Carry Arbitrage in Derivatives

Hi, it's William. Welcome to Learn Finance Free. So, let's talk about carry arbitrage. Carry arbitrage is a technique used in derivative trading. Basically, it's an arbitrage strategy that doesn't involve a lot of investment but allows us to offset risk.

Let me give you an example. When analyzing a derivative problem, I tend to make a timeline. Here's time zero and here is a specific time T. Since it's arbitrage, we're going to borrow money instead of using our own. At time zero, we'll borrow some money to carry the underlying asset. "Carry" means holding the asset until time T.

If you want to buy a specific asset, it has a certain price, which we'll call S0. You borrow money to buy the S0 asset at time zero and hold it until time T. At time T, you sell it at a specific price. If the selling price covers your borrowed amount with interest, you gain; if not, you incur a loss.

The tricky part is determining the selling price at time T. Let's say the money you get from selling the asset is represented by S, which could be stocks, bonds, or any underlying asset. The price at any specific time will be either S0 or ST. To simplify, let's assume the asset doesn't generate cash flow, like gold.

At time T, the price is ST. If the selling price is higher than the borrowed amount plus interest, you gain; if it's lower, you lose. You subtract the repayment amount from ST to determine your gain or loss. The repayment includes the principal and interest, calculated as S0 * (1 + R) for one year or with continuous compounding using e^(RT).

To simplify, the repayment will be the future value of S0. If ST minus the future value of S0 is positive, you gain; if negative, you lose. That's the basic logic behind carry arbitrage.