FIN 377: Investments Topic 8: An Introduction to Derivative Markets and Securities larry Schrenk, Instructor.

FIN 377: Investments Topic 8: An Introduction to Derivative Markets and Securities larry Schrenk, Instructor

Overview 14.1 Overview of Derivative Markets
14.2 Investing with Derivative Securities 14.3 The Relationship between Forward and Option Contracts 14.4 An Introduction to the Use of Derivatives in Portfolio Management

Learning Objectives @

Readings Reilley, et al., Investment Analysis and Portfolio Management, Chap. 14

14.1 Overview of Derivative Markets

A derivative instrument is one for which the ultimate payoff to the investor depends directly on the value of another security or commodity

Two kinds of derivatives available: Forward and futures contracts Option contracts Only one forward contract is needed for any particular maturity date and underlying asset Two types of options Calls Puts For each of these derivatives, an investor can enter into a transaction as: The long position (the buyer) The short position (the seller)

14.1.1 The Language and Structure of Forward and Futures Markets
A forward contract gives its holder both the right and the full obligation to conduct a transaction involving another security or commodity the underlying asset At a predetermined date (maturity date) At a predetermined price (contract price) There must be two parties (counterparties) to a forward transaction The eventual buyer (or long position) The eventual seller (or short position)

Forward and Spot Markets A forward contract is basically a trade agreement The terms that must be considered in forming a forward contract are the same as those necessary for a bond transaction that settled immediately (i.e., a spot market transaction) The settlement date, at time T rather than 0 The contract price, F0, T rather than S0 No payments until expiration

Forward contracts are negotiated in the over-the-counter market, involve credit (or default) risk, and is quite often illiquid Futures contracts try to solve these problems with Standardized terms Central market (futures exchange) More liquidity Less default risk: Margin requirements Settlement price: Daily “marking to market”

The futures exchange will require both counterparties to post collateral, or margin, to protect itself against the possibility of default Margin accounts are: Held by the exchange’s clearinghouse Marked to market daily basis to ensure that both end users always maintain sufficient collateral to guarantee their eventual participatio

Futures price: Analogous to the forward contract price Is set at a level such that a brand-new long or short position would not have to pay an initial premium The futures exchange will require both counterparties to post collateral, or margin, to protect itself against the possibility of default Margin accounts: Held by the exchange’s clearinghouse Marked to market daily basis to ensure that both end users always maintain sufficient collateral to guarantee their eventual participation

14.1.2 Interpreting Futures Price Quotations: An Example
Spot and futures prices for contracts on the Standard & Poor’s 500 Index as of June 26, 2017 At the close of trading, the index level stood at 2,439.07, which can be considered as the spot price of one “share” of the S&P index (S0) Consider the futures contract that expires in September 2017 The settle (or closing) contract price is listed as 2, (=F0,T) An investor taking a long position in this contract would be committing in June to buy a certain number of shares in the S&P 500 Index (250 shares) at a price of $2, per share on the expiration date in September Conversely, the short position in this contract would be committing to sell 250 S&P shares under the same conditions Except for the margin posted with the futures exchange, no money changes hands between the long and short positions at the origination of the contract in June

Payoff and net profit for this contract from the long position’s point of view, assuming a hypothetical set of S&P index levels on the September expiration date (ST): The payoff to the long position is positive when the S&P index level rises (relative to the contract price of 2,436.00), while a loss is incurred when the S&P falls If the expiration date level of the index is 2,475.00, the long position will receive a profit of $39.00 per share If the expiration date level of the index is 2,415, the futures contract still obligates the investor to purchase stock for the contract price, thus resulting in a loss of $21.00

14.1.3 The Language and Structure of Option Markets
An option contract gives the holder the right-but not the obligation to buy or to sell an underlying security or commodity at a predetermined future date and at a predetermined price Option to buy is a call option Option to sell is a put option Buyer has the long position in the contract Seller (writer) has the short position in the contract Buyer and seller are counterparties in the transaction

Option Contract Terms The exercise price (X) is the price the call buyer will pay to-or the put buyer will receive from-the option seller if the option is exercised The option premium (C0,T) is the price that the option buyer must pay to the seller at Date 0 to acquire the option contract European options can only be exercised only at maturity (Date T) American options can be exercised any time before and at the expiration date

Option Valuation Basics Intrinsic value represents the value that the buyer could extract from the option if he or she exercise the option immediately In the money: An option with positive intrinsic value Out of the money: The intrinsic value is zero At the money: When the stock price is equal to exercise price, S0 = X The time premium component is simply the difference between the whole option premium and the intrinsic component

Option Trading Markets Options trade both in over-the-counter markets and on exchanges When exchange traded, just the seller of the contract is required to post a margin account because he is the only one obligated to perform on the contract at a later date Options can be based on a wide variety of underlying securities, including futures contracts or other options

14.1.4 Interpreting Option Price Quotations: An Example

Consider the outcomes of two different investors, one of whom purchases a September S&P call struck at 2,435 (X) and one of whom buys a September 2,435 put At the origination of the transaction in June, these investors will pay their sellers the ask prices of $43.00 (C0,T) and $42.10 (P0,T), respectively

At the current (spot) price of the index of : Call option: The investor holding the call option has the right, but not the obligation, to buy one S&P share for $2,435 at the expiration date in September Call option is in the money Total call premium of $43.00 can be divided into an intrinsic value component of $4.07 and a time premium of $38.93 Put option: The investor holding the put option has the right, but not the obligation, to sell one S&P share for $2,435 at the expiration date in September The put is out of the money, however, as this exercise price is lower than the current index level The put option has no intrinsic value, so the entire $42.10 ask price is a time premium

Call option payoffs: The investor will exercise the contract to buy a share of the S&P index only when the September S&P level is above 2,435 At index levels at or below 2,435, the investor will let the option expire worthless and simply lose his initial investment While the call is in the money at index levels above 2,435, the investor will not realize a net profit until the September index level rises above 2,478.00, an amount equal to the exercise price plus the call premium (X + C0,T)

Put option payoffs For the shown in Panel B, the holder will exercise the contract at September index levels below the exercise price, using the contract to sell for $2,435 an S&P share that is worth less than that The put investor will not realize a positive net profit until the index level falls below 2, (X -P0,T) For September S&P values above 2,435, the put option expires out of the money

14.1 Investing with Derivative Securities

14.2 Investing with Derivative Securities
Although there are differences between forward and option agreements, the two types of derivatives are quite similar in terms of the benefits they produce for investors The ultimate difference between forwards and options lies in the way the investor must pay to acquire those benefits

14.2.1 The Basic Nature of Derivative Investing
Consider an investor who decides at Date 0 to purchase a share of stock in SAS Corporation six months from now, coinciding with an anticipated receipt of funds Assume that both SAS stock forward contracts and call options are available with the market prices of F0,T and C0,T (where T = 0.50 year) and that the exercise price of the call option, X, is equal to F0,T If the investor wants to lock in the price now at which the stock purchase will eventually take place, there are two choices: A long position in the forward Does not require front-end payment Requires future settlement payment Purchase of a call option Requires up front payment Allows but does not require future settlement paymen

14.2.1 The Basic Nature of Derivative Investing

14.2.2 Basic Payoff and Profit Diagrams for Forward Contracts
Payoffs to both long and short positions in the forward contract are symmetric, or two-sided, around the contract price The payoffs to the short and long positions are mirror images of each other In market jargon, forward contracts are zero-sum games

14.2.2 Basic Payoff and Profit Diagrams for Forward Contracts

14.2.3 Basic Payoff and Profit Diagrams for Call and Put Options
The difference between payoff and profit is the option premium (cost), a sunk cost The investor receives expiration date payoffs that are asymmetric, or one-sided For instance, a call option buyer has unlimited upside potential with limited downside risk The payoffs and profits for option buyers and sellers (writers) are mirror images around horizontal line, a result of zero-sum games

When held as investments, options are directional views on movements in the price of the underlying security Call buyers and put sellers count on ST to rise (or remain) above X, while put buyers and call sellers hope for ST to fall (or remain) below the exercise price at the expiration date Option buyers always have limited liability because they do not have to exercise an out-of-the-money position

14.2.4 Option Profit Diagrams: An Example
Suppose that a share of SAS stock currently sells for $40, and six different SAS options (three calls and three puts) are available to investors The options all expire on the same date in the future and have exercise prices of either $35, $40, or $4 Exhibit 14.13

Call options The call option profits indicate that, although it is the most expensive, the deepest in-the-money contract (Call 1) becomes profitable the quickest, requiring only that ST rise to $43:07 (= ) Call 3 is the least expensive to purchase but requires the greatest movement in the price of the underlying stock—to $48.24, in this example—before it provides a positive profit to the investor Put options Put 1 (the out-of-the-money contract) costs the least but needs the largest price decline to be profitable at expiration

Options and Leverage Compare the returns to an investment in either a put or a call option with a direct investment (or short sale) in a share of the underlying SAS stock We will limit the analysis to Call 2 and Put 2, the two at-the-money contracts The holding period returns are for various positions assuming three different expiration date stock prices: $30, $40, and $50 Two different comparisons are made: Long stock versus long call Short stock versus long put

Both put and call options magnify the possible positive and negative returns of investing in the underlying security Long call option position For an initial cost of $5.24, the investor can retain the right to obtain the price appreciation of a share of SAS stock without spending $40 to own the share outright This degree of financial leverage manifests itself in a 100 percent loss when the stock price falls by a quarter of that amount and a 91 percent gain when SAS shares increase in value from $40 to $50 If the stock price remains at $40, then the owner of the share would not have lost anything, while the at-the-money call holder would have lost his entire investment Suggests that the option investor is also taking a view on the timing of that movement If the price of SAS stock had stayed at $40 through Date T and then rose to $50 on the following day, the stockholder would have experienced a 25 percent gain, while the buyer of the call option would have seen the instrument expire worthless

14.3 The Relationship between Forward and Option Contracts

14.3 The Relationship between Forward and Option Contracts
Positions in forward and option contracts can lead to similar investment payoffs if the price of the underlying security moves in the anticipated direction Similarity in payoff structures suggests that these instruments are connected These relationships, known as put–call parity, specify how the put and call premia should be set relative to one another Conditions can be expressed in terms of these two option types and either the spot or the forward market price for the underlying asset They depend on the assumption that financial markets are free from arbitrage opportunities, meaning that securities offering identical payoffs with identical risks must sell for the same current price

Put-Call-Spot Parity Suppose that at Date 0, an investor forms the following portfolio involving three securities related to Company WYZ: Buy a WYZ common stock at price of S0 Purchase a put option for P0, T to deliver WYZ stock at an exercise price of X on expiration date, T Sell a call option for C0, T to purchase WYZ stock at an exercise price of X on expiration date, T

Put-Call-Spot Parity

(Long Stock) + (Long Put) + (Short Call)
Put-Call-Spot Parity The net investment required to acquire this portfolio is (S0 + P0,T – C0,T) The net positive at expiration date no matter at what level the stock price is would be the same, X The result is a risk-free investment Because the risk-free rate equals the T-bill rate: (Long Stock) + (Long Put) + (Short Call) = (Long T-bill)

14.3.2 Put-Call Parity: An Example
Suppose that WYZ stock is currently valued at $53 and that call and put options on WYZ stock with an exercise price of $50 sell for $6.74 and $2.51, respectively If both options can only be exercised in exactly six months, then the equation suggests that we can create a synthetic T-bill by purchasing the stock, purchasing the put, and selling the call for a net price of $48.77 On the options’ expiration date, this portfolio would have a terminal value of $50

The risk free rate implied by this investment can be established by solving the following equation for RFR: If the rate of return on an actual six-month T-bill with a face value of $50 is not 5.11 percent, then an investor could exploit the difference

Suppose that the actual T-bill rate is 6.25 percent and that there are no restrictions against using the proceeds from the short sale of any security An investor wanting a risk-free investment would clearly choose the actual T-bill to lock in the higher return, while someone seeking a loan might attempt to secure a 5.11 percent borrowing rate by short-selling the synthetic T-bill An artificial short position can be obtained as: (Short Stock) + (Short Put) + (Long Call) = (Short T-Bill)

With no transaction costs, a financial arbitrage could be constructed by combining a long position in the actual T-bill with a short sale of the synthetic portfolio Given that the current value of the actual T-bill is $48.51 [= $50(1:0625)-0.5]

14.3.2 Put–Call Parity: An Example

14.3.3 Creating Synthetic Securities Using Put-Call Parity
A risk-free portfolio could be created by combining three risky securities: stock, a put option, and a call option The parity condition developed in the previous example can be expressed in other useful ways as well One of the four assets is always redundant because it can be defined in terms of the others

14.3.3 Creating Synthetic Securities Using Put–Call Parity
Three additional ways of expressing this result are:

14.3.3 Creating Synthetic Securities Using Put–Call Parity

14.3.4 Adjusting Put-Call-Spot Parity for Dividends
The holders of derivative contracts will not participate directly in the payment of dividends to the stockholder If the dividend amounts and payment dates are known when puts and calls are written, then they are adjusted into the option prices

14.3.5 Put-Call-Forward Parity
Instead of buying the stock in the spot market at Date 0, take a long position in a forward contract, allowing the purchase one share of WYZ stock at Date T The price of this acquisition, F0,T, would be established at Date 0 Assume that this transaction is supplemented by the purchase of a put option and the sale of a call option, each having the same exercise price and expiration date

This is a risk-free portfolio Differences in cash flow patterns: The net initial investment of (P0,T C0,T) is smaller than when the stock was purchased in the spot market The riskless terminal payoff of (X F0,T) is also smaller, as the stock is now purchased at Date T rather than at Date 0 This intuition leads to the put–call–forward parity condition:

14.4 An Introduction to the Use of Derivatives in Portfolio Management

14.4 An Introduction to the Use of Derivatives in Portfolio Management
Derivatives are also used to restructure existing portfolios of assets Typically, the intent of this restructuring is to modify the portfolio’s risk Three prominent derivative applications in the management of equity positions: Shorting forward contracts Purchasing protective puts Purchasing equity collars

14.4.1 Restructuring Asset Portfolios with Forward Contracts
Suppose a portfolio manager wants to shift allocation of $100 million portfolio from 100 percent equity to 100 percent T-bills for the next three months There are two ways to make this change: The most direct method would be to sell her stock portfolio and buy $100 million of 90-day T-bills and when the T-bills mature in three months, repurchase the original equity holdings Maintain current stock holdings but convert them into a synthetic risk-free position using a three-month forward contract with $100 million of the stock index as the underlying asset

This is a classic example of a hedge position, wherein the price risk of the underlying asset is offset by a supplementary derivative transaction Basic dynamics of this hedge:

To neutralize the risk of falling stock prices, the fund manager will need to adopt a forward position that benefits from that potential movement The manager requires a hedge position with payoffs that are negatively correlated with the existing exposure Quicker and more cost-effective to convert the pension fund’s asset allocation using a synthetic approach

Suppose that the contract price for a S&P 500 forward contract maturing in three months is F0, 0.25 = $101 The expiration date value of the hedged stock position will be: The value of the unhedged stock portfolio, plus The value of the short forward position, less The initial cost of the derivative position, (zero in the case of a forward contract)

Synthetic restructuring can also been viewed through the effect that it has had on the systematic risk—or beta—of the portfolio Assume that the original stock position had a beta of 1.0, matching the volatility of a proxy for the market portfolio The combination of being long $100 million of stock and short a forward covering $100 million of a stock index converts the systematic portion of the portfolio into a synthetic T-bill, which by definition has a beta of 0.0 Once the contract matures in three months, however, the position will revert to its original risk profile

The net beta for the converted portfolio is simply a weighted average of the systematic risks of its equity and T-bill portions or: If the manager had wished to change the original allocation to a “60–40” mix of stock and T-bills, could have shorted only $40 million of the index forward to leave an unhedged equity position totaling $60 million This in turn would leave an adjusted portfolio beta of [(0.6)(1) + (0.4)(0)] = 0.6

14.4.2 Protecting Portfolio Value with Put Options
Suppose instead that the portfolio manager designed a hedge position correlated to the stock portfolio as follows:

In seeking an asymmetric hedge, this manager wants a derivative contract that allows the sale of stock when prices fall but keep the shares when prices rise The purchase of a put option to hedge the downside risk of an underlying security holding is called a protective put position It the most straightforward example of a more general set of derivative-based strategies known as portfolio insurance

In lieu of the short forward position, suppose the manager purchased a three-month, at-the-money put option on the $100 million stock portfolio for an up-front premium of $1.324 million With the exercise price set equal to the current portfolio value of $100 million, the put contract exactly offsets any expiration date share price decline while allowing the position to increase in value as stock prices increase The put provides the manager with insurance against falling prices with no deductible

Being long in the stock and long in the put generates the same net payoff as an at-the-money long call option holding “elevated” by $100 million The no-arbitrage equation can be rewritten:

Expression says that the protective put position generates the same expiration date payoff as a long position in a call option with equivalent characteristics and a long position in a T-bill with a face value equal to the options’ exercise price The manager has two ways of providing price insurance for the current stock holding: Continue to hold the shares and purchase a put option, or Sell her shares and buy both a T-bill and a call option The choice between them will come down to considerations such as relative option prices and transaction costs

14.4.3 An Alternative Way to Pay for a Protective Put
There is a third alternative for protecting against potential stock price declines, which fits between the short forward position and the protective put position Specifically, suppose that the manager makes two simultaneous decisions: Purchase a three-month, out-of-the-money protective put option with an exercise price of $97 million and a lower initial cost of $0.560 million Sells to the option dealer a call option with a three-month expiration and an exercise price of $108 million that also carries an initial premium of $0.560 million The simultaneous purchase of an out-of-the-money put and sale of an out-of-the-money call on the same underlying asset and with the same expiration date and market price is a strategy known as a collar agreement

Like the forward contract hedge, there is no initial out-of-pocket expense associated with this derivative combination Instead, the manager effectively pays for her desired portfolio insurance by surrendering an equivalent amount of the portfolio’s future upside potential In exchange for being compensated for any stock decline below $97 million, any stock price appreciation beyond $108 million is given up

This upside gain potential stops at the exercise price of the call option The manager has placed a collar around the portfolio for the next three months—its net value will not fall below $97 million and will not rise above $108 million At any terminal value for the stock portfolio between these extreme levels, both of the options expire out of the money and no contract settlement payment will be required of either the manager or the dealer

FIN 377: Investments Topic 8: An Introduction to Derivative Markets and Securities larry Schrenk, Instructor.

Similar presentations

Presentation on theme: "FIN 377: Investments Topic 8: An Introduction to Derivative Markets and Securities larry Schrenk, Instructor."— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

FIN 377: Investments Topic 8: An Introduction to Derivative Markets and Securities larry Schrenk, Instructor.

Similar presentations

Presentation on theme: "FIN 377: Investments Topic 8: An Introduction to Derivative Markets and Securities larry Schrenk, Instructor."— Presentation transcript:

Similar presentations

About project

Feedback