I thought that this note that I have written for my colleagues might be of interest.

Introduction

People often think about markets in terms of who the buyers and sellers are. They think things like:

  • A large, price-insensitive buyer (like a central bank doing QE in the government bond market) will have a large, positive effect on prices.
  • The departure of a large number of buyers will have a large, negative effect on prices.
  • If certain buyers leave a market, it is appropriate to worry about “where the demand is going to come from”.
  • If prices go up, it is because of buyers entering the market.

And so on.

I am sceptical of thoughts like this. It is not that I think that these effects do not exist, but that I think it is plausible that other effects dominate the movements of actual markets. Below, I first set out my reasons for scepticism, and then describe a toy model of a market that I have used to sharpen my intuitions in this area.

Reasons for Scepticism

Imagine that a market consists of two distinct groups, buyers and sellers. The sellers come to market to sell a specific amount of produce; the buyers can buy or sell not as they choose. An auction is conducted that is intended to ensure that all the produce is sold. An auctioneer calls out prices, and buyers submit quantities they would buy at that price, until a price is found where the total quantity submitted is the same as the total quantity for sale. Everybody then trades at that price. This is not a very realistic model of how a market actually works; it is an abstraction intended to make the problem tractable. I hope it does not lose too much of the reality of a market – anyway, it would be surprising if the price established by this method differed markedly from a price established in a more normal market.

Having set out the auction process, we can make some observations about it. What will happen if a large, price-insensitive buyer enters the market (let’s call him Merv)? Merv will always submit the same quantity for purchase, whatever price is called out. Since the quantity for sale is fixed, and assuming that that auctioneer starts from a high price and works down, Merv’s presence will mean that all the goods are sold sooner, at a higher price, than they would have been in his absence. Some people who, in Merv’s absence, would have been prepared to buy at a lower price never see the price fall far enough for them to make a purchase.

In other words, the effect of Merv’s entry into the market is to change the identity of the marginal buyer – the buyer who is prepared to buy at the price that happens to clear the market, but no higher.  This is the crucial insight. If all the usual (i.e. price-sensitive) buyers in the market have a very similar view of the value of the goods on sale, then Merv’s presence will have little effect, because moving a little up the ladder of potential buyers will not result in much of a change in the price that the marginal buyer is prepared to pay. If, on the other hand, there is wide disagreement on the value of the goods, then Merv’s purchases will have much more of an effect, because the marginal buyer in the situation where Merv is present might have a very different view from the person who would have been the marginal buyer in Merv’s absence.

That is the reason for my scepticism. I do not think that the dispersion of views about the value of financial assets is generally especially large – perhaps a few percent one way or another for the majority of participants in a market. Thus I would expect changes in the composition of buyers and sellers in a market to have less of an effect than correlated changes in market participants’ assessments of value in response to new information. In other words, I would expect fundamental factors to be more important than technical factors relating to market structure in driving movements in financial markets.

A Very Simple Model

I have constructed a model of a market in order to allow me to play with some of these ideas. It is not a general model (i.e. all algebra!) but a specific model in which I have entered numerical values. It cannot, therefore, be a mathematical proof of the ideas I have set out above. Rather, it is an example of a market that has essentially the same structure as the auction I set out above that can be used as a sense-check for my intuitions.

Structure of the Market

  • There is one type of financial asset to be bought and sold.
  • There are 1000 market participants.
  • A market clearing price is established by an auctioneer calling out prices, as in the model above.
  • Market participants already hold some of the asset. Their decision is whether to add to, or subtract from, their current holding. This model is therefore more sophisticated than the model considered above, because it allows a single participant to be prepared to buy or sell at different market prices rather than categorising participants as buyers or sellers from the start.
  • Market participants buy and sell in standard sizes that are specific to each participant and range from 0 to 100 (generated using random numbers).
  • Market participants are value investors. Each has a buy price and a sell price for the asset, with the buy price being lower than the sell price. These prices are generated by using a normal distribution with an average central valuation of 10 and a standard deviation of 2 (such that roughly 2/3 of market participants’ mid prices are within 20% of 10). The central valuation of a specific market participant is calculated at random from this distribution. .
  • Buy and sell prices are then generated from the central valuations using different random numbers (such that the buy and sell prices are not symmetrical around the central valuation – to represent the different risk/return  requirements of different investors). Buy and sell prices range randomly between 0 and 25% above and below the central valuation.

Playing with the Market

The market clearing price in the model is 9.92, and the volume transacted is 13,680. This can be taken as a baseline for running tests.

What if a massive buyer enters the market, intending to buy 10,000 assets whatever the price? Then the clearing price rises 6.5% to 10.56 and the volume rises to 19225. This struck me as a surprisingly small move.

What if, rather than a standard deviation of 2, we assume a standard deviation of 4? Then the entry of our buyer raises the market clearing price by 12.3% from  9.79 to 10.99 and the volume from 19136 to 23886. This coheres with my thoughts above, that the entry of a price-insensitive buyer will have more of an effect when there is greater disagreement about the valuation of an asset.

What if, for reasons unrelated to price, half of current buyers decide not to buy under any circumstances? Then the price drops 5.8% to 9.34 and the volume falls to 9270. This, again, did not strike me as a large move for such a large change in market structure. The reason is the one I discuss above – the remaining buyers have similar views on the valuation of the assets as the ones who leave.

These tests in my toy market suggest that large changes in market structure do not actually have large changes in price under plausible assumptions. The dispersion of opinion has to be much larger – a standard deviation of 4 rather than 2, such that 2/3 of participants’ central valuations would fall between 6 and 14 rather than 8 and 12 – for even a massive price-insensitive buyer to move the market more than 10%.

As a final test, I consider an example that is closer to the real world: the Bank of England’s purchases in the Gilt market. According to the Debt Management Office, total volume in the Gilt market in the financial year 2011-12 was GBP 7.1tr. In roughly six months from October 2011 to May 2012, the BoE increased its balance sheet by about GBP 1.2tr, which means that it accounted for 1.2/(7.1/2)=34% of the Gilt market in that time. Making large, price-insensitive purchases equal to 34% of the volume in my toy model, I find that the price rises 3.6% from 9.92 to 10.28. On a representative 10-year bond paying a 3% coupon and with a par value of 10, this is a change in yield from 3.2% to 2.8% — not insignificant, but not a sea change in market yields either, and I think that my assumed standard deviation of 2 is a lot larger than the likely standard deviation of market participants’ central valuations of Gilts (I had equities in mind when building the model). Using a more plausible standard deviation of 0.5, I find a price increase of 1.9% to 10.11, which represents a change in yield from 3.2% to 3% on my invented bond.

Conclusion

I am not trying to deny than changes in market structure can affect prices. My point is that the regularly-observed movements in financial markets are generally much larger than can be accounted for by the effects of the entry and exit of market participants under plausible assumptions. Even massive, completely non-price-sensitive buying interest failed to move the market price in my toy model more than 6%. Most buying and selling interest is price-sensitive, and that would reduce its effect relative to that number in the model. I think that market structure is normally a secondary issue.

What, then, is the primary issue? Changes in the dispersion of central valuations – modelled as a change in the standard deviation – do have an effect, but it is not large. The easiest way to move the market price by a large amount in my model is simply to move the average of market participants’ valuations. In other words, correlated changes of opinion about the value of an asset can easily have a much larger effect than changes in market structure. That is why I spend a lot of effort trying to understand the drivers of such changes, and much less time on market structure.

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