be ill advised to sell this lottery ticket for nine thousand ducats? To me it seems that the answer is in the negative. On the other hand I am inclined to believe that a rich man would be ill-advised to refuse to buy the lottery ticket for nine thousand ducats. If I am not wrong then it seems clear that all men cannot use the same rule to evaluate the gamble.”

Replace “lottery ticket” with “court case” and you can see the situation is analogous. Nicolaus Bernoulli points out that in most cases a fixed sum of money (say 10,000 ducats) is worth more to a pauper who has less than 50 ducats (200x starting capital) to his name, than a wealthy merchant who already has 100,000 ducats in savings (10% of starting capital). 

This seems obvious, but it has the weird implications.  For instance: it does not always makes sense to wager when the odds are in your favour.  Here’s an example based on litigation finance: imagine suing a counterparty, and you are 90% certain that you will win the case (that is 9 times out of 10 you will win).  That’s a realistic example, many litigation funders quote win rates of 85-90%.  But if you lose, you pay not only your own costs, but the other side’s costs.  This would bankrupt you, you lose everything, including your house.  In this case, it makes little sense to pursue the case, despite the odds being heavily in your favour, you will probably reach an out of court settlement.

It’s not just whether the court case has a favourable or unfavourable probability, the consequences of an improbable outcome (that 1 in 10 chance) going against you matter a lot.  A 1 in 10 chance of ruin is not most people’s idea of a sensible gamble. 

Geometric mean

Bernoulli’s great genius was to recognise that the expected return should be calculated using a geometric mean average, not an arithmetic mean.  The geometric mean is calculated by multiplying n values together, then taking the nth root of the product.  Not many people enjoy taking the nth root, so people tend to forget this calculation after GCSE maths.  But the significance is that when there is a small chance of a zero, a geometric average returns a zero (zero multiplied by any number produces a zero).

The same process works in reverse if you have a lot of wealth.  As long as you are only risking a small proportion of your total wealth, it can make sense to bet small amounts on improbable outcomes – Peter Thiel was already wealthy from selling PayPal when he decided to become the first outside investor to put money into Facebook.  In 1998, Jeff Bezos was one of the first investors in Google.

Doubtful enterprise

Or as Bernoulli puts it “It may be reasonable for some individuals to invest in a doubtful enterprise and yet be unreasonable for others to do so.”  Bernoulli doesn’t mention litigation finance, but he does discuss insurance for overseas trade, a merchant who has a single ship that sails from Amsterdam to St Petersburg.  The merchant is well aware that at this time of year, of 100 hundred ships that sail, 5 sink.  He could buy insurance, yet the insurance seems “outrageously high” to the merchant. Insurance is a negative expectation bet (you always pay a premium).  Bernoulli shows that even if the insurance is overpriced it could make sense for a poorer merchant to buy insurance if the consequences of his ship sinking would be losing everything.  At the same time a wealthier merchant who would not be wiped out by the loss of a single ship can afford to sell insurance – both sides gain.

Don’t risk everything on a single outcome

The same goes for a litigant, who doesn’t want to risk everything even if the odds of a favourable outcome are high.  Each case is binary in outcome, but each court case is uncorrelated with the others, so pooling the small risk of unfavourable outcomes makes sense.  This sounds like the modern concept of portfolio diversification – except it too was mentioned in Bernouli’s 1738 paper.

“It is advisable to divide goods which are exposed to some danger into several portions rather than to risk them all together.  Again I shall explain this more precisely by an example.  Sempronius owns goods at home worth a total of 4000 ducats and in addition possesses 8000 ducats worth of commodities in foreign countries from where the can only be transported by sea. However, our daily experience teaches us that of ten ships one perishes.  Under these conditions I maintain that if Sempronius trusted all his 8000 ducats of goods to one ship his expectation of the commodities is worth 6751 ducats*.  But, however, he were to trust equal portions of these commodities to two ships the value of his expectation would be 7033 ducats.**  In this way the value of Sempronius’ prospects of success will grow more favourable the smaller the proportion committed to each ship.  However, his expectation will never rise in value above 7,200 ducats.”

Diversification and insurance can not prevent your ship sinking (or the court ruling against you) – but it can reduce the impact of such an unfavourable event on your finances.  Paradoxically risks that are insurable, can still prove fatal.  The first Joint Stock venture did not end well for many of its participants.  The three ships were separated somewhere north of the Lofoten Islands by a “storm of unusual violence.” Of the three ships that set sail, only Richard Chancellor’s ship reached the Bay of Archangel, and then on Moscow where they arranged a trade deal with Ivan the Terrible.  The leader of the original Muscovy Company’s venture, Sir Hugh Willoughby, was found dead with his ship and crew by Russian fisherman hemmed in by pack ice, near the mouth of the River Varzina on the Kola Peninsula.  It’s presumed they died of scurvy.  Their loss, our gain.




Photo by Ryan Tasto on Unsplash