BM410: Investments

Derivatives: Forwards, Futures, and Options

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

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

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.

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

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

Questions

Any questions on derivatives?

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

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.

500 700300

200

-200

Buyer of Puppy

Seller of Puppy

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

Key Terms

Futures price • Agreed-upon price at maturity

Long position• Agreement to purchase

Short position• Agreement to sell

Profits on positions at maturityLong = spot minus original futures priceShort = original futures price minus spot

PremiumPrice paid or received for the futures contract

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

Trading Mechanics

Clearinghouse • 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

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.

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

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

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

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

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

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 BillFO(1+rf)T - FO(1+rf)T FO

Total for B - FO(1+rf)T ST

Parity Example Outcome

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

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

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

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?

Answer

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

B. The stock price falls to 120 x (1-.03) = 116.40. The futures price falls to 116.4 x (1.06) = 123.38. The investor loses (127.20-123.38) x 1000 = $3,816

C. The percentage loss is 3816/12,000 = 31.8%

Index Arbitrage

• What is index arbitrage?• 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

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?

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.

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.

Problem 18-22 answer

A. The initial futures price is: Fo = 400 x (1 + .005-.002)12 = 414.64. In one month, the maturity of the contract will be only 11 months, so the futures price will be F0 = 410 x (1 + .005-.002) 11 = 423.74. The increase in the futures price is 9.095, so the cash flow will be 9.095 x 500 = $4,547.50

The rate of return is $4,547.50 / $15,000 = 30.3%

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

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

American versus European Options

American • 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

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!

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

Answer 16-8

Stock Price: 80 100 110 120 All Stocks (100) 8,000 10,000 11,000 12,000 All Options (1000) 0 0 10,000 20,000 Bills + options 9,630 9,360 10,360 11,360

Returns: All Stocks -20.0% 0.0% 10.0% 20.0% All Options -100.0% -100.0% 0.0% 100.0% Bills + Options -6.4% -6.4% 3.6% 13.6%

Payoffs and Profits on Options at Expiration–

Call Holder (buyer)

Call Holder

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

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

ProfitProfit

Stock PriceStock Price

0

Call WriterCall Writer

Call HolderCall Holder

Profit Profiles of Calls

Payoffs and Profits at Expiration – Put Holder (buyer)

Put Holder

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

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

0

Profits

Stock Price

Put Writer

Put Holder

Profit Profiles for Puts

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

Questions

Any questions on options?

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?