www.singaracademy.com Derivatives 6.11. DERIVATIES Question 1: What are derivatives? Answer: Derivative s are financial instruments whose values depend on the value of t he underlying assets Question 2: What is forwards contract? Answer: Forward Contract is a simple derivative. It is an agreement to buy or sell an asset at a certain future time for a certain price. A forward contract is traded in the over-the-counter market –usually between a f inancial institution and of its clien t. Forward contracts are widely used in foreign exchange. Question 3: What is future contract? Answer: Future Contract like a forward contract, a future contract is an agreement between two parties to buy or sell an asset at a certain time in the future for a certain price. Unlike forward contracts, Future contracts are normally traded on an exchange with pre-standardized lot. At the expiry of the contract, the future-contract price tends to future spot price of the underlying asset. Otherwise there is no profit or loss on settlement date. A futures contract has a)The date on which the contract is being executed b)The name of the underlying asset c)The quantity of the asset d)The contract price e)The period of the contract. Question 4: Differentiate between Futures and Forwards. Answer: Futures Forwards 1 Trade in organized exchange OTC 2 Contract term Standardize d Customized 3 Liquidity More Less 4 Margin payment Requires Nil 5 Settlement Daily At the end of period 6 Risk of default Taken by clearing corporation Borne the client.
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Question 5: How to determine theoretical futures price?
Answer:
Formula Financial futures Commodity futures
Spot price ××× ×××
Add Cost of carry ××× ×××
Cost of finance × × or
S(− ) – S××× ×××
Storage cost S × Rate of Storage × Not Applicable ×××
Insurance Cost Not Applicable ×××
Others ××× ×××
Less Returns ××× ×××
Future value of dividend or ( × ) ××× Not Applicable
Future Price [Fair Value] ××× ×××
Where: S = Spot rate, r = rate of interest, t = time, e = constant for continuous compounding, d = rate of
dividend, FV = Face Value of share, D = Dividend per share, dy = dividend yield, cy = Convenience Yield
Question 6: What is an index future?
Answer: An index future is a derivative whose value is dependent on the value of the underlying asset
(e.g. BSE Sensex, S&P CNX Nifty). In index futures, an investor buys and sells a basket of securities
comprising an index in their relative weights.
Practical Problems
Question 1: The following quotes were observed by Mr. X on Mar 11, 2005 in the Economic Times.
Contracts Open High Low CloseOpen
Interest
Traded
quantity
Number of
Contracts
1 SBI MAR 05 FUT 735 740 735 738 433 138000 92
2 NIFTY MAY 05 FUT 2800 2830 2800 2830 1016 102400 512
Required: Explain the details that are displayed against the futures.
Answer:
Column Particulars Meaning – Row 2
1 Contracts SBI – stock future expires on Mar 2005
2 Open Day‟s open-rate of SBI-stock future
3 High Day‟s high-rate of SBI-stock future
1 Cost of finance is calculated using simple interest rate [ × × ] or continuous compound interest rate [ ]2 Return is in absolute numbers for shares and in dividend yield (dy) % for index future
Net gain or loss Closing Balance – Initial Margin – Variation margin Paid + Profit Withdrawn
Mr. Tandon‟s gain 14000 – 12000 – [3000 + 5500] + [2000 + 6000] 1,500
Mr. Tilak‟s loss 12250 – 12000 – [9250] + [250 + 4500 + 2750] -1,500
Net position of the two 0
Question 16: Nifty Index is currently quoting at 1300. Each lot is 250. Mr. X purchases a March contractat 1300. He has been asked to pay 10% initial margin. What is the amount of initial margin? To what level
Nifty futures should rise to get a percentage gain of 5%.
Answer:
Particulars Formula Calculation ₹
1 The initial margin Value of Contract × Initial Margin% 1,300×250×0.10 32,500
2 Nifty rise to gain 5% Price +Deposit × ROI
1,300 +32,500×0.05
250 1,306.50
Question 17: A futures contract is available on a company that pays an annual dividend of ₹5 and whose
stock is currently priced at ₹200. Each futures contract calls for delivery of 1,000 shares of stock in one
year, daily marking to market, an initial margin of 10% and a maintenance margin of 5%. The current
Treasury bill rate is 8%.
a. Given the above information, what should the price of one futures contract be?
b. If the company stock decreases by 7%, what will be, if any, the change in the futures price?
c. As a result of the company stock decrease, will an investor that has long position in one futurescontract of this company realize a gain or a loss? Why? What will be the amount of this gain or loss?
d. What must the initial balance in the margin account be? Following the stock decrease, what will be, if
any, the change in the margin account? Will the investor need to top up the margin account? If yes, by
how much and why?
e. Given the company stock decrease, what is the percentage return on the investor‟s position? Is it
higher, equal or lower than the 7% company stock decrease? Why?
Answer:
Formula Calculation (a) ₹ (b) ₹
7% price fall
Spot price 200.00 186.00
Add Cost of finance × × 200 ×8
100× 1 16.00 14.88
Less Dividend 5.00 5.00
Future Price [Fair Value] 211.00 195.88
(c) Loss because of price fall 1,000 (211 – 195.88) 15,120
(d) Initial Margin required for 1000
shares
Value of shares×Initial
Margin% 211×
1,000×
10% 21,100
Balance after loss 5,980
Maintenance Margin required
for 1000 shares
Value of shares
×Maintenance Margin%211×1,000×5% 10,550
Balance after loss is less than maintenance margin hence he has to invest to bring his
balance equal to initial margin else his position will be closed out by the broker15,120
(e) Return percent %
−15,120
21,100% -71.7%
The loss is 10 times higher than the actual decrease in the stock price. The 10-to-1 ratio of percentage
changes reflects the leverage inherent in the futures contract position.
Question: What is the Hedging?
Answer: Hedging is taking an equal and opposite position in another market so that loss that may arise in
one market would be compensated by a gain in another market. The extent of hedging (hedge ratio) is
determined by the beta of a security. If the beta is greater than one (i.e. hedge ratio is greater than one) then
the position hedged would be higher than the underlying position and would be proportionate to the beta of
2. The share of Wrong Ltd. is going to depreciate. He has a short position on the cash market of ₹25 lacs
on the Wrong Ltd. The beta of the wrong Ltd. is 0.9
3. The share of Fair Ltd is going to stagnate. He has a short position on the cash market of ₹20 lacs of
Fair Ltd. The beta of the Fair Ltd. is 0.75
Answer: Future position = Beta × Value of InvestmentStock Original
Position
Beta Value Hedge
Position
Future
position
Futures
Strategy [lacs]
Right Ltd Long 1.25 50 Short 1.25×50 Short 62.5
Wrong Ltd Short 0.9 25 Long 0.9×25 Long 22.5
Fair Ltd Short 0.75 20 Long [Optional] 0.75×20 Long 15
[CA FINAL]
Question 20: Ram buys 10,000 shares of X Ltd. at ₹22 and obtains a complete hedge of shorting 400 NIFTIES at ₹1,100 each. He closes out his position at the closing price of the next day at which point the
share of X Ltd. has dropped 2% and the Nifty future has dropped 1.5%. What is the overall profit or loss of
this set of transaction?
Answer: The gain or loss incurred by Ram can be estimated as follows:
Gain (Loss) (S6 – X)×720 kg (14,400) 14,400 (X – S6)×720 kg 14,400 (14,400)
Net Value 3,60,000 3,60,000 3,60,000 3,60,000
S6 = Spot price at the end of 6th
month
(b) Even though it appears that in each scenario one party has benefited at the expense of the other, both
have really benefited because both parties were able to lock in a price of ₹500 per Kg. and eliminate all
risk.
Question 26: Suppose you are a CFO of Hotels ITC and you purchase a large quantity of coffee each
month. You are concerned about the price of coffee one month from now. You want to guarantee that youwill not pay more than ₹100 per Kg. of “Coffee A” for 15,000 Kgs. You do not want to pay for insurance
but you do want to lock in a current price of ₹100 per Kg for 15,000 Kgs.
a. Show the economics of a futures transaction if the spot price on the delivery date is ₹75, ₹100, or
₹125.
b. What is the variability of Hotels ITC‟s total outlays under the futures contract?
c. If at the time of delivery coffee is ₹75 per Kg, should you have forgone entering into the futures
contract? Why or why not?
Answer:
(a) CFO would sell “Coffee A” futures entailing 15,000 Kgs. at the prevailing price of ₹100 / Kg
CFO Hotels‟ Transaction ₹75/Kg ₹100/Kg ₹125/Kg
Cost of coffee purchased from supplier ₹1125000 ₹1500000 ₹1875000
Cash flow from futures contract +375000 ₹0 (₹375000)
Total outlay ₹1500000 ₹1500000 ₹1500000
a. Outlays are fixed at ₹1500000.
b. Regardless of the outcome of the price of coffee at the delivery date, the Treasurer did the righttransaction if he wanted to lock in a price of ₹100 per Kg. Although he gave up any opportunity to pay
a lower price, he also guaranteed that he would never pay more than ₹100 per Kg. A hedge transaction
is only useful if one does not know the future price of some item, hence the need to hedge the risk of
b) The option gives him the right to sell equity shares of Sesa Goa at ₹1025 on or before March 28, 2006.
Answer:
Nature of option
(a) Option to purchase Satyam at ₹725 Call option
(b) Option to sell of Sesa Goa ₹1,025 Put option
Question 4: Mr. Ramesh purchases the following European Call options on Reliance. He also purchases
the following European put options on ACC. What decision he would take on expiry, if Reliance (RIL)
closes at ₹835 and ACC closes at ₹565? Ignore premium paid.
1. RIL 830 Call
2. RIL 840 Call
3. ACC 510 Put
4. ACC 580 PutAnswer:
X Position Profit
(a) Call Option to purchase RIL ₹830 ₹835 Exercise ₹5
(b) Call Option to purchase RIL ₹840 ₹835 Do not exercise ₹0
(c) Put option to sell ACC ₹510 ₹565 Do not exercise ₹0
(d) Put option to sell ACC ₹580 ₹565 Exercise ₹15
Question 5: Identify which of the following options is In-The-Money (ITM), At-The-Money (ATM) orOut-of-The-Money (OTM) for the buyer of option. Which of these options would be exercised? Treat each
case individually.
1. RIL 840 CALL when the price on expiry is ₹855
2. RIL 830 CALL when the price on expiry is ₹840
3. RIL 800 CALL when the price on expiry is ₹765
4. ACC 510 PUT when the price on expiry is ₹510
5. ACC 520 PUT when the price on expiry is ₹500
6. ACC 540 PUT when the price on expiry is ₹555
Answer:
X ITM / OTM / ATM Position Profit=
Max [S – X, 0]
1 RIL Call Option ₹840 ₹855 In the money Exercise ₹15
2 RIL Call Option ₹830 ₹840 In the money Exercise ₹10
3 RIL Call Option ₹800 ₹765 Out of the money Lapse ₹0
4 ACC Put Option ₹510 ₹510 At the money Lapse ₹0
5 ACC Put Option ₹520 ₹500 In the money Exercise ₹20
Short 100 X May 25 calls 0.89 0.01 0.02 – 8900 – 100 – 200
Long 50 X May 30 Calls 0.76 0.03 0.05 +3800 +150 +250
Long 10 X August 30 Calls 0.74 0.02 0.07 +740 +20 +70
Total – 6360 +70 +120
The Gamma of the current position is +70. To make it neutral we short 70 more X May 25 calls. In that
case the new position Gamma would be = -170×100×0.01 + 50×100×0.03 + 10×100×0.02 = 0. Now our
entire position is gamma neutral. But by selling 70 more May 25 Calls, our position delta would have
changed. The delta of this new position would be = -2000 – 170×100×0.89 + 50×100×0.76 + 10×100×0.74= -12590. The earlier position delta has increased significantly to – 12590. This can be made neutral only
by going long 12590 shares. Since we are already short 2000 shares, the net will be long 10590 shares of
the underlying. Thus the new position would be depicted as under.
Position Individual Position
Delta Gamma Vega Delta Gamma Vega
Long 10590 X 1.00 0.00 0.00 +10590 0 0
Short 170 X May 25 calls 0.89 0.01 0.02 – 15130 – 170 – 340
Long 50 X May 30 Calls 0.76 0.03 0.05 +3800 +150 +250
Long 10 X August 30 Calls 0.74 0.02 0.07 +740 +20 +70
Total 0 0 – 20
We can see that after the portfolio has been converted to delta and gamma neutral, the position Vega is just
– 20. This implies that an increase in implied volatility by 1% our profits would reduce by ₹20 on the
overall position. Obviously, we would make ₹20 for every fall in implied volatility of 1%.
Question 7: X holds 100 contracts each of the following options. Each contract has 100 shares of the
underlying. The theta of the options is as follows:
Option Theta
July 30 call – 0.03
July 30 put – 0.03
(a) What is the position theta?
(b) How much X will lose or gain per day?
(c) How much a seller of this position will lose or gain per day?
(b) Theta is always given as a negative number. A long position holder would witness time decay. In this
case, X‟s overall position would lose ₹600 per day.
(c) Theta (time decay of an option) always favors‟ the seller. Hence the seller of this position would gain
₹600 daily from this position.
Question 8: We have stock P whose price if ₹480. With three months to expiration, we have the following calls available. April 500 call and April 600 call. Each contract has 100 shares of the underlying. Given the
following data
Option Delta Gamma Vega
April 500 Call 0.373 0.009 0.006
April 600 Call 0.095 0.002 0.004
A spreader desires to make a profit of approximately ₹50 for each one percentage decrease in volatility.
Contract a strategy using mathematical approach assuming that he wants his position delta and gamma
neutral. i.e., how many options should be spread to achieve the desired result?
Answer:
Our aim is first to make the portfolio gamma neutral. Then make it delta neutral and finally ensure that
position Vega is – 50. This would ensure that the entire position would give us ₹5000 for every decrease of
1% in implied volatility.
Let X represent the number of April 500 Calls we buy and y represent the number of April 600 calls we
buy. First we make the portfolio gamma neutral i.e. ensure that the weighted average of gamma of both
these calls is zero.
0.009x + 0.002y = 0 [1]
We construct a second equation of Vega to give us the desired ₹50 i.e. o.5 (50/100) on every contract of
100 shares.
0.006x + 0.004y = -0.5 [2]
Multiplying equation [1] by 0.006 & equation [2] by 0.009 and then subtracting [2] from [1], we get
Question 4: The common share of a company is selling at ₹90. A 26 week call is selling at ₹8. The call‟s exercise price is ₹100. The risk free rate is 10% p.a. What should be the price of a 26 week put of ₹100?
Answer:
Formula Calculation
0 0 − 0 + 8 − 90 +
100
0.1×.5
6
Question 5: Mr. Narendra holds an American put option on Delta Airlines a non-dividend paying stock.
The strike price of the put is ₹40, and Delta Airlines stock is currently selling for ₹35 per share. The
current market price of the put is ₹4.50. Is this option correctly priced? If not, should Mr. Narendra buy orsell the option in order to take advantage of the mispricing?
Answer: the option pricing is mispriced, that leads to arbitrage gain as follows
Strategy Cash Flow
1 Buy put option –₹4.50
2 Buy stock –₹35.00
3 Exercise put option +₹40.00
Arbitrage Profit +₹0.50
Therefore, Mr. Narendra should buy the option for ₹4.50, buy the stock for ₹35, and immediately exercise
the put option to receive its strike price of ₹40. This strategy yields a risk less, arbitrage profit of ₹0.50
(=₹5 – ₹4.50)
Question 6: GESCO has both European call and put options traded on NSE. Both options have same
exercise price of ₹40 and both expire in one year. GESCO does not pay any dividends. The call and the put
are currently selling for ₹8 & ₹2 respectively. The risk free rate of interest is 10% p.a. What should the
stock price of GESCO trade in order to prevent arbitrage?
Answer:
Formula Calculation
0 0 = 0 − 0 + 2 = 8 − 0 +
40
0.1 42.36
[CS FINAL]
Question 7: The following quotes are available for 3-months options in respect of a share currently traded
An investor devises a strategy of buying a call and selling the share and a put option. What is his profit /
loss profile if it is given that the rate of interest is 10% per annum? What would be the position if the
strategy adopted is selling a call and buying the put and the share?Answer:
Formula Calculation
0 + 0 = 0 + 31 + 2 = 3 +
30
0.1×0.25
33 = 32.27 LHS ≠ RHS,
Hence arbitrage exist
Arbitrage strategy: Buying a call & Selling a put & spot leading a profit of LHS – RHS [33 – 32.27=0.73]
Cash Flow
< E, = E > E
= 25 = 30 = 35
Buy a call – 3 – 3 – 3
Sell a put and spot 33 33 33
Net Investment @ 10% 30 30 30
Withdraw investment 30.75 30.75 30.75
Call [Exercise | Lapse] Lapse Lapse – 30
Put [Exercise | Lapse] – 5 Lapse Lapse
Buy stock to cover short – 25 – 30 0
Net Flow 0.75 0.75 0.75
Similar strategy if developed by selling the call and buying the share and put would result in an initial out
flow of 0.73, and hence not advisable.
Risk-neutral approach
Question 8: We provided with the following information:Stock price = ₹88; Risk free rate = 3%; In 3 months‟ time the stock could either go up to ₹95 or down to
₹82. The strike price is ₹90. Compute the value of put option using risk neutral probability.
(a) Based on the assumption that APAR Ltd. is not going to declare any dividend over the next three
months, is the option worth buying for ₹25?
(b) Calculate value of aforesaid call option based on Block Schole‟s valuation model if the current price is
considered as ₹380.
(c)
What would be the worth of put option if a current price is considered ₹380? (d) If APAR ltd. share pr ice at present is taken as ₹408 and a dividend of ₹10 is expected to be paid in the
two months‟ time, then calculate value of the all options.
Answer: (a)
Formula Calculation
1 d1 In(
) + (r +2
) T
σ In(
415
400) +(0.05 +
0.222
2)0.25
0.22 0.25
0.5033
2 d2 d1 – σ 0.5033 – 0.22 0.25
0.3933
3 C S N(d1) – Xe-r
N(d2) 415 N(0.5033) – 400e- . × .
N(0.3966) ₹27.58
4 P 0 − 0 + 11.87 − 60 +
50
0.08×0.25 ₹0.88
Since market price of ₹25 is less than ₹27.58 (Black Scholes Valuation model). This indicates that the
option is under priced, hence worth buying.
(b) If the current price is taken as ₹380 the computations are as follows:
Formula Calculation
1 d1 In(
) + (r +
2
) T
σ In(
380
400) +(0.05 +
0.222
2 )
0.25
0.22 0.25
-0.2976
2 d2 d1 – σ -0.2976 – 0.22 0.25
-0.4077
3 C S N(d1) – Xe-r
N(d2) 380 N(-0.2976) – 400e- . × .
N(-0.4077) ₹7.10
(c) P 0 − 0 + 7.10 − 380 +
400
0.05×0.25 ₹22.16
(d) Since dividend is expected to be paid in two months time we have to adjust the share price and then use
Block Schole‟s model to value the option.
Adjusted S = S – Present Value of Dividend = 408 – 10 (
Answer: Option spread means taking position in two or more options of the same type (i.e. calls or puts)
on the same underlying assets.
1. Vertical spread is an option spread, which has different strike prices but the same expiration date .
2. Horizontal spread is the spread, which has different expiration dates but the same strike price .
This spread is also called time spread or calendar spread.
3. Diagonal spread is the spread in which two legs of the spread have different strike prices and
different expiration dates. This position has features of both vertical and horizontal spreads and so may
be called a hybrid product.
Question: Write a note on option strategies.
Answer:
1. Bull call spread: A bull call spread involves the purchase and sale of call options at different
exercise prices but with the same expiry date. The purchased calls should have a lower exercise
price than the written calls.
2. Bull put spread: A bull put spread involves the purchase and sale of put options at different
exercise prices but with the same expiry date. The purchase puts should have a lower exercise price
than the written puts.
3. Bear call spread: A bear call spread involves the purchase and sale of call option at different exercise
prices and the same expiry date. But the purchased calls have a higher exercise price than the written
calls.
4. Bear put spread: A bear put spread involves the purchase and sale of put option at different exercise
prices and the same expiry date. But this time purchased puts have a higher exercise price than the
written puts.
Question: Write a note on straddle and strangle.
Answer: Straddle & Strangle: Straddle & Strangle are strategies tailor made for volatile situations.
Long straddle: Purchase a call option and a put option with the same exercise price.
Short straddle: Sell a call option and a put option with the same exercise price.
Long strangle: Purchase a call and a put with different exercise prices
Short strangle: Sell a call and a put with different exercise prices
Question: Explain Butterfly Spread.
Answer: A Butterfly Spread is an option strategy combining a bull and bear spread. It uses three strike
prices. The lower two strike prices are used in the bull spread, and the higher strike price in the bear
spread. Both puts and calls can be used. A butterfly spread consists of either all calls or all puts and all
options expire at the same time.
Long butterfly spread: A long butterfly spread can be created by buying one option at each of the outsideexercise prices and selling two options at the inside exercise price.
Question 2: Suggest what strategies an investor could adopt on Reliance Industries in the options marketin each of the following, if:
(a) Investor is strongly bullish.
(b) Investor believes the bullish trend would continue but is not very bullish.
(c) Investor believes that the chance of market going up is more than the chance of market going down.
(d) Investor believes that the chance of market going up is more than the chance of market going down
and wants to earn income.
(e) What is common in all the above strategies?
Answer:
(a) It is without doubt, that when an investor is bullish, he would buy a call option on Reliance Industries.
His loss is limited to premium paid. It is generally adopted when the option is undervalued and
volatility is increasing.
(b) When an investor believes the bullish trend would continue but is not very bullish, he may sale a put
option on Reliance Industries. Selling a put is a neutral-bullish position. Here his profit is limited to
premium received. It is generally adopted when the option‟s volatility is increasing.
(c) When an investor believes that the chance of market going up is more than the chance of market going
down, he may buy Call & Sell call of higher strike price, or Reliance industries. This is a buying a Bull
Call Spread strategy. This transaction would provide a range bound payoff, both on the upside and the
downside and maximum loss is limited to the net debit of the position.(d) When an investor believes that the chance of market going up is more than the chance of market going
down and wants to earn income, he would sell Put & but Put of lower strike price, of Reliance
Industries. This is a selling Bear Put Spread strategy. In this case the loss is limited to strike price
difference – premium received. This would be used when the overall position derives a good income.
(e) All the strategies explained above are adopted when the view on the stock / market is bullish.
Question 3: Suggest what strategies an investor could adopt on Reliance Industries in the options market
in each of the following if:
(a) Investor is strongly bearish.
(b) Investor believes the bearish trend would continue but is not very bearish.
(c) Investor believes that the chance of market going down is more than the chance of market going up.
(d) Investor believes that the chance of market going down is more than the chance of market going up
and wants to earn income.
(e) What is common in all the above strategies?
Answer:
(a) It is without doubt, that when an investor is bearish, he would buy a put option on Reliance Industries.
His loss limited to premium paid. It is generally adopted when the option is undervalued and volatility
is increasing.
(b) When an investor believes the bearish trend would continue but is not very bearish, he may sell a call
option on Reliance Industries. Selling a call is a neutral-bearish position. Here his profit limited to
premium received. It is generally adopted when the option is overvalued and market trend is flat to
bearish.
(c) When an investor believes that the chance of market going down is more than the chance of market
going up, he may buy Put & Sell of higher strike price, of Reliance Industries. This is a buying BearPut Spread strategy. This transaction would provide a range bound payoff, both on the upside and the
downside and maximum loss is limited to the net debit of the position.
(d) When an investor believes that the chance of market going down is more than the chance of market
going up and wants to earn income, he would sell Call & buy Call of higher strike price, of Reliance
Industries. This is selling Bear Call Spread strategy. In this case the loss is limited to strike price
difference – credit.
(e) All the strategies explained above are adopted when the view on the stock / market is bearish.
Bull Call Spread
Question 4: X is moderately bullish on the market and wants to capitalize on a modest advance in price of
the L&T. He is not very bullish on L&T. He has a discomfort with the cost of purchasing and holding the
long call alone. On 1st November, the share price of L&T is 204. Suggest a suitable strategy if call options
on L&T with strike prices of ₹200 & ₹220 are available for ₹16 & ₹8 respectively. Explain with the help
of payoff table and diagram, what strategy he would adopt.
Answer: X = ₹200 and ₹220, Apply Bull Call Spread [purchase call at lower X, and sell call at higher X]
X P S 150 170 190 200 208 210 216 220 240 260
CE B 200 16 Max (S-X, 0) -16 -16 -16 -16 -8 -6 0 4 24 44
CE S 220 8 Max (S-X, 0) 8 8 8 8 8 8 8 8 -12 -32
Payoff -8 -8 -8 -8 0 2 8 12 12 12
Bull Put Spread
Question 5: X is moderately bearish on the market and wants to capitalize on a modest decrease in price of
the L&T. He is not very bearish on L&T. He has a discomfort with the cost of purchasing and holding the
long put alone. He needs a small income on the spread. On 1 November, the share price of L&T is 204.
Suggest a suitable strategy if put options on L&T with strike prices of ₹200 & ₹220 are available for ₹7 &
₹18 respectively. Explain with the help of payoff table and diagram, what strategy he would adopt.
If the stock price is less than or equal to ₹35, the collar preserves the ₹350000 in principal. If the price
exceeds ₹45 Ashok gains up to a cap of ₹450000. In between, his proceeds equal 10000 times the
stock price.
(d) The best strategy in this case would be (c) since it satisfies the two requirements of preserving the
₹350000 in principal while offering a chance of getting ₹450000. Strategy (a) seems ruled out since it
leaves Ashok exposed to the risk of substantial loss of principal. The ranking would be (c) (b) and (a),
in that order.
Protective Put
Question 17: Ram and Shyam purchase an Index at 1200. However, they decide to seek downside
protection by buying put option of different strike prices. Whereas, Ram prefers at the money Put option
costing ₹60, Shyam buys In-the-Money Put option with a strike price of 1170, costing ₹45. Compare and
contrast their profits of the respective protective puts they have purchased.
Answer:
Ram‟s strategy
Initial cost Payoff
S ≤ 1200 S > 1200
Stock Index 1200 S SPut option (X = 1200) 60 1200 – S 0
Total 1260 1200 S
Profit = Payoff – 1260 1200 – 1260 = -60 S – 1260
Break Even Point = 1260
Shyam‟s strategy
Initial cost Payoff
S ≤ 1170 S > 1170
Stock Index 1200 S S
Put option (X = 1170) 60 1170 – S 0
Total 1245 1170 S
Profit = Payoff – 1245 1170-1245= -75 S – 1245
Break Even Point = 1245
Shyam does better when the stock price is high, but worse when the stock price is low. Both Ram &Shyam
incur same losses of ₹60, at the break -even point of S = ₹1185. Shyam‟s strategy has greater systematicrisk. Profits are more sensitive to the value of the stock index.