Arbitrage presentation

1. Arbitrage Process
Arbitrage
It is the act of buying and selling same asset in two different market so as
to earn profit through price differential.
For example
One dealer is selling a dollar for Rs 63 and another is intending to buy the
same for Rs 64. Then , we can immediately buy dollar from Dealer A and
sell the same to Dealer B , making gain of Re 1 per dollar (ignoring
transaction cost). Such situations arise due to market imperfection and it is
the act of arbitrageur which creates equilibrium in the market.
In foreign exchange market , there are two types of arbitrage
•Price arbitrage
•Covered Interest rate arbitrage

2. Arbitrage Process
Price Arbitrage
Example: The following quotations of dollar rupee
relationship are available in two different markets.
In the above situation, an arbitrager would buy dollars from
Dealer 1 at the rate of Rs 63.95 and would sell the same to
Dealer 2 for Rs 64.15 . In this process, his gain per dollar would be
Rs 64.15 – Rs 63.95 = Rs 0.20
Buy Sell
Market A Dealer 1 63.15 63.95
Market B Dealer 2 64.15 64.65

3. Arbitrage Process
Interest rate arbitrage
In this kind of arbitrage, an arbitrageur earns through different
interest rates prevailing in two different countries and the
relationship between currencies of these countries in the spot and
forward market.
Example :
Given Spot exchange rate : Rs 55/ $
3-month forward rate Rs 54.84/$
3 month interest rate
Re: 6% p.a.
Dollar: 8% p.a.

4. Arbitrage Process
Step1 : Calculate forward discount/ premium
Discount = (54.85 – 55.00)/ 55 x (12/3) x 100 = 1.09
percent
Interest rate differential = 8 – 6 = 2 percent
Rule . In case interest rate differential is higher than
premium or discount, then borrow that currency which has
lower interest rate and place that currency in money
market which has higher interest rate. Conversely , in case,
interest rate differential is smaller than premium or
discount, then borrow that currency which has higher
interest rate and place that currency in money market
which has lower interest rate.

5. Arbitrage Process
Step 2 Following the above rule, Borrow Rs
1000 at 6% p.a. for 3 months.
Step 3. Convert Rs into dollar, using spot rate
We will have (1000/55) = 18.1818 dollars
Step 4: Invest 18.1818 dollar at the rate of
8% p.a.
After three months , we will have
18.1818 ( 1 + 0.08 x 3/12) = 18.5454 dollars

6. Arbitrage Process
Step 5: Convert dollars back into rupee using forward
rate
We will have
18.5454 x 54.85 = Rs 1017.22
Step 6 : Refund loan of Rs 1000 with interest on it.
Refunded amount will be
Rs 1000 ( 1+0.06x3/12) = Rs 1015
Net gain in the process 1017.22 – Rs 1015 = Rs 2.22
This is a gain on transaction of Rs 1000 . In actual
practice , one conducts arbitrage in large amount so
the gain will accordingly increase.

7. Arbitrage Process
If the rule is not followed, loss will occur as can
be seen from this example.
Example :
Given Spot exchange rate : Rs 63/ $
6-month forward rate Rs 63.90/$
6 month interest rate
Re: 12% p.a.
Dollar: 8% p.a.

8. Arbitrage Process
Step1 : Calculate forward discount/ premium
Premium = (63.9 – 63)/ 63 x (12/6) x 100 =
2.85percent (dollar is at premium)
Interest rate differential = 12 – 8 = 4 percent
Rule . In case interest rate differential is higher than
premium or discount, then borrow that currency which has
lower interest rate and place that currency in money
market which has higher interest rate. Conversely , in case,
interest rate differential is smaller than premium or
discount, then borrow that currency which has higher
interest rate and place that currency in money market
which has lower interest rate.

9. Arbitrage Process
Step 2 Contradicting the above rule, we
borrow rupees 10000 at 12% p.a. for 6
months.
Step 3. Convert Rs into dollar, using spot rate
We will have (10000/63) = 158.73 dollars
Step 4: Invest 158.73 dollars at the rate of 8%
p.a.
After six months , we will have
158.73 ( 1 + 0.08 x 6/12) = 165.07dollars

10. Arbitrage Process
Step 5: Convert dollars back into rupee using
forward rate
We will have
165.07 x 63.90 = Rs 10548.57
Step 6 : Refund loan of Rs 10000 with
interest on it. Refunded amount will be
Rs 10000 ( 1+0.12x6/12) = Rs 10600
Net loss in the process 10548.57– Rs 10600
= Rs 51.42

11. Arbitrage Process
Now, let us work as per rule
Example :
Given Spot exchange rate : Rs 63/ $
6-month forward rate Rs 63.90/$
6 month interest rate
Re: 12% p.a.
Dollar: 8% p.a.

12. Arbitrage Process
Step1 : Calculate forward discount/ premium
Premium = (63.9 – 63)/ 63 x (12/6) x 100 =
2.85percent (dollar is at premium)
Interest rate differential = 12 – 8 = 4 percent
Rule . In case interest rate differential is higher than
premium or discount, then borrow that currency which has
lower interest rate and place that currency in money
market which has higher interest rate. Conversely , in case,
interest rate differential is smaller than premium or
discount, then borrow that currency which has higher
interest rate and place that currency in money market
which has lower interest rate.

13. Arbitrage Process
Step 2 Following the above rule, we borrow
dollars 10000 at 8% p.a. for 6 months.
Step 3. Convert dollars into rupees, using
spot rate
We will have (10000 x63) = Rs 630000
Step 4: Invest Rs 630000at the rate of 12%
p.a.
After six months , we will have
63000 ( 1 + 0.12 x 6/12) = Rs 667800

14. Arbitrage Process
Step 5: Convert rupees back into dollar using
forward rate
We will have
667800/63.90 = $ 10450.70423
Step 6 : Refund loan of 10000 dollars with
interest on it. Refunded amount will be
$ 10000 ( 1+0.08x6/12) = $ 10400
Net Gain in the process 10450.70– $ 10400 =
$ 50.70

15. • Consider the data given below
• Given
• Home Country : India
• Foreign Country : U.S.
• Spot Rate (Rs/$) = 62
• 6 mths Forward rate = 63
• Interest rate in India = 12% p.a.
• Interest rate in U.S. = 10% p.a.
• Find the arbitrage gain .

16. • Step 1: Calculate forward premium/discount using the formula
• (F-S)/S X 12/N x 100
• Forward premium/discount = [(63 – 62)/62 ] x (12/6) x 100 =
3.225806
• Dollar is at premium
• Step 2: Given interest rate differential ( RIndia – R u.s.) = 2%
• Step3: Since interest rate differential is smaller than forward
premium, borrow from the country where interest is higher and
invest in the country where interest rate is lower.

17. • Step 4: Borrow Rs 10000 at the rate of 12% p.a.
• Rupees to be refunded after six months = 10000 + Interest for six months
@ 12% (600) = $ 10,600
• Step 5 Convert rupees into dollars using spot rate
• 10000 / 62 = 161.29
• Step 6 Invest dollars at the rate of 10% p.a. for six months
• 161.29 ( 1.05) = 169.35
• Step7: Convert $ 169.35 into rupees using forward rate
• 169.35 x 63 = 10669.35484
• Step 8: Gain = Rs (10669.35 – 10600) = Rs 69.35

18. Interest rate Arbitrage
• Consider the data given below
• Given
• Spot Rate (Rs/$) = 44.0030 =$1
• 6 mths Forward rate = 45.0010=$1
• Annualised Interest rate on 6 month Rupee=
12%
• Annualised Interest rate on 6 month dollar =
8% p.a.
• Is there an arbitrage opportunity ?