Life is a series of linear and non-linear optimisation problems with non-trivial objective functions - and the markets are worse than that

Let’s start with a story: An old lady walks into a bank and says “I’d like to make a deposit please.” “Certainly madam, for how long?” “Some just overnight and the rest up to 7 days.” replied the old lady. “Well madam, at the moment we are offering an attractive rate of 4.5%.” “Never mind about that”, said the old lady, “I will be happy to take only 3%. I am worried about the state of the economy and I want to ease the burden of borrowers. I may be back with more cash tomorrow.” The cashier, not wishing to look a gift horse in the mouth, takes the deposit and the old lady leaves the bank.

Ten minutes later, the old lady’s angry husband (let's call him Mr Chancellor, who is married to the former Miss Threadneedle-Street) storms in asks why the bank hasn’t dropped the rate on his neighbour’s floating rate mortgage, by 1.5%. “But” replies the cashier, “your wife’s deposit is only a small part of or depositor base, and while it may influence sentiment, it hasn’t as yet filtered through to the rest of the market to lower the cost at which we borrow generally, nor I daresay has it altered the cost at which you can borrow, so your wife, well intentioned though she may be has simply given the bank 1.5% of extra interest without any discernable impact on the market”

Jesus was a great communicator and he knew that complex issues could be illustrated with simple stories. Would that are politicians and central bank see things in such simple terms. Unfortunately they can’t. They cloud their minds with ideas from economics and try to predict future consequences of their actions using models based on prior behaviour. In normal times those models may work, but these are not normal times.

Let's ignore the economists’ mindset and consider a mindset that looks at many financial situations as optimisation problems, the objective of which is maximise (or minimise) a value, often defined in terms of a combination of parameters subject to set of constraints. It is a methodology widely used in engineering and logistics. I do it all the time. Why? Well first of all I just do, because I have spent many years looking at financial structures in exactly that way, and secondly because it provides a very good framework for how both markets and businesses behave. In practice there may be no rigorous evaluation of optimal positions and the constraints may be somewhat fuzzy, but there is an undeniable tendency in business for each party to seek to maximise its value (objective function) within the constraints imposed by prices, capital, capacity, legislation and a myriad of other factors.

A simple example would be cross currency interest rate arbitrage, using the simple 4 way relationship between spot and forward rates between 2 currencies and their relative interest rates. For most of the time the rates will move independently but usually ensuring that there is no arbitrage opportunity by using three of the instruments to create a synthetic version of the fourth instrument at a cost that ensures an arbitrage profit because the bid and offer prices have become so far out of line. Generally that happens rarely because the markets move within well understood constraints.

Now, let's not think much more about optimisation (you can read about it in undergraduate mathematics texts), but let's think about binding and non-binding constraints. Imagine legislation that says all motor vehicles must be sold for a price between £5.00 and £50,000,000.00. It is a valid law and applies to all buyers and sellers of cars, but in practice it has no effect. It is a non-binding constraint. On the other hand, an alternative law that required all cars to be sold between £25,000 and £26,000 would be binding not only on all sales of Fiat 500s but also on Mercedes sedans. Widening the band of permitted prices would increase the number of types of car that would be sold, and narrowing the band would reduce that number. Varying the constraints has an impact because they are binding.

Now let us think about the Bank of England’s interventions in the money market. Why does that work? The commercial banks do not take all of their funding from the Bank of England. As we know from HBOS, Bradford & Bingley and Northern Rock the banks fund their assets from the capital markets. They also hold a lot of our cash on short term and longer term deposits. The Bank of England funding is a relatively small part of their borrowing. So how does it affect interest rates in general? Is it a question of sentiment? No, the money market is a rational optimisation problem. So what is the limiting constraint? The answer is that an increase in the central bank discount rate generally greats a greater drag on the banks’ capital making them less willing to lend and interest rates will tend to rise as the demand for capital increases. The banks have limited capital and are obliged to maintain minimum ratios between their equity capital and the asset books. Creating a small drag on profits can constrain capital and reduce lending appetite. Conversely, a fall in the central bank discount rate reduces the drag on capital, making banks more willing to lend and leading to lower interest rates to match the lower demand for capital. That is the economists' and the central bankers' model, but it only works because there is a binding or near binding constraint: the ratio between the banks' assets and the banks Tier 1 & Tier 2 capital.

Unfortunately, this model doesn’t work at present. The banks have been told to raise extra capital in anticipation of the coming recession. In addition, the government has set aside £35 billion of bank equity underwriting capacity. So in one version of reality (the version where the banks’ reported balance sheets reflect the value of their assets and any credit losses are fully and accurately reported) the banks are flush with capital. So long as the audience keeps clapping and the sound balance sheet fairy is kept alive, the capital constraints that in normal times would have made the Bank of England interventions work are no longer binding.

On the one hand the government is offering the banks plentiful equity through its underwriting facility and on the other it is reducing interest rates in the expectation that this will give the banks more capital to lend. But the banks already have more capital than they can use, because they can't find safe homes for the funds they already have. The capital constraint is no longer binding, so easing the constraint by reducing the discount rate will have no effect. To use another metaphor the Bank of England is revving the engine, but the gears are in neutral. To reduce central bank discount rates at the present time is like pushing on a piece of string.

So what are the binding constraints? The answer is the remaining distrust between the banks puts a floor on the risk premium for interbank lending. In a fair market interbank rates are always a tad higher than government rates because the government is OK, they can always lean on the tax payer, but you never know what is just around the corner for the banks. But these days the picture is very different. The banks look at each other and think “I know there is probably still some bad news left in the bank over the street, but I don’t know how much. It might be enough to knock them over, or they might be OK”. And they are probably right. The Bank of England’s interventions will be pointless until the bank regulators get to the heart of every bank’s asset book and strips out all of the poor quality assets and brings back on the books all of the off-balance sheet trades.

So Dr King, your model is wrong. Put away your Lipsey, and get out your Dantzig.