- CFA Exams
- 2024 Level I
- Topic 8. Derivatives
- Learning Module 4. Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives
- Subject 1. Arbitrage and Replication

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##### Subject 1. Arbitrage and Replication PDF Download

**Arbitrage**is a process through which an investor can buy an asset or combination of assets at one price and concurrently sell at a higher price, thereby earning a profit without investing any money or being exposed to any risk.

In a well-functioning market, arbitrage opportunities should not exist. If they do exist, arbitrage activities would quickly eliminate the price differential. The

**no-arbitrage principle**states that any rational price for a financial instrument must exclude arbitrage opportunities. This is the minimal requirement for a feasible or rational price for any financial instrument. There is no free money.

The role of arbitrage:

__It facilitates the determination of prices.__The combined actions of many investors engaging in arbitrage result in rapid price adjustments that eliminate any arbitrage opportunities, thereby bringing prices back.__It promotes market efficiency.__Efficient markets are those in which it is impossible to earn abnormal returns, which are returns that are in excess of the return required for the risk assumed. Arbitrage activities will quickly eliminate arbitrage opportunities available in the market, thereby promoting market efficiency.

Arbitrage means taking advantage of price differences in different markets. In well-functioning markets, arbitrage opportunities are quickly exploited, and the resulting increased buying of underpriced assets and increased selling of overpriced assets return prices to equivalence.

**Arbitrage and Derivatives**

Assume the risk-free rate is 5%. The current price of gold is $300 per ounce and the forward price of gold is $330 in one year's time. Is there an arbitrage opportunity?

Here is what you can do:

- Borrow $300 at 5% today.
- Buy one ounce of gold (price $300).
- Enter into a short forward to sell one ounce of gold for $330 in one year's time.
- After one year you sell the gold for $330, and repay the bank $300 plus $15 interest.

Hence, a profit of $15 can be made without any risk!

In fact, any delivery price above $315 will result in a risk-free profit using this strategy.

What if the delivery price is $310?

- Sell one ounce of gold for $300.
- Deposit the $300 in the bank at 5% interest.
- Enter into a forward to buy one ounce of gold in one year's time for the delivery price ($310).
- After one year, buy one ounce of gold for $310 and keep the $5 profit.

Again, a profit of $5 can be made without any risk.

Investors in the gold market will take advantage of any forward price that is not equal to $315, eventually bring the price to $315, which is known as the

**arbitrage-free price**.

The arbitrage principle is the essence of derivative pricing models.

**Arbitrage and Replication**

A portfolio composed of the underlying asset and the riskless asset could be constructed to have exactly the same cash flows as a derivative. This portfolio is called the replicating portfolio. Since they have the same cash flows, they would have to sell at the same price (the law of one price).

Assume the forward price of gold is $315 in one year's time, and the spot price is $300. You have $300.

- You can deposit $300 in the bank at 5% interest. One year later you will get $315.
- You can also buy one ounce of gold, and a forward contract to sell it in one year for $315. One year later you will also get $315.

Why replicate?

- To explore pricing differentials
- Lower transaction costs

Replication is the essence of arbitrage.

Replication generally has more costs than simply taking a position in the asset. So, if all the assets are priced correctly, the replication seems useless. However, the ability to replicate something with something else can be valuable to investors as it helps them in making arbitrage profits. Sometimes, replication can even have lower transaction costs. For example, replicating return of an index fund has lower transaction costs with derivative and risk-free rate rather than purchasing every security in the index fund.

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**User Contributed Comments**
14

User |
Comment |
---|---|

myanmar |
there is no free lunch |

valeris |
There is always free lunch - you just gotta look for it :) |

omer123 |
A socialist will love to give out free lunches. :) |

vadimmuchnik |
except that same socialist will want to strangle you (or be invited for dinner) after the lunch giveaway :) |

danieltan782 |
lame |

gracecfa |
There is no free lunch even if you look for one...Someone ultimately has to pay, either directly or indirectly...Thank you very much... |

rahuls2609 |
if you are not paying for it either directly or indirectly, it is free for you |

johntan1979 |
omer123 must be talking about how the wealthiest 1% enrich themselves at the government's expense (and stick you with the bill) |

cbracho54 |
lol.. great CFA curriculum discussion!! |

jiba |
You want to price a derivative on gold, a gold certificate. The product just pays the current price of an ounce in $. Now, how would you price it? Would you think about your risk preferences? No, you won't, you would just take the current gold price and perhaps add some spread. Therefore the risk preferences did not matter (=risk neutrality) because this product is derived (= derivative) from an underlying product (=underlying). This is because all of the different risk preferences of the market participants is already included in the price of the underlying and the derivative can be hedged with the underlying continuously (at least this is what is often taken for granted). As soon as the price of the gold certificate diverges from the original price a shrewd trader would just buy/sell the underlying and sell/buy the certificate to pocket a risk free profit - and the price will soon come back again... So, you see, the basic concept of risk neutrality is quite natural and easy to grasp. Of course, the devil is in the details... but that is another story. |

ankurwa10 |
@rahuls2609 maybe this lunch is free for you. but in the context of the overall marketplace, the losers must be equal to the winners. Otherwise, no one would play. enjoy this free lunch while it lasts ;) |

fobucina |
Guys, the most important thing is that we are having fun and participating! Now let's all hold hands and have a picnic. |

gomez1234 |
i do make my life as an arbitrage trader,, send me that fools claiming there is no free lunch :) |

bushi |
As in the case of forward commitment, the replication of option contracts uses a combination of long (for a call) or a short (for a put) positions in an underlying asset and borrow or lending cash. The replicating transaction for an option is based on a proportion of the underlying, which is closely associated with the moneyness of the option. |

I was very pleased with your notes and question bank. I especially like the mock exams because it helped to pull everything together.