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**Derivatives: Forwards, Futures, and Options**

BM410: Investments Derivatives: Forwards, Futures, and Options

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**Objectives A. Understand derivatives**

B. Understand the basics and terminology of Forwards C. Understand the basics and terminology of Futures D. Understand the basics and terminology of Options

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**A. Understand Derivatives**

What are derivatives? Derivatives are financial contracts whose values are determined by (or derived from) a traditional security (stock or bond), an asset (a commodity), or a market index. Derivatives are not ownership, but the right to become (or quit being) owners in the fundamental security

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**Derivatives (continued)**

What are derivatives based on? Derivatives are based on the same math as particle physics. Most models are based on the Black-Scholes Options Pricing Model If you don’t understand the model, its implications, uses, strengths, and weaknesses, you will be at a disadvantage to those who do.

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**Derivatives (continued)**

What is so risky about derivatives? Derivatives can be either risk creating or risk eliminating The key is how they are used What is so hard to understand about derivatives? Conceptually, they are easier to understand Mathematically, it is extremely difficult

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**Derivatives (continued)**

What about derivatives for individual investors? Derivatives are a zero-sum game--for every winner, there is an offsetting loser On the other side of the transaction, is a multi-billion dollar financial institution with millions in computer systems and truckloads of Ph.D.s who understand the math They are inappropriate for virtually all non-professional investors For individual investors: stick to what you know

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Questions Any questions on derivatives?

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**B. Basics of Forwards and Futures**

What is a forward? An agreement calling for a future delivery of an asset at an agreed-upon price and agreed-upon day Example: Your son wants a puppy really bad, and your neighbor’s dog just had pups. Your son goes and picks his favorite puppy, you and your neighbor agree to the price ($500), and you agree to a date to pick up the puppy (after its weaned in 3 weeks). This is a forward contract

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Forwards (continued) Now assume the price, between when you made the agreement and when you were to pick up the puppy changed. Your chart would look like this. Buyer of Puppy 200 300 500 700 -200 Seller of Puppy

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**Futures (continued) What are Futures?**

Similar to forward but feature formalized and standardized characteristics on specific exchanges What are the hey difference between forwards and futures? Futures have secondary trading – liquidity Futures are marked to market daily Futures have standardized contract units The futures clearinghouse warrants performance

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**Key Terms Futures price Agreed-upon price at maturity Long position**

Agreement to purchase Short position Agreement to sell Profits on positions at maturity Long = spot minus original futures price Short = original futures price minus spot Premium Price paid or received for the futures contract

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Types of Contracts What are the major types of forwards and futures contracts? Agricultural commodities Metals and minerals (including energy contracts) Foreign currencies Financial futures Interest rate futures Stock index futures

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**Trading Mechanics Clearinghouse Closing out positions**

Acts as a party to all buyers and sellers. Obligated to deliver or supply delivery Clients benefit as they do not have to do any credit checks on opposite party Closing out positions Reversing the trade Take or make delivery Most trades are reversed and do not involve actual delivery

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**Margin and Trading Arrangements**

Key terminology Initial Margin Funds deposited to provide capital to absorb losses Marking to Market Each day the profits or losses from the new futures price and reflected in the account. Maintenance or variance margin An established value below which a trader’s margin may not fall.

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**Margin and Trading Arrangements**

Margin call When the maintenance margin is reached, broker will ask for additional margin funds Convergence of Price As maturity approaches the spot and futures price converge Delivery Actual commodity of a certain grade with a delivery location or for some contracts cash settlement

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**Trading Strategies What are the different types of trading strategies?**

Speculation Short - believe price will fall Long - believe price will rise Hedging Long hedge - protecting against a rise in price Short hedge - protecting against a fall in price

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**Basis and Basis Risk Basis**

The difference between the futures price and the spot price Over time the basis will likely change and will eventually converge Basis Risk The variability in the basis that will affect profits and/or hedging performance

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**Futures Pricing Spot-futures parity theorem**

Two ways to acquire an asset for some date in the future: Purchase it now and store it Take a long position in futures These two strategies must have the same market determined costs

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**Parity Example Stock that pays no cash dividend No storage costs**

No seasonal patterns in prices Strategy 1: Buy the stock now and hold it until time T Strategy 2: Put funds aside today to perform on a futures contract for delivery at time T that is acquired today

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**Parity Example Outcome**

Strategy A: Action Initial flows Flows at T Buy stock -So ST Strategy B: Action Initial flows Flows at T Long futures 0 ST - FO Invest in Bill FO(1+rf)T - FO(1+rf)T FO Total for B - FO(1+rf)T ST

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**Price of Futures with Parity**

Since the strategies have the same flows at time T FO / (1 + rf)T = SO FO = SO (1 + rf)T The futures price has to equal the carrying cost of the stock

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Problem 18-9 A hypothetical futures contract on a non-dividend-paying stock with current price $150 has a maturity of one year. A. If the T-bill rate is 6%, what should the futures price be? B. What should the futures price be if the maturity of the contract is 3 years? C. What if the interest rate is 12% and the maturity of the contract is 3 years? Answers: A. F = S0 (1 + r) = 150 x (1.06) = $159 B. F = S0 ( 1 + r)3 = 150 x (1.06)3 = $178.65 C. F = 150 x (1.08)3 = $188.96

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Stock Index Contracts Available on both domestic and international stocks Advantages over direct stock purchase Lower transaction costs Better for timing or allocation strategies Takes less time to acquire the portfolio

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Problem 18-14 The Chicago Board of Trade has just introduced a new futures contract on Brandex stock, a company that currently pays no dividends. Each contract calls for delivery of 1,000 shares of stock in one year. The T-bill rate is 6% per year. A. If Brandex stock now sells at $120 per share, what should the futures price be? B. If the Brandex stock price drops by 3%, what will be the change in the futures price and the change in the investors margin account? C. If the margin on the contract is $12,000, what is the percentage return on the investors position?

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**Answer A. The price should be 120 x (1.06) = $127.20**

B. The stock price falls to 120 x (1-.03) = The futures price falls to x (1.06) = The investor loses ( ) x 1000 = $3,816 C. The percentage loss is 3816/12,000 = 31.8%

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**Index Arbitrage What is index arbitrage? Is it doable?**

Exploiting mis-pricing between underlying stocks and the futures index contract Futures Price too high - short the future and buy the underlying stocks Futures price too low - long the future and short sell the underlying stocks Is it doable? Yes, but very difficult to do in practice Transactions costs are often too large Trades cannot be done simultaneously

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Problem 18-21 The margin requirement on the S&P500 futures contract is 10%, and the stock index is currently at 1,200. Each contract has a multiplier of $250. A. How much margin must be put up for each contract sold? B If the futures price falls by 1% to 1,188, what will happen to the margin account of an investor who holds one contract? What will be the investor’s percentage return based on the amount put up as margin?

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Answer A. The dollar value of the index is thus: $250 x 1,200 = $300,000 x 10%= required margin of $30,000 B. If the futures price decreases by 1% to 1,188, the decline in the futures price is 1,200-1,188 = 12. The decrease in your margin account would be 12 x $250=$3,000, which is a percent loss of $3,000 / $30,000 = -10%. Cash in the margin account is now $30,000 - $3,000 = $27,000.

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Problem 18-22 The multiplier for a futures contract on a certain stock market index is $500. The maturity of the contract is 1 year, the current level of the index is 400, and the risk-free interest rate is 0.5% per month. The dividend yield on the index is 0.2% per month. Suppose that after one month, the stock index is at 410. A. Find the cash flow from the mark-to-market proceeds on the contract. Assume that the parity condition always holds exactly. B. Find the holding-period return if the initial margin on the contract is $15,000.

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Problem answer A. The initial futures price is: Fo = 400 x ( )12 = In one month, the maturity of the contract will be only 11 months, so the futures price will be F0 = 410 x ( ) 11 = The increase in the futures price is 9.095, so the cash flow will be x 500 = $4,547.50 The rate of return is $4, / $15,000 = 30.3%

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**C. Option Basics What is an option?**

An option is the right, but not the obligation, to buy or sell a specific security at a specific date and price Option Terminology Buy - Long or Sell - Short Call – right to buy or Put – right to sell Writer – Seller or Holder – Buyer of the option Key Elements Exercise or Strike Price Premium or Price Maturity or Expiration

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**Market and Exercise Price Relationships**

In the Money Exercise of the option would be profitable Holder of the Call: Market price (MP) > exercise price (EP) (buy at lower price) Holder of the Put: EP > MP (sell at higher price) Out of the Money Exercise of the option would not be profitable Holder of the Call: MP < EP Holder of the Put: EP < MP At the Money Exercise price and asset price are equal

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**American versus European Options**

The option can be exercised at any time before expiration or maturity European The option can only be exercised on the expiration or maturity date Bermuda The option can be exercised only during specific periods of time, as stated in the contract Asian The option can be exercised, not based on the final price, but on any price during the entire options history

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**Different Types of Options**

What are the different types of Options? Stock Options Index Options Futures Options Foreign Currency Options Interest Rate Options Options are zero sum games. Remember that for every winner there is a loser Use them at your risk!

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Problem 16-5 Suppose you think Wal-Mart stock is going to appreciate substantially in value in the next six months. Say the stock’s current price, So, is $100, and the call option expiring in 6 months has an exercise price, X, of $100, and is selling at a price, C, of $10. With $10,000 to invest, you are considering three alternatives: A. Invest all $10,000 in the stock, buying 100 shares B. Invest all $10,000 in 1,000 options (10 contracts) C. Buy 100 options (1 contract) for $1,000 and invest the remaining $9,000 in a money market fund paying 4% interest over six months (8% per year). What is your rate of return for each alternative for four stock prices six months from now: $80, $100, $110, $120

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Answer 16-8 Stock Price: All Stocks (100) , ,000 11, ,000 All Options (1000) , ,000 Bills + options , ,360 10, ,360 Returns: All Stocks % % 10.0% 20.0% All Options % % 0.0% 100.0% Bills + Options % % 3.6% 13.6%

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**Payoffs and Profits on Options at Expiration– Call Holder (buyer)**

Buyer of the right to buy an asset at the exercise price Notation Stock Price = ST Exercise Price = X Premium = P Payoff to Call Holder (ST - X) if ST >X 0 if ST < X Profit to Call Holder Payoff - Purchase Price (ST – X – P) Max. loss: Premium Max. gain: unlimited

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**Payoffs and Profits on Options at Expiration – Call Writer (seller)**

Call Writer (or seller) Seller of the right to buy an asset at the exercise price Payoff to Call Writer - (ST - X) if ST >X 0 if ST < X Profit to Call Writer Payoff + Premium (P – ST + X) Max. loss: unlimited Max. gain: Premium

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**Profit Profiles of Calls**

Call Holder Call Writer Stock Price

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**Payoffs and Profits at Expiration – Put Holder (buyer)**

Gives the buyer of the put the right to sell an asset at the exercise price Payoffs to Put Holder 0 if ST > X (X - ST) if ST < X Profit to Put Holder Payoff – Premium - P + X – ST Max. loss: Premium Max. gain: unlimited

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**Payoffs and Profits at Expiration – Put Seller (writer)**

Put Writer Seller of the right to sell an asset at the exercise price Payoffs to Put Writer 0 if ST > X -(X - ST) if ST < X Profits to Put Writer Payoff + Premium P – X + ST Max. loss: unlimited Max. gain: Premium

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**Profit Profiles for Puts**

Profits Put Writer Put Holder Stock Price

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**Key Note Risk characteristics of Options**

While return is limited to the premium, the writer of the options have unlimited risk! I do not recommend anyone writing options, unless you already own the stock While loss is limited to the premiums, the buyer of the options have unlimited upside While I don’t recommend options, if you must used this, be a buyer and not a seller

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Questions Any questions on options?

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Review of Objectives A. Do you understand the basics and terminology of Options? B. Do you understand the basics and terminology of Futures and Forwards?

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