# Conrad Hall: The lesson in backgammon for LOBO management

0## Calculating whether LOBOs are a good risk is controversial. Conrad Hall uses lessons drawn from the famous board game to help devise a plan for managing the contentious loans.

LOBOs are back in the news again. Reflecting on the recent CIPFA/LASAAC clarification made me think, curiously enough, about the similarities between LOBOs and backgammon, the ancient dice game. Bear with me for a moment.

Some historians argue that Alexander the Great spread backgammon in his conquest of what was then the known world, and it is now popular everywhere, often played for very high stakes. The stakes inherent in LOBOs are certainly high, if not always their popularity. For a few pounds you can download an app which will play backgammon, and offer advice, to world champion standard. Advice on LOBOs won’t be as cheap, and many argue that there are serious issues with at least some of the advice previously provided.

In backgammon two players take turns to throw two dice, and to move any of their fifteen pieces accordingly. For example, if you threw a two and a four you could move one piece two spaces and another four, or the same piece six spaces. The player who gets all their pieces around the board first wins. What makes this more skilful than Snakes & Ladders?

Two dice can produce 21 different combinations, and for each you could move any combination of two pieces or one piece twice. Simple maths then tells you that each turn you have thousands of possible moves, and there is considerable skill in selecting between them.

### Doubling

Curiously, however, the real complexity (and similarity to LOBOs) comes from a player’s option to “double”, which is a simple binary choice each turn — you can either double or not.

In backgammon, each game is, in principle, worth one point. However, there is also a “doubling dice”. At the start of the game either player has access to the doubling dice, and before any of their throws may offer to double the stakes. On being doubled the other player may:

- Resign the game, and concede one point; or
- Continue playing, in which case:

a) The stake is doubled; and

b) The player accepting the double acquires the exclusive right to double again on the same terms.

So, when you double, you increase the stakes (because you expect to win) but you give your opponent something of value: the exclusive option to double subsequently (condition 2b). By analogy, taking out a LOBO gives you a benefit, such as a lower interest rate, but gives the bank an option, so you can already see the similarity.

If, after you double, your opponent later doubles again, then the doubling dice goes back to you under the same exclusive terms. The price of a single game can therefore rise quickly, which may explain its popularity with gamblers if not, of course, with responsible stewards of public finance.

You could easily fill a library with books written about the strategy and tactics for backgammon. Most of those are on how to move your pieces once you’ve thrown the dice, perhaps not surprisingly given the multiple possibilities every turn.

However, a noted world champion once said that only three of those books had anything worthwhile to say about doubling, and that one of those was wrong. Why is something so simple — a binary yes/no choice — so complex compared to the choice of thousands of possible moves every turn?

### Schrodinger’s cat

Well, imagine that you and I are playing backgammon. It’s my turn, and before I throw the dice I double. What are you going to do?

This article isn’t about backgammon, so let’s discuss decision making, risk management and option pricing.

You need to decide what chance of winning you need in order to accept my double, let’s call it X%, and then evaluate the position to decide whether your chances of winning are better, or worse, than X%. I won’t write about the second part of that decision, which is only to do with backgammon, and if it were not for condition 2b calculating X% is too trivial for me to need to do so here.

But 2b complicates things. In doubling, I’m offering you an exclusive option: the right to double me again later. That option has a value (call it Y), so formally you only need (X–Y) chance of winning to accept the double. Y is harder to calculate than X, but accountancy has developed since the days of Alexander the Great, so you, or someone in your department, will calculate X–Y easily.

This is exactly the process that you go through in deciding whether to take out a LOBO (analogous to doubling in backgammon). You assess the benefit if the option isn’t called, then estimate the chance of it being called, and the potential cost if it is.

The difficulty in pricing the option isn’t in evaluating any given situation. If you have a LOBO at say 5%, and your bank exercises its option to increase that to 7%, then your decision is easy (and will be easy at whatever interest rates you insert into this example). You’ll simply consider the PWLB lending rate, and if it’s lower than (in my example) 7% you’ll exercise your option to repay the LOBO without penalty by refinancing from the PWLB.

Otherwise, however reluctantly, you’ll accept the higher rate your bank is now charging you. Insert an X% for the numbers and you can see that it’s exactly the same decision making process as in backgammon.

It’s a bit like Schrodinger’s Cat. When the situation crystallizes, and the option is called, your decision is simple. However, until then it’s very hard to value the likelihood that the option will be exercised at some future date, and the potential cost if it is. There are just too many future possibilities in a LOBO for the calculation to be easy; although fewer than in a backgammon position.

A new accounting interpretation for some LOBOs may have thrown this into sharper relief, but you’ve always needed to know what your LOBOs (and any other contract containing options) might cost you over time. And, as I hope I have shown, the underlying principles of how to value options are exhibited in a simple dice game invented 5,000 years ago.

### Planning for LOBOs

So, do you know the value of the options against you? And if not, what would a plan to resolve that look like?

Focusing just on LOBOs (although I wonder if the bigger risks aren’t in complex regeneration contracts) I think a plan might look like this.

- Self evidently, you need to collect all the contracts and review the terms.
- For each you need to calculate X, which (as set out above) is the indifference point, where refinancing and accepting the revised terms are equally good options. Since accepting the revised terms probably gives the bank another future option you need to value Y as well.
- That calculation requires complex modelling of future interest rate scenarios, so you need either to buy in some expertise or, my preference, develop it yourself. The concept of how to value future events isn’t hard to express (or at least I hope I’ve shown that it isn’t) so, even though you should want your models externally validated at some point, you should be able to build the basic version yourself.
- I have some sympathy with a view that’s it’s not very relevant in today’s interest rate climate, but sooner or later that will change. And the real issue may be if all of those indifference points are fairly similar, which I suspect they may be. Might the cumulative impact of all your LOBOs being called at around the same time be rather uncomfortable? If you don’t know now the interest rate climate that triggers that position, then it’s probably a good time to start calculating it and perhaps adjusting your borrowing strategy accordingly.

There is an alternative. You could just hope, in backgammon terms, that I, as your opponent, don’t double you, which is analogous to hoping that the LOBO is never called.

Do you feel lucky?

**Conrad Hall is chief financial officer at the London Borough of Brent.**