What Are Derivatives

DERIVATIVES

What are derivatives • Financial contract whose payoff structure is determined by the value of an underlying commodities, security, interest rate, share price, exchange rate, oil price. • A derivative carries its valve from same underlying variable.

Financial Derivatives FORWARDS

FUTURE

OPTIONS

SWAPS

Forwards • Its an agreement to buy or sell an asset on a certain date at a agreed price. • Its a contract between two parties. • Its a contract where no middlemen is involved and no sunk cost.

Forwards • Buyers – takes long term position. • Seller – takes a short term position. Money Buyers

Sellers Security

Problems • Counter party risk : a party may not fulfill the obligation. Thus each party faces the risk of default. • Low degree of liquidity : both the parties have to wait till maturity. No one can cum out from the contract.

Future Contracts • It’s a standardized forward contract.. • Its an agreement to buy or sell an asset on a certain date at a agreed price. • Its a contract between two parties. • Its a contract where middlemen is involved and also sunk cost. • Future contract = Spot price + carry cost – carry return.

Future Contract

A

Buyer Seller

Clearing house

Seller Buyer

B

Future Vs Forward Futures Exchange traded & transparent. Standardized Settlement through clearing house. Require margin payment Settlement of trade is guaranteed.

Forwards. Private contract. Customized. Settlement between buyers & sellers. No margin payment. Counter party risk.

Futures Futures

Stock future underlying asset is the stock BSE SENSEX – 20 shares S & P Nifty – 50 shares

Index future underlying asset is the index

BSE SENSEX Future 1 lot = 50 indices S & P Nifty Future I lot = 200 indices.

4700 4600 Future price

4590

4568 4570 4535

Spot price

4500

Op

Cl

Cl 2

Cl 3

Cl 4

Cl 27 Jan

Future Price of Jan Index Future ( maturing on 27th Jan, last Thursday)

MARGIN MONEY Margin money @ 5% = Rs 4568 * 50 *5/100 = Rs 228400 * 5/100 = Rs 11420.

MARKING TO MARKET • Ist day when price decreases from Rs 4568 to Rs 4535 loss per index = Rs 33. • Total loss = Rs 50 * 33 = Rs 1650 • 2nd day gain (4590 – 4535) * 50 = 2750 • 3rd day loss (4590 – 4570) * 50 = 1000 • 4th day gain (4600 – 4570) * 50 = 1500

Margin at the beginning = Rs 11420 1st day less : loss 1650 2nd day add : gain 2750 3rd day less : loss 1000 4th day add : gain 1500 = Rs 13020 Total gain up to 4th day (4600 – 4568)*50 = 1600

VALUATION OF FUTURE PRICE Price = spot price + carry costs – carry return.

Case 1 : securities providing no income F = soert Where F = future price S = spot price R = risk free rate of interest p.a with continuous compounding T = time to maturity E = exponential value = 2.7183

EXAMPLE • Consider a forward contract on a non dividend paying share which is available at Rs 70 to mature in 3 months time. r = .08 ( compounded continuously) (.08)(.25) F = soert = 70 e(.08)(.25) = Rs 70 e.02 = Rs 70 (1.0202) = Rs 71.41

Case 2 : Securities providing a known cash income.

F = (S-I)ert I = PV of income D received after T time. I = De-rt

EXAMPLE • Let us consider a 6 month future contract on 100 shares with a price of Rs 38 each. Risk free rate of interest (continuously compounded) is 10% p.a. The share in question is expected to yield a dividend of Rs 1.50 in 4 months from now. Div. received after 4 months = 100 * 1.50 = 150 PV of the div; I = 150e -(0.1)(0.33) = 150*0.9672 = Rs 145.08 F = (3800 – 145.08)e (0.1)(0.5) = 3654.92 *1.05127 = Rs 3842.31

Case 3 : Securities Providing a Known Yield F = S e (r - y) t y = Yield rate (continuously compounded)

EXAMPLE Assume that the stocks underlying an index provide a dividend yield of 4% p.a., the current value of the index is Rs. 520 and that the continuously compounded risk free rate of interest is 10% p.a. Here S = 520, r = 0.10, y = 0.04, t= 3/12 = 0.25 Thus : F = 520 e (0.1 - 0.04) (0.25) = 520 e (0.06) (0.25) = 520 x 1.0151 = Rs. 527.85.

OPTION An option is a contract which gives the right, but not the obligation, to buy or sell the underlying at a stated date and at a stated price.

UNDERLYING ASSETS

Individual stock Introduced on 02.07.2001 Option

Call option

Put option

Indices S&P CNX Nifty Introduced on 04.06.2001 in NSE

OPTION TYPE OPTION TYPE BUYER OF OPTION (OPTION HOLDER)

SELLER OF OPTION (OPTION WRITER)

CALL

Right to buy

Obligation to sell

PUT

Right to sell

Obligation to buy

Exercise Price : the price at which the contract is settled (strike price) Expiration date : the date on which the option expires. Style of option : • American option( exercised at any time prior to expiration) • European option (exercised on the expiration day) Option Premium : The price that the holder of on option pays and the writer of on option received for the rights conveyed by the option.

OPTIONS ON INDIVIDUAL STOCKS Call Option : X = option writer (Seller) Y = option buyer (holder) Size of the contract = 100 R I Shares Spot price on 22.01.2003 = Rs. 40 per share Exercise price = Rs. 42 per share Date of maturity = 21.03.2003 Option price = Re 1 per share for call option

PROFIT & LOSS PROFILE FOR SELLER AND BUYER POSIBLE SPOT PRICE AT CALL MATURITY

X (Rs)

Y (Rs)

40

300 (100 X 3)

- 300

41

200 (100 X 2)

- 200

42

100 (100 X 1)

- 100

43( BEP )

0

0

44

-100 ( 100 x 1 )

100

45

-200 ( 100 x 2)

200

PROFIT

300 200 100 Share price 40

41

42

43

44

45 46

-100 -200 -300 For call option writer X

Profit 300 200 100

-100

40

41

share price 42

43

44

45

46

-200 -300

For call option buyer Y

EXAMPLE OF PUT OPTION X = Option writer (obligation buy) Y = Option buyer (right to sell) Exercise price = Rs. 100 per share; Size of the contract = 100 R I shares, Spot price today = Rs. 105 per share; Option premium = Rs. 10 per share

POSIBLE SPOT PRICE

X

Y

60

-3000(100*30)

3000

70

-2000(100*20)

2000

80

-1000(100*10)

1000

90(BEP)

0

0

100

1000

-1000

110

1000

-2000

120

1000

-3000

Profit 3000 2000 1000 Share Price -1000

60

70

80

90

100

110

-2000 -3000 Option Writer X

120

Profit 3000 2000 1000 Share Price 60 70 -100

80

90 100 110 120

-2000 -3000 Option Buyer Y

Have a view on the market A. Assumption : Bullish on the market over the short term: Action : Buy Nifty Calls Example : Current Nifty is Rs. 1400 Buy one Nifty. The strike price 1430 Option premium = Rs. 20 Total premium = Rs. (20 X 200) = Rs. 4000 If at expiration Nifty advances by 5% i.e. 1470 Option Value : = Rs. 40 (1470 - 1430) Less : option Premium = 20 Profit per Nifty:

20

Profit on the contract = 20 X 200 = 4000

B. Assumption : Bearish on the market over the short term. Possible Action : Buy Nifty Put Example : Nifty in cash market is Rs. 1400 Buy one contract of Nifty puts for Rs. 23 each. The strike price is 1370 if at expiration Nifty declines by 5% i.e. Rs. 1330. Option Value = 40 (1370 - 1330) Option Premium = 23 Profit per Nifty =

17

Profit on the contract = Rs. 3400 (17 X 200)

Use Put as a portfolio hedge ? To protect your portfolio from possible market crash. Possible Action : Buy Nifty Puts You held a portfolio valued at Rs. 10 lakhs Portfolio Beta = 1.13 Current Nifty = 1440 Strike price = 1420 Premium = Rs. 26 To hedge, you bought 4 puts [800 Nifty, equivalent to Rs. (10 X 1.13) lakhs or 11,30,000] If at expiration Nifty declines to 1329 and your portfolio falls to Rs. 948276, then Option Value Option premium

= 91 (1420 - 1329) = 26

Profit per Nifty = 65 Profit on the contract = Rs. 52000 (65 X 800) Loss on Portfolios = Rs. 51724 Net Profit

= Rs. 276

SPREADS A spread trading strategy involves taking a position in two or more options of the same type.

EXAMPLE • An investor buys for $3 a call with a strike price of $30 and sell for $1 a call with a strike price of $35. • Payoff from this bull strategy is $5 is stock price is above $35 & zero if it is below $30. • If between $30 & $35 the payoff is the amount by which the stock price exceeds $30. • Cost of the strategy is $3 - $1 = $2

Stock price Profit range ST <= 30

-2

30 < ST < 35

ST – 32

ST >= 35

3

EXAMPLE •

An investor buys for $1 a call with a strike price of $35 and sell for $3 a call with a strike price of $30. • Payoff from this bear spread strategy is -$5 is stock price is above $35 & zero if it is below $30. • If between $30 & $35 the payoff is –(ST – 30)

Stock price Profit range

•

Investment generates $3 - $1 = $2

ST <= 30

+2

30 <ST<35

32 – ST

ST >= 35

-3

Call Option. (right to buy) * Level of Existing Spot Price (s) relative to Exercise Price (E). The higher the spot rate (S) relative to exercise price (E), the higher the option price. If S>E, higher option price, higher probability, of exercise of option. If S = 40, E = 42 33 34 35 36 37 38 39 40 If S = 40, E = 37 i.e. S>E lower E compared to S, higher is the probability to exercise the option => higher option price 41 42 43 44 45 46 If E = 42 option is exercised when S is greater than or equal to 43

Put Option (right to Sell) The lower the spot rate (s) relative to exercise price (E), the higher the option price. Relating S>E, the higher probability to exercise the option 33 34 35 36 37 S> E If E1 = 39, S = 40 Option will be exercised when price is less than or equal to 39 38 39 40 41 42 43 44 45 46 47 If S= 40 E2 = 45 S < E S is relatively low, the higher the probability to exercise the option. High option premium

The Black and Scholes Model (1973) C = S0 N (d1) - E e -rt. N (d2) Where d1 = log (S0 / E) + (r + 0.5σ 2) t σ(t)½ d2 = log (S0 / E) + (r - 0.5 σ 2) t σ ( t ) 1/2 C = Current value of the option r = Continuously compounded riskless rate of returns S0 = Current price of stock E = Exercise Price T = time remaining before the expiration date (expressed as a fraction of a year) σ = S.D. of continuously compounded annual rate of return Log = Natural togarithen N(d) = value of the commulative normal distribution evaluated at d

Example : Consider the following information with regard to call option on the stock of X Ltd., S0 = Rs. 120 E = Rs. 115 Time period = 3 months; thus t = 0.25 year σ = 0.6 r = 0.10 d1 = log (120/115) + (0.10 + 0.5 X 0.6 2).25 0.6 V – .25 = .37 d2 = log(120/115)+(.10 -0.5 *.6 2) *.25 0,6 - .25 = 0.7 N (d1) = 0.6443 N (d2) = 0.5279

The value of the Call is C = S0 N (d1) - E e -rt. N (d2) = 120 X (0.6443) - 115 e -0.10 (.25) X (0.5279) = 18.11 Using the put- call parity, we can determine the put option value on the share as follows: P = C + E e -rt. -S0 = 18.11 + 115 X e - 0.10 (0.25) – 120 = Rs. 10.27

Relationship between European Call and put options: Portfolio P1: One European call option & cash for an amount of E e -rt.. Portfolio P2: One European put option & one share of stock worth S0 Determination of TERMINAL Values of Portfolios Portfolio

Cash Flow at t = 0

S1> E

S1≤ E

P1

C E e -rt.

S1 - E E

0 E

Total

S1

E

P S0

0 S1

E- S1 S1

Total

S1

E

P2

Since both the portfolios have identical values on expiration, they must have equal values at present as well. Accordingly we have C + E e - rt.. = P + S0 or P = C + E e - rt.. - S0

SWAP A SWAP transaction is one where two or more parties exchange (SWAP) one set of predetermined payments for another. (i) Interest rate SWAP (ii) Currency SWAP Interest Rate SWAP. Company Fixed (%) Floating (%) A 7.5 M IBOR + 0.5% B 9 M IBOR + 3.5% A borrows Rs. 10,000 from a bank at Floating rate . B borrows Rs. 10,000 from a bank at Fixed rate. As a separate transaction A and B agree as follows: (i) A will pay B a fixed rate of 7% (ii) B will pay A a floating rate of MIBOR + 0.5%

SWAP A To understand the benefits from the swap consider the net cash flows of A and B Party Swap Swap Swap outflows on Total Outflow(%) Inflow(%) loan from bank (%) A -7 (MIBOR + 0.5%) -(MIBOR + 0.5%) -7 B - (MIBOR + 0.5%) + 7% - 9% - (MIBOR+2.5) It may be seen that the net result is (a) For A, a fixed rate obligation at 7% (this is better than the 7.5% which A would have paid if it had directly taken a fixed rate loan). (A gains 0.5%) (b) For B, a floating rate obligation at LIBOR + 2.5% (this is better the LIBOR + 3.5%) (B gain 1%)

Presence of a Broker C As a separate transaction A,B, and C agree as follows: (iii) A will pay C a fixed rate of 7% (iv) A will receive from C a floating rate of LIBOR + 0.5%. (v) B will pay C a floating rate of LIBOR + 0.5% (vi) B will receive from C a fixed rate of 6.5% C gains (7% - 6.5%) = 0.5%

To understand the benefits from the Swap consider the net cash flows of A, B, and C Party Swap Swap Outflows Total Outflow (%) inflows (%) on loan A - 7.0 + (L + 0.5) - (L + o.5) .7 B - (L+0.5) + 6.5 -9 - (L + 3) L + 0.5 L + 0.5 C + Nil + 0.5 + 6.5 +7 It may be seen that the net result is (a) for A, fixed rate obligation at 7% (this is better than the 7.5% [A gains 0.5% (7.5 - 7)] (b) for B, a floating rate obligation at (LIBOR+ 3%) which is better than (LIBOR + 3.5%). [B gains 0.5%] (c) for C, a profit of 0.5% for earning the transaction.

EXAMPLE • Three year swap initiated on March5 2003 between Microsoft and Intel. • Microsoft agrees to pay to Intel rate of 5% p.a. on a notional principal. • Agreement specifies that payment are to be exchanged every 6 month & the 5% int rate is quoted with semi annual compounding.

Date

6months LIBOR rate

Floating cash flow received

Fixed cash flow received

Net cash flow

March5’03

4.20

Sept5’03

4.80

+2.10

-2.50

-0.40

March5’04

5.30

+2.40

-2.50-

-0.10

Sept5’04

5.50

+2.65

-2.50

+0.15

March5’05

5.60

+2.75

-2.50

+0.25

Sept5’05

5.90

+2.80

-2.50

+0.30

March5’06

6.40

+2.95

-2.50

+0.45

Date

6months LIBOR rate

Floating cash flow received

Fixed cash flow received

Net cash flow

March5’03

4.20

Sept5’03

4.80

+2.10

-2.50

-0.40

March5’04

5.30

+2.40

-2.50-

-0.10

Sept5’04

5.50

+2.65

-2.50

+0.15

March5’05

5.60

+2.75

-2.50

+0.25

Sept5’05

5.90

+2.80

-2.50

+0.30

March5’06

6.40

+102.95

-102.50

+0.45

COMPARATIVE ADVANTAGE EXAMPLE : Fixed

Floating

AAA Corp

10.0%

6 months LIBOR + 0.3%

BBB Corp

11.2%

6 months LIBOR + 1.0%