FDRM PROJECT

ON

“ARBITRAGE PROFIT IN STOCK

FUTURES”

Submitted To: Submitted By:

Prof. Dheeraj Mishra Paritosh Kumar Singh JL13FS35

Rajneesh Kumar Sharma JL13FS44

Soumen Aich JL13PGDM 118

Prashant Singh Rathore JL13PGDM094

Sarthak Jeswani JL13PGDM108

Ankit Kanojia JL13PGDM069

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Acknowledgement

Every project big or small is successful largely due to the effort of a number of wonderful people who have

always given their valuable advice or lent a helping hand. We sincerely appreciate the inspiration; support and

guidance of all those people who have been instrumental in making this project a success.

We, the students of Jaipuria Institute of Management, Lucknow (PGDM), are extremely grateful to our project

guide for the confidence bestowed in us and entrusting our project entitled “ARBITRAGE PROFIT IN STOCK

FUTURES” and impact of working capital management on profitability performance.

At this juncture we feel deeply honoured in expressing our gratitude to our Project Guide, Dr.Dheeraj Mishra,

for assisting us in compiling the project and providing valuable insights leading to the successful completion of

the project.

Paritosh Kumar Singh JL13FS35

Rajneesh Kumar Sharma JL13FS44

Soumen Aich JL13PGDM 118

Prashant Singh Rathore JL13PGDM094

Sarthak Jeswani JL13PGDM108

Ankit Kanojia JL13PGDM069

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Table Of Contents

Introduction ............................................................................................................................................................ 4

Difference Between Stock Futures And Stock Option ............................................................................................ 5

Opportunities Offered By Stock Futures ................................................................................................................. 5

Market to Market Margin ....................................................................................................................................... 7

Spread Trading ........................................................................................................................................................ 7

Arbitrage Opportunities in Futures Market ............................................................................................................ 9

How arbitrage opportunity arises? ....................................................................................................................... 10

Rollover of futures contract .................................................................................................................................. 10

Arbitrage Profit in Bajaj-Auto stock futures ......................................................................................................... 11

Regression Output ................................................................................................................................................ 12

Regression Analysis ............................................................................................................................................... 16

Conclusion ............................................................................................................................................................. 17

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Stock Futures

Introduction

Stock Futures are financial contracts where the underlying asset is an individual stock. Stock Future contract is

an agreement to buy or sell a specified quantity of underlying equity share for a future date at a price agreed

upon between the buyer and seller. The contracts have standardized specifications like market lot, expiry day,

unit of price quotation, tick size and method of settlement. Stock Future Pricing

The theoretical price of a future contract is sum of the current spot price and cost of carry. However, the actual

price of futures contract very much depends upon the demand and supply of the underlying stock. Generally,

the futures prices are higher than the spot prices of the underlying stocks.

Futures Price = Spot Price + Cost of Carry

Cost of carry is the interest cost of a similar position in cash market and carried to maturity of the futures

contract less any dividend expected till the expiry of the contract.

Example:

Spot Price of Infosys = 1600, Interest Rate = 7% p.a. Futures Price of 1 month contract=1600 +

1600*0.07*30/365 = 1600 + 11.51 = 1611.51

Difference Between Stock Futures And Stock Option

In stock options, the option buyer has the right and not the obligation, to buy or sell the underlying share. In

case of stock futures, both the buyer and seller are obliged to buy/sell the underlying share.

Risk-return profile is symmetric in case of single stock futures whereas in case of stock options payoff is

asymmetric.

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Also, the price of stock futures is affected mainly by the prices of the underlying stock whereas in case of stock

options, volatility of the underlying stock affect the price along with the prices of the underlying stock.

Opportunities Offered By Stock Futures

Stock futures offer a variety of usages to the investors. Some of the key usages are mentioned below:

Investors can take long term view on the underlying stock using stock futures.

Stock futures offer high leverage. This means that one can take large position with less capital. For example,

paying 20% initial margin one can take position for 100 i.e. 5 times the cash outflow.

Futures may look overpriced or underpriced compared to the spot and can offer opportunities to arbitrage or

earn risk-less profit. Single stock futures offer arbitrage opportunity between stock futures and the underlying

cash market. It also provides arbitrage opportunity between synthetic futures (created through options) and

single stock futures.

When used efficiently, single-stock futures can be an effective risk management tool. For instance, an investor

with position in cash segment can minimize either market risk or price risk of the underlying stock by taking

reverse position in an appropriate futures contract.

Stock Futures Settlement

Presently, stock futures are settled in physical . The final settlement price is the closing price of the underlying

stock.

Squaring Position From Stock Futures

The investor can square up his position at any time till the expiry. The investor can first buy and then sell stock

futures to square up or can first sell and then buy stock futures to square up his position. E.g. a long (buy)

position in December ACC futures, can be squared up by selling December ACC futures.

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Market to Market Margin

The outstanding positions in stock futures are marked-to-market daily. The closing price of the respective

futures contract is considered for marking to market. The notional loss / profit arising out of mark to market is

paid / received on T+1 basis.

Profits and Losses in case of Stock Futures Position

Profits and losses would depend upon the difference between the price at which the position is opened and the

price at which it is closed. Let an investor have a long position of one November Stock "A" Futures @ 430. If

the investor square up his position by selling November Stock "A" futures @ 450, the profit would be Rs. 20

per share. In case, the investor squares up his position by selling November Stock "A" futures @

400, the loss would be Rs. 30 per share.

Spread Trading

One can trade in spread contracts on the Derivative Segment of BSE. Spreads are the contracts for differential

price. This means that in case you want to buy a December contract and sell November contract, you can enter

an order for Buy Nov Dec stating the difference you want to pay. This would mean that you are buying a

December Contract and selling a November contract.

Deposit upfront the initial margin Similarly, you can enter an order for Sell Nov Dec stating the difference you

want to receive. This would mean that you are selling a December Contract and buying a November Contract

and receiving the difference.

Investors benefit from predicted rise or predicted fall in the price of a stock

An investor can benefit from a predicted rise in the price of a stock by buying futures. As the price of the

futures rises, the investor will make a positive return. As the investor will have to pay only the margin (which

forms a fraction of the notional value of contract), his return on investment will be higher than on an equivalent

purchase of shares.

An investor can benefit from a predicted fall in the price of stock by selling futures. As the price of the future

falls in line with the underlying stock, the investor will make a positive return.

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Pair Trading

This trading strategy involves taking a position on the relative performance of two stocks. It is achieved by

buying futures on the stock expected to perform well and selling futures on the stock anticipated to perform

poorly. The overall gain or loss depends on the relative performance of the two stocks.

Similarly it is possible to take a position in the relative performance of a stock versus a market index. For

example, traders who would like to take only company specific risk could buy/sell the relative index future.

Arbitrage Opportunities in Futures Market

Buying in one market (say, spot market) and simultaneously selling in another market (say, futures market) to

make risk free profits when there is substantial mismatch between two prices is called arbitrage. Arbitrage is

described as risk free because participants are not speculating on market movements. Instead, they bet on the

miss-pricing of a share/asset that has happened between to related markets.

In short, when you earn by selling and buying same security at different rates in different markets, it is called

Arbitrage. It is a highly technical field. Market’s miss-pricing is taken advantage by traders to make risk free

gains.

A futures contract is a contract to buy (and sell) a specified asset at a fixed price in a future time period. There

are two parties to every futures contract - the seller of the contract, who agrees to deliver the asset at the

specified time in the future, and the buyer of the contract, who agrees to pay a fixed price and take delivery of

the asset. If the asset that underlies the futures contract is traded and is not perishable, you can construct a pure

arbitrage if the futures contract is mispriced. In this section, we will consider the potential for arbitrage first

with storable commodities and then with financial assets and then look at whether such arbitrage is possible.

The basic arbitrage relationship can be derived fairly easily for futures contracts on any asset, by estimating the

cash flows on two strategies that deliver the same end result, the ownership of the asset at a fixed price in the

future. In the first strategy, you buy the futures contract, wait until the end of the contract period and buy the

underlying asset at the futures price. In the second strategy, you borrow the money and buy the underlying asset

today and store it for the period of the futures contract. In both strategies, you end up with the asset at the end of

the period and are exposed to no price risk during the period, in the first, because you have locked in the futures

price and in the second because you bought the asset at the start of the period. Consequently, you should expect

the cost of setting up the two strategies to exactly the same. Across different types of futures contracts, there are

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individual details that cause the final pricing relationship to vary, commodities have to be stored and create

storage costs whereas stocks may pay a dividend while you are holding them.

How arbitrage opportunity arises?

In general, fair value of future price of the underlying asset should equal to spot price of

the underlying asset + cost of carry. When there is mispricing in cost of carry and future

price of the underlying asset is at premium or discount to its fair value, arbitrage opportunity arises.

Cost of carry (CoC) is the cost of holding the asset till expiry. It includes storage cost, interest cost etc and

excludes any income earned on the asset.

For equity derivatives, cost of carry is the interest cost incurred on holding the security till expiry minus any

dividends on the security and is calculated as difference between future and spot price of the underlying security

(spread).

Spreads are determined by market sentiments, interest rate levels in the economy, FII holdings.

Rollover of futures contract

At expiry, investors square off their positions and let futures contract expire. However

investors can also carry forward their position by entering into a similar contract at a

future date. This is known as rollover of futures contract.

It is a process where investors carry forward their futures contract from one expiry date to another.

For example, investor has Nifty long futures (buy) which expires in May, if investor decides to rollover his

contract means he will square off his position on expiry date and buy Nifty futures expiring in June i.e. carry

forward his Nifty futures contract.

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Arbitrage Profit in Bajaj-Auto stock futures

The main objective of our study is to find out the factors affecting the arbitrage profit in Bajaj-Auto stock

futures. In order to study this relationship we have taken the data of the last 24 months of Bajaj-Auto stock

futures which include expiry, open, close, low, high, last traded price, settlement price of that futures and it also

includes data such as no. of contracts, open interest and underlying value of the stock futures from NSE India’s

official website.

We have calculated time to maturity by subtracting expiry date form current date.

Theoretical value of the stock futures is computed by using formula F= Spot price*e^(r*t).

Where spot price was under lying value of particular day of which theoretical value is calculated and we have

taken the risk free rate as 8% and t is time to maturity value in days which we have calculated.

Then we have calculated arbitrage profit by taking the absolute value of difference of settlement price and

theoretical price of past 24 months.

Regression was run to find the relationship between arbitrage profit and various other factors such as time to

maturity, open interest and no. of contracts.

Regression Output

SUMMARY OUTPUT

Regression

Statistics

Multiple R

0.23038

662

R Square 0.05307

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7995

Adjusted R Square

0.05066

6479

Standard Error

11.3704

7856

Observations 1182

ANOVA

df SS MS F

Significan

ce F

Regression 3

85

36

.9

56

64

7

2845.6

52216

22.01021

75

7.17363E-

14

Residual 1178

15

23

129.28

77826

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01

.0

07

9

Total 1181

16

08

37

.9

64

5

Coeffici

ents

St

an

da

rd

Er t Stat P-value

Lower

95%

Upper

95%

Lower

95.0% Upper 95.0%

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ro

r

Intercept

3.32622

7484

1.

41

59

97

61

3

2.3490

34669

0.018986

64

0.5480687

9

6.1043861

78

0.5480

6879 6.104386178

Time to maturity

0.11334

9328

0.

02

46

82

50

8

4.5922

93751

4.8548E-

06

0.0649227

46

0.1617759

11

0.0649

22746 0.161775911

Open Interest

-

3.34418

E-07

1.

12

01

5E

-

-

0.2985

46348

0.765338

86

-

2.53214E-

06

1.8633E-

06

-

2.5321

4E-06 1.8633E-06

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06

No. of contracts

1.05454

E-05

0.

00

02

30

26

9

0.0457

96109

0.963480

52

-

0.0004412

38

0.0004623

29

-

0.0004

41238 0.000462329

Regression Analysis

Value of adjusted R2 is 0.05 which shows that whenever there is a change in the independent variables then

arbitrage profit will change by 0.05 paisa.

Significance value is less than 0.05 which shows that results are reliable.

Coefficient of time to maturity is 0.025 which shows that when time to maturity change by 1 day there is a

change of 0.025 paisa in arbitrage profit. So when time to maturity declines by 1 day then arbitrage profit

declines by 0.025 paisa. It means that as expiry date approaches the opportunity to exploit arbitrage profit

declines so arbitrage opportunity is more when any new contract opens.

Coefficient of open interest is highly negative which shows that when open interest increases value of arbitrage

profit declines sharply and when open interest decreases then value of arbitrage profit increases. Which shows

that because of high liquidity arbitrage profit is exploited very soon and on the other hand if liquidity is not so

high then arbitrage profit will exist for long.

Coefficient of number of contracts is highly positive which shows that as numbers of contracts increases then

opportunity of arbitrage profit increases sharply.

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Value of t-stat for time to maturity is significant which shows that value of arbitrage profit for Bajaj-Auto for

last 24 months depends on time to maturity.

Standard deviation of arbitrage profit of Bajaj-Auto futures for past 24 months comes out to be 11.67.

Average of arbitrage profit of Bajaj-Auto futures for past 24 months comes out to be 7.29.

Maximum arbitrage profit for Bajaj-Auto futures for past 24 months comes out to be 68.55.

Conclusion

There is no denying that arbitrage funds are relatively less risky as compared to pure equities. However, to slot

them as "risk-free", amounts to mis-representation. Arbitrage funds do have an element of risk; we have seen

some of the scenarios wherein risk is imminent. Investors who are being told that arbitrage funds are less risky

or are well placed to clock a definite return have been misled.

By the way, the reason why we have put 'risk-free' in quotes is that we picked this term from the presentation of

a large fund house; they had used this term to describe their arbitrage fund.