## Introduction to Derivatives Example

The following derivative example provides an overview of the most prevalent kinds of derivative instruments. A derivative is a financial security whose value is derived from an underlying asset. Underlying assets can be equity, index, foreign exchange, commodity, or any other assets. So from the above definition, it is clear that derivative products do not have their own value, its value is decided by any particular underlying assets. The main participant in derivative markets are hedgers, speculators, and arbitragers. Below examples of a derivative illustrate of the most common derivatives. It is impossible to provide all types of derivative examples, since there thousands of such derivatives, and which vary in every situation.

### Examples of Derivatives (With Excel Template)

Let’s try to understand derivatives through the below examples.

#### #1 Derivatives Example – Futures Contract

**ABC Co. is a delivery company whose expenses are tied to fuel prices. ABC Co. anticipated that they use 90,000 gallons of gasoline per month. It is currently, July 1 ^{st} and the company wants to hedge its next 3 months of fuel costs using the RBOB Gasoline future contracts. Information on these contracts is as follows.**

**Each contract is for 42,000 gallons.****Contracts expire at the end of the prior month. For example, if we have to buy the August contract that will expire at the end of July.****The initial margin is $11,475 and the maintenance margin is $8,500.**

**Given,**

**Question-1 – Should ABC Co. Buy (Long) or Sell (Short) the Future to Initiate its Position.**

**Solution: **

ABC Co. exposure is to the gas price if the gas price goes up, its expenses will go up, due to expenses profit will go down. So if an ABC Co want to hedge that risk exposure and protect its profit, they need a situation where future position going to increase in value when gas prices go up. So if a company go for long contract buy gasoline futures so that the company will make a profit on that futures when gas goes up so this will offset with natural risk exposure. So the ABC Co. hedge position here is to go long (buy) the contract.

**Question 2 – How many contracts should ABC Co. use?**

**Solution: **

ABC Co. uses 90,000 Gallons of Gas every Month and each Contract was for 42,000 Gallons.

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- Number of Contracts = Anticipated Gas Use / Contract for
- Number of Contracts = 90000/42000
- Number of Contracts =
**2**

For Two Contract:

- One contract = 42,000
- Two contracts = 2 × 42,000
- Two contracts = 84,000 Gallons of Gas.

So how many should be used the answer is 2.

**Question 3 -What is ABC Co. initial cash flow?**

Initial Cash Flow or Margine is Calculated as :

**Solution: **

- So here number of Contract = 2
- Initial Cash Flow/Margin = $11,475
- = 2 × $11,475
- = $22,950 per month

So for 3 month

- Initial Cash Flow/ Margin For 3 month = $22,950 × 3
- Initial Cash Flow /Margin For 3 month
**= $68,850**

So initially ABC Co. has to put $68,850 into its margin accounts in order to establish its position which will give company two contacts for next 3 month.

**Question 4 – The price of gasoline for the August future is $2.8974, September future is $2.8798 and the October future is $2.7658 and which closed at August $2.6813, September $2.4140 and October $2.0999 How much did ABC Co. lose on a futures contract?**

**Solution:**

**Loss = (Closing Price – Opening Price) × Total Gasoline**

Loss is Calculated as Below:

** **

- Loss = (2.6813-2.8974) * 84000
- Loss =
**-18152.4**

Similarly for all,

- Total Loss = Loss In (Aug) + (Sep) + (Oct)
- Total Loss = -18152.4 + -39127.2 + -55935.6
- Total Loss =
**-113215.20**

So Total loss on Futures Contracts $**-113215.20**

#### Derivatives Example#2 – Long Futures

**On 1 ^{st} March an Indian importer enters a contract to import 1,000 bales of cotton with payments to be made in dollars on 1^{st} September. The price of one bale of cotton was fixed at USD 50 per bale. The present exchange rate is 1 USD = 69.35 INR. The importer has the risk of paying the more if USD strengthens. The dollar strengthens in the coming months and on the 1^{st} of September, the exchange rate climbs to 1 USD = 72.35 INR. Let us look at the following two scenarios.**

**Now what has happened here that Importer has to pay more due to rate difference i.e. 72.35 INR – 69.35 INR = 3 INR**

**So 1000×50×3 = INR 1, 50,000 extra amount to pay.**

**Given,**

**Case -1:- When the Importer has not hedged his position.**

**Solution:**

**The Total Payment made in USD as on 1 ^{st }March = No. Of cotton bales × per unit price**

The Total Payment made in USD as on 1^{st }March is as calculated below:

- The Total Payment Made on 1
^{st }March = 50×1000 - The Total Payment Made on 1
^{st }March =**$50,000**

**Amount of INR required to make a payment on 1 ^{st} March**

Amount of INR required to make a payment on 1^{st} March are as calculated below:

- Amount of INR Required to make a Payment on 1
^{st}March = $50,000 × 69.35 - Amount of INR Required to make a Payment on 1
^{st}March =**34, 67,500 INR**

**Amount of INR Required to Make a Payment on 1 ^{st} Sep**

- Amount of INR Required to make a Payment on 1
^{st}Sep = $50,000 × 72.35 - Amount of INR Required to make a Payment on 1
^{st}Sep =**36, 17,500 INR**

**Total Loss Suffered due to an Increase in the Exchange Rate**

- Total Loss Suffered due to an Increase in the Exchange Rate = 34, 67,500.00 – 36, 17,500.00
- Total Loss Suffered due to an Increase in the Exchange Rate =
**-1, 50,000 INR**

**Conclusion**– The Importer has to pay an extra 1, 50,000.00 INR on 1^{st} September due to an increase in the exchange rate thus incurs a loss compared to his payment obligation as on 1^{st} March.

**Case -2:- The Importer decided to hedge his position by going in the currency futures market. The importer expected that USD will strengthen and he decided to USD-INR contract to hedge his position.**

**Solution: **

**No of USD –INR Contracts**

No of USD –INR Contracts are calculated as:

- No of USD –INR Contracts = Amount to Pay/1000 (Lot size for 1USD-INR Contract)
- No of USD –INR Contracts = 50,000/1000
- No of USD –INR Contracts =
**50 Contracts**

**Total Amount Incurred on buying a Currency Futures Contract**

Total Amount Incurred on buying a Currency Futures Contract is calculated as :

- Total Amount Incurred on buying a Currency Futures Contract = 50 × 1000 × 69.55
- Total Amount Incurred on buying a Currency Futures Contract =
**34, 77,500 INR**

**Proceeds from the Sale of Future Contract**

Proceeds from the Sale of Future Contract is Calculated as :

On 1^{st }September the Exchange Rate moves to 72.35 and the Future Price Moves to 72.55

- Proceeds from the Sale of Future Contract = 50 × 1000 × 72.55
- Proceeds from the Sale of Future Contract =
**36, 27,500 INR**

**Profit on Sale of Future**

Profit on Sale of Future is calculated as :

**Profit on Sale of Future = Sale of Future Contract – Purchase of Future Contract**

- Profit on Sale of Future = 36, 27,500.00 – 34, 77,500.00
- Profit on Sale of Future
**= 1, 50,000 INR**

Conclusion: The Importer has effectively hedged his loss by entering in the future contracts and thereby null and void his loss because of adverse movement in the exchange rate.

#### Derivatives Example#**3 – Stock Index Futures**

**John owns a stock portfolio and detail related to the portfolio as mentioned below.**

**Value of portfolio: V =$95 Million (Spot Price)****Beta of portfolio: β =0.90**

**Future contract S&P Future price:**

- f= 1,513.40
- S&P futures contract has a size of multiple of $250
- So future contract price = $250 × $1,513.40 = $378,350
- Note contract size = $250 × S&P futures price.

**Solution:**

**Hedge Ratio (HR) = (S/f) β**

- HR = (Dollar value of portfolio/Dollar price of S&P Futures contract) × β
- HR = ($95,000,000/$378,350) × 0.90
- HR=
**225.98 ≈ 226**

Now let’s try to understand the above example through below two scenarios:

**Suppose Market fall by, say 5%**

Since John owns a portfolio he will lose the money due to fall in the market by 5%, but since John is short in the future (Sold Futures), he makes again.

- Stock portfolio value fall by = β × 5%
- Stock portfolio value fall by = 0.9 × 5% = 4.5% or by 0.045 × $95,000,000)
- Stock portfolio value fall by =
**-$4,275,000**

Futures Contract Price will also decrease by 5% so it will be $378,350 × 5% = $18,917.50

- Futures Contract Price = $378,350 – $18,917.50
- Futures Contract Price =
**$359,432.50**

Futures Gain = ($378,350 – $359,432.50) × 226 = $4,275,355

- Hedge Profit = Spot Position + Future Position
- Hedge Profit = -$4,275,000 + $4,275,355
- Hedge Profit
**=**__$355__

**Suppose Market rise by , say 5%**

Since John own a portfolio he will gain the money due to rise in market by 5%, but since John is short in futures (Sold Futures), he will lose.

- Stock portfolio value rise by = β × 5%
- Stock portfolio value rise by = 0.9 × 5% = 4.5% or by 0.045 × $95,000,000)
- Stock portfolio value rise by =
**$4,275,000**

Future Contract Price will also rise by 5% so it will be $378,350 × 5% = $18,917.50

- Future Contract Price = $378,350 + $18,917.50
- Future Contract Price =
**$ 397,267.50**

Future Loss = ($378,350 – $397,267.50) × 226 = -$4,275,355

- Hedge Loss = Spot Position + Future Position
- Hedge Loss = $4,275,000 + (-$4,275,355)
- Hedge Loss
**=****-$355**

### Conclusion

So the above examples give us a brief overview that how derivative markets work and how it hedges the risk in the market. The above examples show us that derivatives provide an efficient method for end-users to better hedge and manage their exposures to fluctuation in the market price/rates. The risks faced by derivative dealers depend on the actual strategy being adopted by the dealer. The above examples explain to us how hedging protects the hedger from unfavorable price movements while allowing continued participation in favorable movements. The above examples clear that derivative is distinctly more complex than traditional financial instruments, such as stocks, bonds, loans, banks deposits, and so on.

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