Executive Summary
Arbitrage is created when there is a mismatch in the pricing of the same asset in a different
exchange. Arbitrage is also present in a different market segments, like spot price from the equity
segment and future price from the derivative segment. As there was a lot of volatility in March 2020
due to the coronavirus pandemic, lots of arbitrage opportunities were created. So to better understand
the arbitrage concept and analyze the opportunity of arbitrage created in the year 2020, data from
National Stock Exchange, India for the security Powergrid from equity and derivative segments are
considered in this report. The report shows a relevant calculation of profit/loss due to arbitrage. Cost
to arbitrage is one of the important aspects of arbitrage, which is also considered while analyzing
profit/loss in this report.
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1. Introduction to Concept of Arbitrage
1.1 Concept of Arbitrage
Arbitrage is an investment opportunity where investors buy and sell the same security on
different markets to take advantage of a mismatch in pricing between two markets. Arbitrage can occur
in different securities, indexes, commodities, currency pairs, and credit derivatives. One of the important
aspects of arbitrage is the risk-free return of the country where we intend to seek profit through arbitrage.
If our profit percentage is very less than the risk-free rate of the country then it is not worth creating an
arbitrage. One should carefully consider the cost while calculating the return generated by arbitrage. If
the cost associated with it is too high, it will reduce our return. Arbitrage is a relatively low-risk
investment strategy.
Traders frequently try to lock in profits by arbitrage. High-Frequency Trading allows traders to
lock in a profit by simultaneously buying and selling the same security on different exchanges. Arbitrage
is one of the safest strategies in terms of risk. It is one of the oldest strategies which can generate small
profits. So if arbitrage strategy is traded in large volume, it can create numerous returns.
Fig. 1.1 Arbitrage
Image source: https://cdn.corporatefinanceinstitute.com/assets/arbitrage.jpg
1.2 Arbitrage in future Contracts and how it can be used
Arbitrage in the future segment is created when there is a difference between the spot
price of the security and the future price of the security. It is more common that future prices are at a
premium or discount. When this premium or discount is large enough then one can create an arbitrage
strategy after carefully considering the cost. In NSE India, the cost includes brokerage, Securities
transaction tax, SEBI charges, Exchange transaction charges, Depository charges, stamp duty and GST.
This cost is in addition to the risk-free rate at which we intend to borrow the money.
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Fig. 1.2 Arbitrage in future and spot price
Image source: https://static.seekingalpha.com/uploads/2021/2/28/saupload_derivatives-lecture3-4-
futures-27-728.jpg
When the future price of any security is at a premium to the spot price, we can sell the future
contract in the derivative segment and buy the same security from the equity segment. Theoretically,
when the contract will expire at the expiry date, the difference between the future price and spot price
will be reduced to zero and we can gain some profit. Due to the rapid movement of security price, buying
of security at the spot rate and selling of future of the same security at the start of the expiry must occur
at the same time or within a fraction of a minute. On the day of expiry covering the position i.e buying
the future contract and selling a security on spot must occur at the same time or within a fraction of a
minute.
1.3 Arbitrage in commodity and how it can be used
Arbitrage in a commodity contract is created when the commodity’s future price is at a premium
to its spot rate. One can create arbitrage by buying the commodity at a spot price from the market and
storing it till the expiry date of the future contract and selling the future contract of that commodity. As
the price movement of the commodity is very fast, buying of commodity and selling of futures contract
at starting of expiry and selling of commodity and buying of futures contract at the expiry must occur at
the same time or within a fraction of a minute. Theoretically the expiry difference between the spot rate
of the commodity and the future rate will be reduced to zero.
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As a commodity needs to be stored due to its physical presence, we must consider its storage
cost and transportation cost in addition to the cost associated with buying and selling future contracts.
1.4 Arbitrage in the currency market and how it can be used
Arbitrage in the currency market can be done by borrowing money from one country where the
risk-free rate is low and then investing it at the risk-free rate in a foreign country where the risk-free rate
is higher. So theoretically we can earn profit from this arbitrage opportunity as there will be a price
mismatch between quotes of future prices and the spot at which we borrow money.
Arbitrage in the Currency market also occurs when there is mispriced rate of exchange between
two forex brokers. A trader can exploit the opportunity by quickly buying and selling the same currency
pair in different forex brokers. Arbitrage in this way requires high-frequency trading algos as manually
we might not be able to spot and trade.
Fig. 1.3 Arbitrage due to broker quotes and spread
Image source: https://forexop.com/assets/uploads/2014/12/x-broker-arbitrage-example.png
1.5 Arbitrage in CDS and how it can be used
Arbitrage in CDS can be done by issuing a Bond at a theoretical price of CDS and using that
money to invest in risk-free rate of the country and at the same time issuing CDS at future value. This
way we can earn profit from arbitrage in CDS. When there will be difference between theoretical price
of CDS and the future price of CDS we can implement an arbitrage strategy using CDS.
1.6 Arbitrage due to Mergers and Acquisitions and how it can be used
Arbitrage opportunities arise in securities when the merger is announced of a publicly traded
company. Mostly when the merger is announced by any company, it offers to buy the shares of the target
company at a premium. So after the announcement currently market price will try to get closer to the
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announced premium price. But it will stay at some discount due to the risk of the deal may fail. So in
merger arbitrage investors/traders buy the discounted price of the target company and then profit after
the merger is successfully completed.
1.7 Arbitrage in convertible bonds and how it can be used
Convertible bonds are those which can be converted to share of the company at a later date,
which is often at a discounted rate. Investors can arbitrage by buying convertible bonds and selling the
underlying shares. When a bond is converted to shares, it is mostly at discount. So the investor can profit
by arbitraging this way.
2. Example of Arbitrage with detailed calculation
Due to very high volatility during the corona virus pandemic, a big arbitrage opportunity was
created in many companies. In this report, Powergrid Corporation of India Ltd. (Powergrid) is taken for
arbitrage strategy. In India, last Thursday of every month is the expiry day of the monthly future contract.
So spot rate and future rate from 28.02.2020 to 26.03.2020 is taken from the NSE website for calculation.
The different future contract has different lot size. Powergrid had a lot size of 4000 shares. In India 3
months future contracts are available for equity and that is near month, next month and far month.
2.1 Calculation of fair price
On 25.03.2020 closing spot price of powergrid was INR 150.25 and closing future price of the
March Expiry(30.04.2020) was INR 152.50. One can create an arbitrage strategy to gain profit from this
mispricing. To gain profit using arbitrage we need to short the 1 future contract and buy an equal number
of shares(4000) at the spot rate. For that purpose first step is to borrow money at risk-free rate. During
March 2020, India 1 year government bond yield was 5.18% as per official RBI data. In India, 3 month
contracts are available for equity but only near-month contracts are liquid. So during calculation, this
rate is discounted for one month. Charts for the future and spot for this period is shown below in fig. 1.4
and 1.5.
Risk-Free Rate (R) 5.18%
No of Days (T) 23
Future price at beginning 152.5
Spot price at the beginning 150.25
Calculation of fair price 152.5 * e(-5.18%*(23/360) = 152.00
Table: 1.1 Calculation of Fair Price
From table 1.1 we can see that the fair price of a security is not justified so we can use arbitrage to gain
profit from this strategy.
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Fig. 1.4 Future chart of powergrid from March – April 2020
Image source: created by author from icharts website
Fig. 1.5 spot rate chart of Powergrid from March-April 2020
Image source: created by author from tradingview website
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2.2 Calculation of requirement of money to implement the strategy
To buy one lot of powergrid one needs approximately INR 2,74,000 as future margin as per NSE
norms. To sell 4000 shares one needs approximately INR 7,26,000. To manage this position and settle
MTM, extra INR 1,00,000 is needed. In total, one will need approximately INR 1,100,000 to create
arbitrage using one lot.
The money needed for arbitration needs to be borrowed at risk-free rate. The cost of borrowing
INR 1,100,000 at risk-free rate of 5.18% is INR 56,980 for one year. So when we discount it for 1 month
it will be INR 3,640. So this cost must be taken into consideration while calculating profit. In this
arbitrage strategy, we must square off our contract in the future and spot at the same time or within a
fraction of a minute.
2.3 Gap between the spot rate and future rate
Fig. 1.6 shows how the gap between the spot rate and future rate behaved from 25th March 2020
to 28th April 2020.
Gap between future and spot
170
165
160
PRICE
155
150
145
140
DATE
Fig. 1.6 Gap between the spot rate and future rate of Powergrid
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Image source: created by the author
As the expiry will be near, the gap between the spot and the future rate is reduced and had
become zero on the day of expiry. This phenomenon applies to each security traded on an exchange.
Sometimes due to settlement, there may be a negligible gap difference between spot and future prices.
2.4 Arbitrage Strategy Execution for powergrid
We shorted future contract at 152.5 at the beginning and cover it at 162.05 thus giving loss of
38,200. We buy equity at 150.25 and cover it at 162.05 thus giving a profit of 47,200. By this
arbitrage, we were able to generate INR 9000. The graph in fig. 1.7 shows the day-to-day MTM of net
position. MTM is cash settled. From fig 1.7 it can be seen that MTM fluctuates sharply.
DAILY MTM
(FUTURE+SPOT)
4200
3200 3200
2800
2600 2600
2200
1600 1600
1000 1000
PNL
400 400
-1000
-1400
-1600
-1800 -1800 -1800
-2200
-2800
-3400
Date
Fig. 1.7 MTM of Arbitrage in powergrid
Image source: created by author
2.5 Cost of arbitrage strategy for powergrid
If we consider the brokerage, charges, and taxes associated with the transaction than it would be
INR 1559.65. This value is taken from the broker's website. The screenshot is shown in fig. 1.8 for
brokerage and other charges. So our net profit after cost will be INR 7440.35.
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Fig. 1.8 Charges for buying and selling equity and future
Image source: https://zerodha.com/brokerage-calculator/#tab-equities
We need to subtract risk-free rate value of borrowed money which is INR 3640. So we are in net
profit of INR 3800.35. This profit is obtained on the capital of 11,00,000. So our monthly Profit
percentage would be 0.33% which is a good risk free profit. Following table 1.1 shows the calculation
of profit by arbitrage strategy in powergrid. Currency Data in this table INR.
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Spot (Buy) Future (Short)
(Quantity 4000) (1lot=4000 Quantity)
Entry 150.25 152.5
Exit 162.05 162.05
Net points 11.80 -9.55
Lot size 4000 4000
Profit/Loss(Net point*Lot size) 47,200 -38,200
Brokerage & other charges with transaction 1407.27 152.38
Profit after tax and brokerage 45792.73 -38352.38
Profit on the day of Expiry(Spot+Future) 7440.35 (after tax and brokerage)
Cost of borrowing at Risk-free rate of 5.18% 3640
Net profit after all costs 3800.35
Table 1.1 Calculation of PNL
2.6 Summary of arbitrage strategy for powergrid
We shorted the future contract and buy an equal number of shares at spot rate. Initially, there
was a gap of INR 2.25, which vanished at the end of the expiry. So by arbitraging, we were able to get
INR 2.25 for one lot. If we subtract the cost then also we were able to generate a profit.
By borrowing money at risk-free rate and using it for arbitration we were able to generate a good
amount of profit. If this strategy is implemented in large volumes then it can generate enormous profits.
From calculation, we can see that cost associated with the arbitrage consumed approximately 50% of
our profit. So We need to be careful enough while making arbitrage otherwise we may end up with loss
or net zero.
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3. Conclusion
• Mispricing is always present in the market so to take advantage of this mispricing we can use an
arbitrage strategy.
• When prices of the securities in the future and spot are not justified we can look for the arbitrage
opportunity.
• Arbitrage is an extremely low risk strategy to generate consistent profit.
• While implementing an arbitrage strategy, cost should be carefully considered.
• Mispricing will be more during increased volatility due to large fluctuations in prices of a
security and future contract.
• Gap between the future and spot rate will be zero on the day of expiry.
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References:
https://online.hbs.edu/blog/post/what-is-arbitrage
https://corporatefinanceinstitute.com/resources/wealth-management/arbitrage/
https://www.investopedia.com/ask/answers/what-is-arbitrage/
https://www.rbi.org.in/Scripts/BS_NSDPDisplay.aspx?param=4
https://www1.nseindia.com/products/content/derivatives/equities/historical_fo.htm
Appendix A: Selected company for arbitrage and its data
1. Powergrid Corporation of India Ltd.
Date Closing spot price Closing future price
25-Mar-20 152.5 150.25
26-Mar-20 159.55 158.35
27-Mar-20 160.8 160
30-Mar-20 156.8 155.65
31-Mar-20 159.6 159.1
01-Apr-20 154.4 154.6
03-Apr-20 156.85 156.2
07-Apr-20 159.35 158
08-Apr-20 159.05 158.35
09-Apr-20 164.6 164.45
13-Apr-20 160.65 159.95
15-Apr-20 160 159.55
16-Apr-20 164.3 163.4
17-Apr-20 168.4 167.75
20-Apr-20 165.75 165.5
21-Apr-20 162.8 162.65
22-Apr-20 162.8 162.2
23-Apr-20 158.5 158
24-Apr-20 158.85 159.15
27-Apr-20 159.75 159.6
28-Apr-20 157.6 157.2
29-Apr-20 157.65 158.05
30-Apr-20 162.05 162.05
Source of data: NSE India Website
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