Arbitrage in Stock Futures

1. 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.