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**University of Mauritius Monetary and Financial System ACF 3116(5)**

Lecture 4: Financial Derivatives- Forwards and Futures

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Derivatives Derivatives have become increasingly important in finance over the last 3 decades. According to one of the world’s leading derivatives experts, Paul Wilmott, $1.2 quadrillion is the so-called notional value of the worldwide derivatives market. This is to show the growing importance of Financial derivatives. Main examples: Futures, Forwards, Options and Swaps.

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**Derivative What is a derivative?**

A derivative is a financial instrument whose value depends on the values of other variables/assets, known as underlying assets. Example: Stock Option = derivative whereby its value is dependent on the prices of a share. The underlying asset can be securities, commodities, indexes, currencies, or anything else. So, we can say that the price of a derivative rises and falls in accordance with the value of the underlying asset.

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Derivative We have said that derivatives are financial instruments. So? So, it means that derivatives represent a contractual agreement between two parties whereby it promises to transfer the ownership of the asset (not necessarily the asset itself). Before we get into forwards and futures, you still remember the three main types of traders of derivatives?

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**Traders of derivatives**

Types of traders: Hedger: Hedging is a trading technique used to manage risk. Companies buy or short futures to protect their investment against the risk of future price fluctuations. Consider a Mauritian firm importing raw materials from China, and is expected to pay ¥ 2m in 3 months time to the Chinese exporter. What if ¥ appreciates in 3 months time? Then, the Mauritian firm has to pay more Mauritian Rupees for the same amount of ¥2m debt. How to hedge? Remember your Homework?

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**Traders of derivatives**

The speculator is here to look for profit. The latter speculates on future price fluctuations and thereby exploits such fluctuations through their expectations about future price rise or fall without intending to take physical delivery of the contract. The current exchange rate as at January 2013 is dollars per pound. Suppose a speculator expects that the £ will strengthen against the $ in 3 months time. The speculator decides to engage in futures contracts where the latter buys 10 futures costing £62,500 each. The April futures price is dollars per pound. What will be the investor’s position if the exchange rate in April turns out to be dollars per pound? dollars per pound?

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**Traders of derivatives**

Arbitrageurs look for arbitrage opportunities whereby they lock in a riskless profit by simultaneously entering into transactions in two or more markets. XYZ International Stock: London Stock Exchange (LSE): £1 New York Stock Exchange (NYSE): $ 1.77 Foreign exchange: 1.75 $/ £ All these rate are at a particular point in time. Is there arbitrage opportunities? How an arbitrageur can make a profit if he engages 1,000,000 shares?

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Forward A forward contract is an agreement between two parties to exchange an asset at a future settlement date at a forward price specified today. The date at which the exchange takes place is called the delivery price. There are no expenses at the time of the agreement. 2 parties: Long position and Short position Bear the risk of counterparty default in mind. Depending on which way the price moves there may be a strong incentive for one of the parties to default on the contract.

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Forward Both parties can eliminate their risk if they agree now on the details of the future transaction. The details are the quantity of wheat, the price per unit and when (and where) delivery will take place. Farmer Flour Mill Sells wheat Sows seed in spring Needs to know income at harvest time. Income depends on future price. Price Risk Buys wheat Needs to know cost at time of purchase. Cost depends on future price.

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**Forward-Pricing Forward price: Basic investment asset**

Forward price: Asset with discrete income Forward price: Asset with continuous income (not at this stage) Forward price: Commodities (not at this stage)

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**Forward Pricing: Basic investment asset**

The simplest forward contract is the one having an underlying asset which neither incur costs nor provide income. Eg: Non-dividend shares and zero coupon bonds Remember continuous compounding? We will use this formula FV = PV erT For forward contracts: F0 = S0erT FV is the forward price (F0) and PV is the spot price (S0) that provides no income.

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**Forward Pricing: Basic investment asset**

Suppose you go long on a forward contract to buy gold in 3 months. The current price is $ 100 and the risk-free three-month rate of interest is 5%, and there are no costs of holding the gold. What is the three-month forward price for the asset? What if F0 (forward price) is not equal to (101.26) S0erT This brings in Arbitrage opportunities. How to make profit if F0 > S0erT or F0 < S0erT

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**Forward Pricing: Basic investment asset**

F0 > S0erT

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F0 < S0erT

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**Forward Pricing: Discrete income asset**

The assumption that there are no holding costs or benefits is often not a reasonable one. Holding financial assets such as bonds or equities may result in holding benefits in the form of coupons or dividends. Examples of such assets are shares with dividend payments and bonds with coupon payments. The arguments are based on the previous approach where instead there will be an adjustment of the additional income (dividend, or coupon).

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**Forward Pricing: Discrete income asset**

Assuming that S0 is the current price of a bond having a coupon payment of J; or assume S0 is the current price of a share having a dividend payment of J. J is the present value of the dividend/coupon payment and is therefore required to be deducted from the current price since it has a different borrowing rate and time period. Thus, (S0 – J) is considered instead of only S0. No income: F0 = S0erT Income, J: F0 = (S0 – J) erT, where J is the present value of dividend/coupon payment (X) = X e-rT

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**Forward Pricing: Discrete income asset**

Suppose you go long on a forward contract for a coupon-bearing bond in 6 months. The current price is $ 1000 and the risk-free six-month rate of interest (continuously compounded) is 5%. A coupon payment of $ 50 is expected in 3 months time at a rate of interest of 4% (continuously compounded).What is the six-month forward price for the asset? F0 =

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Future contract Similar to forward contract agreements but are traded through exchanges. The exchange mitigates the counterparty risk through its trading arrangements. It guarantees delivery and payment by use of a clearing house. In practice delivery of the underlying seldom takes place. The obligation to deliver or receive a product at maturity of the contract may be avoided by closing the contract. Examples of future exchanges: CGOT, GBOT, LIFFE, Tokyo commodity exchange.

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Futures contract There is a tomato farmer who wants to secure his selling price for his next crop and there’s KFC who wants to fix the price of its Zinger for next year. The current price is $2.50 per bushel and the future price is $ 2.75. The farmer and KFC can enter into a futures contract whereby they agree to trade an asset (tomato) at a price set today ($ 2.75) for a specified amount (1 million bushel) for a future period in time (3 months time). What happens in 3 months time? Trading of 1 million bushel of tomatoes takes place at $ 2.75 per bushel. Is it not same as a forward contract? No. The trading mechanisms from the contract period till the maturity period (discussed later).

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**Forward vs. Futures Forward Futures**

Private contract between two parties Traded on an exchange (centralised trading pit) Not Standardised, Tailor Made (private negotiation) Standardised terms of contract (delivery places and dates, volume, technical specifications) Usually one specified delivery date because of no secondary market. Range of delivery dates since exchange traded enables more liquidity. Settled at end of contract Settled daily (through daily mark to market process which is later discussed). Delivery or final cash settlement usually takes place Contract is usually closed out prior to maturity (No actual delivery in most cases). Some credit risk What if the counterparty fails to perform? Virtually no credit risk (Regulated by Exchange clearing house)

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Futures mechanism A margin in the futures market is the amount of cash an investor must put up to open an account to start trading. This cash amount is the initial margin requirement, which is, at the end of each day, adjusted to reflect the capital gain or loss (mark to market process). The seller also is required to put the initial margin. The account balance must always be above the maintenance margin. If the margin balance falls below the maintenance margin, a margin call is required to top up the balance to its initial amount.

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**Futures mechanism Initial margin requirement: $ 100.**

Maintenance margin: $ 50 Get into the futures contract. Price of commodity falls over time period and cause a loss to you. Your margin account leads to a balancing amount of $ 40. Margin acc. < Maintenance margin, a Margin call is required. By how much? Top up till the initial margin (100). Therefore, margin call of $ 60 (100-40).

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**Futures mechanism What if I don’t meet my margin call?**

The contract is closed out the broker is allowed to liquidate the investor’s position without receiving explicit permission to do so.

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Futures mechanism Just as an investor is required to maintain a margin account with a broker, the latter is required to maintain a margin account with a clearinghouse member and that member is required to maintain a margin account with the clearinghouse. The clearinghouse guarantees the performance of the parties to each transaction. It has a main task of keeping track of all the transactions that take place during a day so that it can calculate the net position of each of its members. The clearinghouse acts as a buyer to the seller and a seller to the buyer; eliminating the counterparty risk.

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