<p>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.”</p>

<p>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.</p>

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

<p>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.</p>

<p>(I would recommend looking up the history of the Hunt Brothers and silver.)</p>

<p>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.</p>

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

<p>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.</p>

CC BY-SA 3.0
2018-03-29T01:59:12.817Z
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.
Enhao Lan
CC BY-SA 3.0
2018-03-28T22:32:49.507Z
2018-03-28T22:32:49.507Z
Brian Romanchuk
<p>I would like a mathematical model to describe the arbitrage of a single commodity.</p>
<p>If I have a lot of money, I can buy out or buy most of some commodity, such as apples. Then the price of apples will go up.  Next, I sell my apples at a high price. Seemingly, I can make a profit by this method. But in fact, there are some questions. When I bulk sell my apples, the price will decline quickly, so, I only profit a little, or maybe even incur losses.  But if I slowly sell my apples, the new apples will be produced, and the price will decline too, but slowly; but I need more time to sell my apples, and as time goes on, the price will return to normal, so I still make a little profit.</p>
<p>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 ?</p>

CC BY-SA 3.0
2018-03-28T10:35:25.720Z
“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.
Brian Romanchuk
CC BY-SA 3.0
2018-03-28T12:25:09.460Z
@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.
Enhao Lan
CC BY-SA 3.0
2018-03-28T22:17:39.793Z
I’ll put up a tentative answer.
Brian Romanchuk
<mathematical-economics>
Simple arbitrage model of a single commodity
Enhao Lan
# Simple arbitrage model of a single commodity

(Asked by: username_0 on 2018-03-28)

I would like a mathematical model to describe the arbitrage of a single commodity.

If I have a lot of money, I can buy out or buy most of some commodity, such as apples. Then the price of apples will go up. Next, I sell my apples at a high price. Seemingly, I can make a profit by this method. But in fact, there are some questions. When I bulk sell my apples, the price will decline quickly, so, I only profit a little, or maybe even incur losses. But if I slowly sell my apples, the new apples will be produced, and the price will decline too, but slowly; but I need more time to sell my apples, and as time goes on, the price will return to normal, so I still make a little profit.

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 ?

**Tags:** mathematical-economics

> **Comments:**
> **username_1**: “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.  
> **username_0**: @username_1  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.  
> **username_1**: I’ll put up a tentative answer.  

---

## 1 answers

### Answer by username_1 on 2018-03-28. Score: 3 | Accepted answer

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.

> **Comments:**
> **username_0**: 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.  

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