Derivatives Strategies
Changing Risk Exposures With Swaps,
Futures, and Forwards
Derivative strategies can be:
• speculative, designed to make a profit, or
• defensive, providing protection against an adverse event.
An investment manager should be able to explain how derivative
strategies might logically be used in an investment portfolio.
Changing Risk Exposures With Swaps,
Futures, and Forwards
• A primary use of derivatives is to change a portfolio’s risk
exposure. This can be done using:
• swaps (interest rate, currency, or equity)
• futures
• forwards
• Derivatives permit the portfolio manager to select any point
along the bullish/bearish spectrum.
Changing Risk Exposures With Swaps,
Futures, and Forwards
Swaps are used to substitute the investment characteristics of a new
asset for those of an asset already in the portfolio. For example, in
an interest rate swap the periodic cash flows might be:
Changing Risk Exposures With Swaps,
Futures, and Forwards
These derivatives can be useful in managing different types of risk.
• Interest rate swap: The two parties exchange the returns on
a high duration asset for the returns on a low duration asset,
reducing interest rate risk.
• Currency swap: The two parties exchange one currency for
another currency and periodically pay each other interest at a
fixed interest rate, reducing foreign exchange risk.
• Equity swap: The two parties trade the return on an equity
portfolio for the return on another asset, reducing market risk.
Equivalent Asset Sell for the Same Price
Stock Price at Option Expiration 0 20 50 80 100
ALTERNATIVE 1:
Long 50-strike call payoff 0 0 0 30 50
Short 50-strike put payoff –50 –30 0 0 0
Total Value –50 –30 0 30 50
_____________
ALTERNATIVE 2:
Buy stock at 50
Gain/Loss -50 -30 0 30 50
A long call and a short put with the same strike replicate the returns
on the underlying asset.
Covered Call Investment Objectives
• Covered Call: Strategy in which the owner of the underlying shares
sells a call option giving the call buyer the right to buy the shares at
the exercise price.
• Income Generation: A stock is at 33; the owner expects it to be
stable for the next month. She writes an out-of-the-money call with
strike price of 36 for a premium of 1.15, which she keeps regardless of
the future stock price. If the stock remains stable, as expected, the
option expires worthless.
• Improving on the Market: An investor owns 1,000 shares of stock
worth 45 and needs to sell shares to raise cash. A near-term 35 strike
call sells for 10.50. The investor writes ten contracts. Because the
calls are deep in-the-money they are very likely to be exercised for net
proceeds to the investor of (35 + 10.50) × 1, 000 = 45, 500. This is
500 more than the outright sale at 45.
• Target Price Realization: A stock sells for 37, above the investor’s
target price of 34. The investor sells a near-term 34 strike call for
3.75. The call is likely to be exercised, giving the investor
34 + 3.75 = 37.75, a better price than the current stock price of 37.
Covered Call Risk
• Writing a covered call means the call writer has sold the most
desirable part of the expected return distribution.
• If the owner of the call option exercises it, this usually results
in an opportunity loss for the covered call writer.
Covered Call Profit and Loss Diagram
Protective Puts Are Analogous To Buying
an Insurance Policy
Protective Put: The simultaneous holding of shares and a long
put position on those same shares.
Insurance Policy
• Premium
• Value of an asset
• Face value
• Term of policy
• Likelihood of loss
Put Option
• Time value
• Price of stock
• Exercise price
• Time until option expiration
• Volatility of stock
The Put Provides Protection Against a Decline in the Price
of the Underlying Asset
Protective Put Profit and Loss Diagram
Delta
Delta measures how an option price changes with changes in the
underlying asset.
Long Option Position Short Option Position
Call delta ranges from 0 to +1 Call delta ranges from -1 to 0
Put delta ranges from -1 to 0 Put delta ranges from 0 to +1
This means a long call (short call) and a short put (long put) might
have the same delta and therefore the same sensitivity to a change
in the value of the underlying asset.
Position Equivalences
• A long stock position can be combined with a short forward
position to create a position delta equal to either a covered call
or a protective put.
• Positions with equal position deltas will show approximately the
same change in value for small movements in the underlying
asset.
Covered call + 50 Protective Put +50 Hedged stock + 50
Long stock + 100 Long stock + 100 Long stock + 100
Short call – 50 Long put – 50 Short forward – 50
For small changes in the stock price, the three positions will show a
similar gain or loss.
Option Collar
• A collar is a position in which an investor owns the underlying
stock, writes an out-of-the-money call option, and buys an
out-of-the-money put option.
• Often the options are selected such that the respective
premiums nearly offset.
• The collar provides downside protection by sacrificing upside
potential.
• Collars are usually established on an existing stock position
that has risen in value.
Option Collar Profit and Loss Example I
Option Collar Profit and Loss Example II
Option Collar Risk
Long Position With Same Strike Collar
If the short call and the long put have the same striking price (here
50), the collar will be worth the striking price at option expiration.
Stock price at expiration 0 25 50 75 100
Long stock value 0 25 50 75 100
Short 50 call value 0 0 0 –25 –50
Long 50 put value 50 25 0 0 0
Combined Position 50 50 50 50 50
Bull Spread
• Becomes more valuable as the underlying asset rises in price
• Involves buying one option and writing another with a higher
striking price but the same expiration
• May be done with calls or with puts
• Typically a directional bet
• Gives up some profit potential for a lower cost
Call Bull Spread Profit and Loss Diagram
Bear Spread
• Becomes more valuable as the underlying asset falls in price
• Involves buying one option and writing another with a lower
striking price, but the same expiration
• May be done with puts or with calls
• Typically a directional bet
• Gives up some profit potential for a lower cost
Put Bear Spread Profit and Loss Diagram
Calendar Spread
• May be done with either puts or calls
• Long calendar spread: buy distant option, write shorter-term
option, each having the same striking price
• Short calendar spread: write distant option, buy shorter-term
option, each having the same striking price
• Time decay is more pronounced for a short-term option than
for one with a long time until expiration
• A long calendar spread trade seeks to exploit this time decay
characteristic by purchasing the longer-term option and writing
the shorter-term option
Calendar Spread Example
Straddle
• In a long straddle, the investor buys both puts and calls on the
same underlying asset, with both options having the same
striking price
• In a short straddle, the investor writes both options
• The straddle buyer is usually motivated by one of two beliefs:
• The price of the underlying asset is likely to either rise or fall
sharply; or
• The implied volatility of the options on the underlying asset is
likely to rise
Long Straddle Profit and Loss Diagram
Strategy Selection
• The risk of a derivative product depends on what you do with
it.
• Derivatives are neutral products that can be combined with
other assets to create a more preferred risk–return trade-off.
• If used wisely, derivatives can help an investor or a portfolio
manager quickly adapt to changing market conditions or client
needs.
Two Markets: Direction and Speed
• Every trade should begin with an opinion on the underlying
market.
• Option users need to think about both direction and
volatility.
• An option buyer may be correct about the direction of a stock
price change, but if it does not change quickly enough, the loss
of time value may erode any gain from the delta effect.
• Volatility is sometimes referred to as the speed market. A
volatile market is a fast market, while a stable market is a slow
market.
Option Strategies: Direction and Volatility
Direction Bearish Neutral Bullish
High Buy puts Buy straddle Buy calls
Volatility Average Write calls, Spreads Buy calls,
buy puts write puts
Low Write calls Write straddle Write puts
Risk Adjustment Tools
• With derivatives there are many ways to accomplish a
particular risk/return profile.
• A portfolio manager who seeks to reduce market exposure to a
particular equity holding could:
• Sell some of the equity (underlying)
• Enter into a futures or forward contract to sell part of the
underlying
• Write covered calls
• Buy protective puts
• Enter into a collar
Summary I
• Interest rate, currency, and equity futures and swaps can be
used to modify risk and return by altering the characteristics of
the cash flows of an investment portfolio.
• Buying a call and writing a put with the same exercise price
creates a synthetic long position.
• A long position plus a short futures position in the same
underlying asset creates a synthetic risk-free asset earning the
risk-free rate.
• A covered call, in which the holder of a stock writes a call
giving someone the right to buy the shares, is one of the most
common uses of options by individual investors.
• Covered calls can be used to generate income, to acquire
shares at a lower- than-market price, or to exit a position when
the shares hit a target price.
Summary II
• A covered call position has a limited maximum return because
of the transfer of the right tail of the return distribution to the
option buyer.
• The maximum loss of a covered call position is less than the
maximum loss of the underlying shares alone, but the covered
call carries the potential for an opportunity loss if the
underlying shares rise sharply.
• A protective put is the simultaneous holding of a long stock
position and a long put on the same asset. The put provides
protection or insurance against a price decline.
• Although the continuous purchase of protective puts is
expensive and probably suboptimal, the occasional purchase of
a protective put to deal with a bearish short-term outlook can
be a reasonable risk-reducing activity.
Summary III
• The maximum loss with a protective put is limited because the
downside risk is transferred to the option writer in exchange for
the payment of the option premium.
• With an option spread, an investor buys one option and writes
another of the same type. This reduces the position cost but
caps the maximum payoff.
• A bull spread is normally constructed by buying a call option
and writing another call option with a higher exercise price.
• A bear spread is normally constructed by buying a put option
and writing another put option with a lower exercise price.
• With either a bull spread or a bear spread, both the maximum
gain and the maximum loss are known and limited.
• A collar is an option position in which the investor is long
shares of stock and simultaneously writes a covered call and
buys a protective put.
Summary IV
• A calendar spread involves buying a long-dated option and
writing a shorter-dated option of the same type with the same
exercise price, or vice versa. The primary motivation for such a
spread is to take advantage of the faster time decay with the
shorter-term option.
• A straddle is an option combination in which the investor buys
puts and calls with the same exercise price. The straddle holder
typically needs a substantial price movement in the underlying
asset in order to make a profit.
• The risk of a derivative product depends on how it is used.
Derivatives should always be used in connection with a
well-defined investment objective.