# Simple arbitrage model of a single commodity

Maybe, my question is a little chaotic. I want a mathematical model to describe the arbitrage of a single commodity.

As I know , if I have much money, I can buy out or buy most of some commodity, such as apple. Then, the price of apple will go up. Next, I sell my apple at high price. Seemly, I can make profit by this method. But, in fact, there are some question. When I bulk sell my apple, the price will decline quickly, so, I make profit a little or loss. But if I slowly sell my apple, the new apple will be produced, the price decline too, although decline slow, but I need more time to sell my apple, as time go on, the price will return to normal, so I still make profit little.

Obviously, this process has not a clear expression by language. So, I guess there must be a mathematical model to describe this process. What is the relation of supply, demand, price, and what is the best method of arbitrage ? What paper or book I should read ?

• “Arbitrage” is not the word you should be using. An arbitrage trade formally implies that you enter a number of trades that result in zero market price risk, yet you lock in an “above normal” return (greater than the risk-free rate). All modern financial mathematics is built around a “no arbitrage condition.” What you are describing is “cornering the market.” This puts you into a position with very large return risk. Not sure how well developed the theory of that is, but in the real world, there are laws/regulations designed to prevent such tactics. Look up the Hunt Brothers and silver. Commented Mar 28, 2018 at 10:35
• @BrianRomanchuk Thanks your explain. I never thought to do it in the real world, since I am a poor man :) . One side, I am curious about the mathematic model of "cornering the market". On other side, there is not laws prevent it in game, I want to verify it in game, but seemly, there is not relevant theory. In fact, I think “cornering the market” can't make profit, if maket is not dull. I mean "not dull" is the supply and demand is undelayed to price. I just guess it , I have not suitable way to describ it. In fact, it is a little disappoint there is not theory about it. Commented Mar 28, 2018 at 12:25
• I’ll put up a tentative answer. Commented Mar 28, 2018 at 22:17

As I noted in the comment, buying a major position in a commodity does not qualify as an arbitrage, rather it would be informally referred to as “cornering the market.”

I am unsure whether there is any theoretical work on such strategies. However, from a practical perspective, we can see that it is hard to characterise what would happen.

I will assume that we are talking about a physical commodity; things might be different for a financial asset.

Firstly, going into a market and trying to buy up the supply is difficult. There will be both physical commodities to buy, as well as derivatives (such as futures). How exactly can you get the physical inventories away from other commodities traders and consumers, when they see someone buying up all the other sources? You need to find a way to buy up the commodity ahead of time quietly, and then you need some event (such as a bad harvest) wiping out the holdings of the other commodity traders. Cornering a market has been done, but you need particular circumstances to make it work.

(I would recommend looking up the history of the Hunt Brothers and silver.)

The next problem is your ability to take advantage of your high inventory position. The producers of the commodity will ramp up production (and demand may be destroyed) if you try to only sell at a high price. You could get stuck with a large inventory of a commodity that has fallen in price. If you borrowed to finance your position, you might be forced into distressed selling - and everyone will know about it.

In other words, there are a lot of possibilities, and there is no easy way to characterise what will happen to the price.

Things are different if you control the production of the commodity. That ends up just being te situation of a monopoly (or oligopoly). There is a large literature on monopolies in economics; I am not familiar with it.

• Tomorrow I read the Hunt Brothers in Wiki. I think it is a example of failure. Since, the "go up" of silver futures contracts knocks down them, we don't know the process of making profit. Commented Mar 29, 2018 at 1:59