This word can be unfamiliar to many people who has never done any finance courses. Arbitrage simply means riskless profit.
From
Dictionary.com, the definition of Arbitrage from Financial Dictionary is:
The simultaneous purchase and selling of an asset in order to profit from a differential in the price. This usually takes place on different exchanges or marketplaces. Also known as a "riskless profit".
Basically, this mean that someone can profit from something by doing a few transaction simultaneously, and gain a profit without sacrificing anything. Note that the profit can be obtained now, or in the future.
Well, to make our life simplier, we need to assume a few things.
First, everyone can borrow and lend at a fixed interest rate (called it
r), this removes the advantage of people who can actually borrow with lower interest rate (such as credible companies).
Second, this interest rate
r is actually the inflation rate, which means that the ratio of future value of money to the current value of money is related to
r. For example, if a dollar now is gonna worth a dollar twenty in a year time (means after a year, the dollar we have actually becomes less valuable), and if we save the money in a bank, we would get a dollar twenty in a year time too. This effectively is saying that there is zero Real Infation rate.
Third, money market is riskless. Here we are saying that we can save or lend money without worrying about risk, no bank and people will go bankcrupt or default on the payment. (contributes to the riskless aspect of Arbitrage)
Last, there is no external cost associated with any transaction. Example of external cost includes: transportation, value of time, personal preference. These costs exist in real life, let say in a rural village, for Ken to deposit some money in a bank in the city, he would need to drive to the city to deposit (Need to waste time and money on travelling), besides, he is afraid of doing bank transaction because he seldom do it (personal preference), this induces an extra cost to him although sometimes the cost can be hard to measured. However, in a technology advance era, we can safely assume away such cost, take internet banking and ATM machines for example.
Now back to the main point, how does arbitrage work? Remember we might need to make a few transactions simultaneously. A simplest example that I can think of is, let's say your friend, Paul want to borrow some money from you for a year and he is willing to pay you an interest
i which is greater than the market interest rate
r, so do you think you can make a riskless profit out of this?
To do it step by step:
1. By lending the money to Paul, let's say
x amount, you would lose
x dollars now, but he is required to pay you back
x(1+i) after a year time. (This is your first transaction)
2. Since now
i is greater than r, you can borrow a riskless amount of money
x from a bank, and pay
x(1+r) back to the bank in a year time.
Effectively, you are borrowing money from the bank with a lower interest rate and lending it to Paul for a higher interest rate, hence making a profit in return. Since no party will default on payment, the profit is riskless and you don't lose anything! The amount you earn is
x(1+i) - x(1+r) = x(i-r) , which you can claim in a year time.
The money you earned, in fact, need not to be claimed in a year time, you can actually realise the money anytime, by doing another transaction:
3. By borrowing the present value of your profit, in this case
x(i-r)/(1+r), and returning
x(i-r) in the future gives you the power to get a hold of your profit anytime.
Take a note that a positive expected value on something is not an arbitrage, for example, if I gamble $10, I got the chance of getting $110 with a 90% chance or lose my initial $10 with 10% chance. Clearly, the expected value in this case is $80, which is high (so I will definitely do it). However, this is not an arbitrage because the profit is not riskless, I have 10% of losing my ten dollars here.
Back to the previous Paul example, if assumption three (no one default on payment) does not hold, even if you charge Paul higher interest rate to compensate that Paul might default on payment with a 5% chance, it is not an arbitrage. However if the expected value is positive, it might still be worth it to lend the money to him.
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