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Given the recent gold price inflation, I thought it would be a good moment to explain how the spread works, together with formulae, graphs and possible applications. I fear that it is yet another commonly misunderstood mechanism and it would help if we used it more consciously. A potentially overlooked element here is the time component, but before we get to that let us look at the spread itself.

Whatever commodity we take, there will be a natural tendency to buy it cheap and sell high. This does not happen with friendly trade or loans, but when we look at the international market with thousands of anonymous transactions, it is the profit that everyone seeks. At any given point in time it makes sense to expect that there will be a gap between the best (cheapest) sell offer and the best (highest) buy offer, this gap is called the spread.

The immediate consequence is that one can both sell and buy the same good and earn thanks to the spread. If the prices are given in the same currency then their ratio determines the percentage gain

r_s = spread ratio = price_sell/price_buy,
profit = 100% × (1 - r_s).

Which is easily seen when you consider selling a 100 units of your goo😛 you earn 100*price_sell; and then buy it back cheaper, the number of units you recover is (100*price_sell)/price_buy. Since you started with 100, what you gain is the difference
100*( price_sell/price_b - 1)

In our case, the price at which gold is sold, p_g, is given in cc and the price of currency being sold, p_cc, is given in gold. What is the price of gold in cc when bought? As p_cc is the amount of gold worth 1cc, the amount of cc worth 1g is the inverse 1/p_cc. Hence, for our purpose (neglecting the formal 100% factor)

r_s = p_g × p_cc.

So far nothing out of ordinary, but here is where the rounding comes into play. Because only 3 decimal places are allowed, and the cc is worth so much less than gold, its price will be change in relatively huge steps. For example, if 1g was worth 210cc, 223cc or 249cc, the price of 1cc should be 0.0047619...g, 0.0044843...g and 0.004016...g, respectively. Due to the rounding, all three end up as just 0.004g or 0.005g.

Which of the two is it? That is dictated by the buy price always being lower. If we convert the rounded prices back to cc, we have 250cc (= 1/0.004) and 200cc (= 1/0.005) – a huge gap of 50cc. Since it would make no sense to sell gold for 210cc while buying it for 250cc, the buyers settle for 200cc/g or 0.005g/cc.

To write this compactly, the so called ceiling function is useful. The ceiling of x, denoted ⌈x⌉, is the lowest integer not smaller than x. Or, to put it simply, it is the closest whole number going up from x (hence the ceiling name). So ⌈1.1⌉ = 2, ⌈3.7⌉ = 4 and ⌈5⌉ = 5.

Taking into account we want to round numbers at the 3rd decimal place, we need to take ⌈1000 x⌉/1000. So that 0.0042 becomes ⌈4.2⌉/1000 = 5/1000 = 0.005. Thus, given the price of gold p_g, the corresponding price of cc will be ⌈1000* 1/p_g⌉ / 1000, and the spread will be

r_s = (p_g/1000) × ⌈1000/p_g⌉.

Note that without the ceiling it would become just 1. That would be the ideal case of a commodity being sold and bought for the same price.

The formula is simple, but not very illuminating, so here is the graph, showing r_s as a function of p_g in orange with corresponding cc prices:



As you can see, it is not a continuous function. Each time the price of gold goes through 1000/integer the spread ratio falls to 1, which means 0% of profit (the blue line). On the other hand, when the price of gold is just below such value (like 125, 166.(6), 200, 250, 333.(3)) the ratio is at its locally greatest value. Those maxima are joined by the green line which is simply given by r_s = 1 + p_g/1000. Accordingly, the maximal profits are r_m - 1 = 1/n, for integer n.

The numbers above this line give the limiting (greatest) profit for each orange segment. This is a rather unfortunate feature of our market, that the potential spread profits get higher as the price of gold increases. We are currently oscillating around the 250cc/g point, so the profit changes abruptly from 25% to 0% and back. (With the current price of 253cc/g it is 1.2%.)

If gold were much (much) cheaper, the price of cc would be for example 0.021g, and the change of 0.001g would be 5% instead of 20% like today. If, on the other hand, gold were to become much more expensive the spread profit could be higher, but who would buy gold for 500cc?

This brings us to the basic limitation of spread-based earning. As gold gets more expensive, less and less people are willing to buy it. Likewise, less people are willing to buy cc, as it becomes worthless. This translates into a huge queue of offers we see in the market. Because each offer times out after 10 days, most of them are not realized at all.

For an individual citizen there is also the limit of 10g bought per day or, in effect, per offer. So with the extremal 25% profit spread over 10 days that is 2.5% profit per day, giving 0.25g or 50cc.

More realistically, with the price at 230cc the profit is 1.5%, but usually only a fraction of the offer is realized, say 1/2, so that becomes 0.75% daily. With 2000cc frozen for 10 days, you earn 15cc per day. And if some of your offers remain unsold after 10 days it gets even worse. This is the overlooked time element: instead of using the money every day, it is like using it one day, and doing nothing for the next 9.

Compare that to buying weapons for 6.5cc, and selling for 6.8cc – that is 4.6%, which would give 15cc profit per 326cc used daily. Or how about food raw materials, which you can find for 0.01cc and sell for 0.02cc – that is 100% of profit! And unlike monetary offers, those do not time out after 10 days, so you can stack them every day, nor do they have a 10g limit.

There are many other possibilities and they depend on opportunities appearing every day of course, but in general I would not recommend the monetary market spread as an income source for the individual. There is no point in diversifying your business if you know for a fact one of them is worse. The story is different with governments who have organizations at their disposal, but that is a topic for another article.

Finally, I wish to comment on a psychological element of trading, which is guessing the price someone else wants. Imagine the lowest offer to sell gold is 253cc and you want to sell as well. Will you ask for 253cc as well? Better make that 252.99cc which is almost the same... But wait the other guy will then make it 252.98cc! How about 240cc? It would probably get bought immediately, and you could have sold it for 242cc. Or maybe 245cc?

There is no way to tell, because when you go to the buy offers, there are only the 250cc or 200cc ones available. Not much help because you already knew it is somewhere between those numbers. If you knew the buyer was willing to pay 245cc, you would not waste your time with the 249.99cc offer. Nor would you place the 240cc one. You could use the buyer's offer immediately. Or you could barter more accurately, stating you want 246cc and see if the buyer changes his mind.

The same holds for the other side of course. The buyer does not want to pay 253cc if he could pay 243cc. If he sees only the higher offer he has to wait for a global price drop. He has no way of communicating to the sellers he is willing to pay at most 244cc, because he can only place those 0.004g or 0.005g offers. In both cases bad decisions are more likely when traders are pressed for time.

Fortunately, there now is a solution, and it is a project in which I am involved personally, so I want the potential conflict of interest to be clear. With the introduction of the Free Market of Japan (FMJ), a gold trading system with prices in the country currency has been started. You can read more about the FMJ itself here.

As said before, such system eliminates the spread, so is not a place for countries to earn off of that. But it gives individual citizens a much better tool to ask for prices they want exactly. It thus solves the difficulties described above. The project is new, and there is no telling how it goes, but with enough participation it might become a great solution to the gold inflation, so be sure to give it a try!