BM410-07 Forwards Futures and Options 22Sep05_2
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Transcript of BM410-07 Forwards Futures and Options 22Sep05_2
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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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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 tounderstand
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
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?