CFA 2018 Level 1 Derivatives Ebook 9

(1)

TM

JuiceNotes

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eBook 9

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CFA Level 1 JuiceNotes 2017

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LOS a

LOS b

LOS c

Deﬁne a derivative

Forward commitments

Contingent claims

Derivative Markets and Instruments

Both Forwards and Futures are deliverable/cash-settled contracts Both of them have contract value of zero at initiation

It is average of the prices of the trades during the last period of trading (closing period)

Settlement price

Exchangetraded derivatives Overthecounter derivatives

-A derivative is a security that derives its value from the value of underlying asset

These are standardized and backed by a clearinghouse Eg. Options and Futures

These are traded by dealers in a market with no central location. OTC markets are unregulated and each

contract is with a counterparty

This may expose the owner to default risk Eg. Forwards, swaps and options

Legally binding promise to perform some action in

the future

Eg. forwards, futures and swaps

Claim that depends on a particular event Eg. Options and Credit

derivatives

Forwards

Futures

Buyer (long) agrees to buy an asset (physical/ﬁnancial) from seller (short) at

speciﬁc price on speciﬁc date in future

Do not require payment at initiation

Customized contracts

Illiquid

There is default risk associated

Do not trade in organized markets

Not regulated

These are forward contracts that are standardized and exchange-traded

Require security deposit (margin)

Liquid

Backed by a clearinghouse

Require daily cash settlement (mark to market)

Traded in secondary market

Subject to regulation

1

(3)

Investors are required to bring the margin back up to the maintenance margin if the margin balance in the account falls below maintenance margin because of daily cash settlement

It is the amount that is required to be deposited while opening a futures account

It is the minimum amount of margin that must be maintained in a futures account

Investors are required to bring the margin back up to the initial margin amount

Equity account - (variation margin)

Initial margin -Maintenance

margin

Futures account -(variation margin)

2

Right to buy

Pays premium Pays premium

Right to sell

Obligation to sell

Receives premium Receives premium

Obligation to buy

Options

Call Put

Long Short Long Short

Maximum Point for call:

10 90

Breakeven Point Breakeven Point

0

Breakeven Point for put:

X + P X − P

ª Seller of the option is also called as writer

ª Premium is also referred to as price of the option

ª American options - Can be exercised at any time between purchase date and expiration date

ª European options - Can be exercised only on expiration date

ª Bermudan options - Can be exercised only on certain days. Eg. Once a month

ª At expiration, an American option and a European option on same asset with same strike

price are identical

Eg.

X = 100, P = 10 Calculate Proﬁt/Loss for long and short if,

Call Put

Proﬁt/

Loss ProﬁtLoss/

X = Strike price P = Premium

(4)

Eg.

Plain vanilla interest rate swap

Some important points of Swaps

It is a contract that provides a bondholder (lender) with protection against a downgrade or a default by the borrower

Credit default swap (CDS) is the most common type of credit derivative. It is essentially an insurance contract against default Another type of credit derivative is a credit spread option. It is a call option that is based on a bond’s yield spread relative to its benchmark

Fixed rate - 8% Floating rate - LIBOR + 2% Notional principal = 100,000

A

Floating rate Net rate Net amount

−8% −8% −8%

LIBOR = 6% LIBOR = 9% LIBOR = 4%

8%

0%

0 3000 2000

+3% −2%

11% 6%

Fixed rate payer

Floating rate receiver

Will be

received by A Will be by Apaid

4 Credit derivatives

ª Swaps do not require payment at initiation by either party (except currency swaps) ª They are custom instruments

ª They are not traded in any organized secondary market ª They are largely unregulated

ª There is default risk associated with swaps

ª Participants in the swaps market are generally large institutions. Individuals are rarely participants of swap market

3 Swaps

Agreements to exchange a series of payments on periodic settlement dates

At each settlement date, the two payments are netted so that only one payment is made

The length of the swap is termed as tenor

Simplest type of swap is plain vanilla interest rate swap

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It means riskless proﬁt

If a return greater than the risk-free rate can be earned by holding a portfolio of assets that produces a certain (riskless) return, then an arbitrage opportunity exists

It is often referred to as the law of one price

Arbitrage

Two arbitrage arguments

LOS e

Law of one price

Borrow at RFR and invest at a return higher than RFR (if reurn is certain)

Protective Put Fiduciary Call

=

Two portfolios that have identical cash ﬂows in the future, should have the same price

S + P

B + C

Sip Pepsi Be Cool

Stock + Put Bond + Call

1

2 Criticism of derivatives

Beneﬁts of derivatives

LOS d

è Too risky è Provides price information è Allows risk to be managed and

shifted among market participants

è Reduces transactions costs è Because of the high leverage

involved in derivatives payoffs, they are sometimes likened to gambling

(6)

LOS a

LOS b

Basic of Derivative Pricing and Valuation

FV of costs + Interest cost − FV of beneﬁts

Long value - 0

Long value - +ve

Long value - −ve

Long value - +ve

Spot (S) = 100 Forward = 110

When the equality holds we say the derivative is currently at its no-arbitrage price

No-arbitrage derivative price is sometimes called risk-neutral pricing

1 Value of forwards and futures

Price of forwards and futures

-Risk-neutral

investor

Risk-seeking/loving

investor

An investor that simply

dislikes risk

Given two

investments that have equal expected returns,

a risk-averse investor will choose the one

with less risk

An investor that prefers more risk to less

Given two

investments that have equal expected returns,

a risk-loving investor will choose the one

with more risk

Such investor has no preference regarding risk

He would be indifferent

between two such investments

Zero at initiation

n

Spot × (1 + RFR)

=

S + P

B + C

Costs of owning an asset

Beneﬁts of owning an asset

Storage cost Insurance cost Opportunity cost of funds that are invested in the asset

Monetary Non-Monetary

Dividend payment on stock Interest payment

on bond

Referred to as

Convenience yield

Intangible beneﬁt of holding the asset

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S =100 S =130 Long = 110

0.6

0 1

Price of the contract

Value at expiration (1)

Today (0.6)

-Spot price + PV costs − PV beneﬁts −

It is a forward contract where the underlying asset is the interest rate

FRA 1 X 3

Value of the contract

Forward Rate Agreement (FRA)

Value of forward at

any point in time

Value of the contract today (0.6) =24.06

1 X 3 FRA = 2 X 5 FRA = 3 X 6 FRA = 2 X 6 FRA =

Borrow for 60 days, after 30 days

Borrow for 90 days Lend for 30 days

90

Beneﬁt if interest

rate increases Beneﬁt if interest rate decreases

Right and Obligation

to borrow Right and Obligation to lend/invest

Long Forward Contract Short Forward Contract

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Relation between forwards and futures

Moneyness

-Intrinsic value and time value

Interest rate swap is equivalent to forward rate agreement

when forward contract rate equal to the swap ﬁxed rate

If interest rates are uncorrelated with futures prices, futures and forwards have the same value

Off market FRAs - FRAs that do not have value of zero at inititation

S = 9000 X = 8800 P = 225 Expiry - 21 days

Interest ratesÇ

Interest ratesÈ

AssetÇ

AssetÈ

Invest at higher rate Borrow at lower rate

Preference for futures Preference for

futures $$$

−$$$

Payer swap

Receiver swap

Can be replicated by using a series of

LONG off market FRAs

Can be replicated by using a series of

SHORT off market FRAs

LOS f

LOS g & h

LOS i & j

It refers to whether an option is in the money or out of the money

In the money - If immediate exercise of the option generates positive payoff, it is said the option is in the money.

Out the money - If immediate exercise of the option generates negative payoff, it is said the option is out of the money.

At the money - If immediate exercise of the option generates neither positive payoff nor negative payoff, it is said the option is at the money.

Call option

Put option

In the money S > X Out of the money

S < X At the money

S = X

In the money X > S Out of the money

X < S At the money

X = S

Eg. Intrinsic value(exercise value) = S - X = 200

Time value(speculative value) = P - Intrinsic Value = 25

Option Premium = Time Value + Intrinsic Value Intrinsic value is never negative

Time value can be negative if the option is deep in the market for European put options

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Factors that determine the value of an option

Put-call parity

LOS k

LOS l

Factor

Value of call

option

Value of put

option

Spot

Ç

È

Strike

Ç

È

Ç

Volatility

Ç

Maturity

Ç

RFR

Ç

È

Dividend yield

Ç

_È

_Ç

Protective Put Fiduciary Call

=

S + P

B + C

Synthetic call S + P - B Synthetic put B + C - S

S + P - _{(1 + RFR)}X n _{(1 + RFR)}X n + C - S

If RFR Bond Call If RFR Bond Put

Put-call forward parity for European options

LOS m

n

F = S X (1 + RFR)0

F

n

(1 + RFR) S =

Putcall parity

Putcall forward parity

-S + P = B + C

=

= C + P

+ P

+ C F

n

(1 + RFR)

F - X

n

(1 + RFR)

X

n

(1 + RFR)

(10)

Value of an option using one-period binomial model

LOS n

LOS o

100

100 x 1.25 = 125

280 x 0.87 = 245.61

Su

66.7%

33.3%

Sd S

IV = 45 TV = 0

IV = 0 TV = 0

Eg. S = 100 X = 80 Uptick factor = 1.25 RFR = 10% Downtick factor = 1/1.25 = 0.8

Prices of European and American options will be equal unless the right to exercise prior to expiration has positive value If there is no beneﬁt of early exercise then value of American

call option is equal to European call option (AO = EO) For a call option on an asset that has no cash ﬂows during its

life, there is no advantage to early exercise

Two scenarios where early exercise is useful:

Risk neutral probability - (1 + RFR) − D_{U - D} = (1 + 0.1) − 0.8_{1.25 − 0.8} = 66.67%

Expected value of the option in one period

-Œ American call - Expecting signiﬁcant amount of dividend American put that is deep in the money

45 X 66.7%

(1 + 0.1) = 27.27

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Long Call

Long Put

Short Call

Short Put

X

X P

X − P

X − P P

X + P

X - P X - P

X + P X

X BEP

BEP BEP

BEP

Risk Management Applications of Option Strategies

LOS a

LOS b

Graphs of options

Stock price

Stock

price Stock price

Stock price 0

0 0

0 Proﬁt

Proﬁt Proﬁt

Proﬁt

ª Long is always below zero

ª Short is always above zero

ª Call has unlimited proﬁt/loss

ª Put has limited proﬁt /loss

Covered call

Protective put

ª Buying a stock and selling

short (writing) the call

ª Purpose is to earn premium ª Maximum proﬁt = X − S + P ª Maximum loss = S − P

ª Buying a stock and put ª Purpose is to protect against

decline in the value of stock

ª Maximum proﬁt = Unlimited ª Maximum loss = S − X + P