BM410-07 Forwards Futures and Options 22Sep05_2

7/31/2019 BM410-07 Forwards Futures and Options 22Sep05_2

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BM410: Investments

Derivatives: Forwards,Futures, and Options


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Objectives

A. Understand derivatives

B. Understand the basics and terminology of

ForwardsC. 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 dont understand the model, its

implications, uses, strengths, and weaknesses,

you will be at a disadvantage to those who do.


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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 tounderstand

Mathematically, it is extremely difficult


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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

neighbors 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.

500 700300

200

-200

Buyer of Puppy

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 andfutures?

Futures have secondary tradingliquidity

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

Acts as a party to all buyers and sellers.

Obligated to deliver or supply delivery

Clients benefit as they do not have to do anycredit 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 traders

margin may not fall.


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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 andwill eventually converge

Basis Risk

The variability in the basis that will affectprofits 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 acquiredtoday


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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

Parity Example Outcome


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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 thestock


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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 ifthe 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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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%


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Index Arbitrage

What is index arbitrage? Exploiting mis-pricing between underlying

stocks and the futures index contract

Futures Price too high - short the future andbuy the underlying stocks

Futures price too low - long the future andshort 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 investors

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 conditionalways holds exactly.

B. Find the holding-period return if the initial margin on

the contract is $15,000.


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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 contractwill 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 be9.095 x 500 = $4,547.50

The rate of return is $4,547.50 / $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

Callright to buy or Putright to sell

Writer Seller or HolderBuyer 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

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 specificperiods 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 entireo tions histor


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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 stocks 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: 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%


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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 = PPayoff to Call Holder

(ST - X) if ST >X

0 if ST < X

Profit to Call Holder

Payoff - Purchase Price (STXP)

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 >X0 if ST < X

Profit to Call Writer

Payoff + Premium (PST + X)

Max. loss: unlimited Max. gain: Premium


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Profit

Stock Price

0

Call Writer

Call Holder

Profit Profiles of Calls


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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

PayoffPremium - P + XSTMax. 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 PX + ST

Max. loss: unlimited Max. gain: Premium


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0

Profits

Stock Price

Put Writer

Put Holder

Profit Profiles for Puts


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Key Note

Risk characteristics of Options

While return is limited to the premium, the writer

of the optionshave 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 dont recommend options, if you mustused 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?

Documents

BM410-07 Forwards Futures and Options 22Sep05_2