## Statistical Arbitrage

Statistical Arbitrage or StatArb is an arbitrage strategy in which an investor benefit when statistical mispricing occurs between a set of securities, futures or derivatives on two different exchanges at different prices.

The first step is to identify the two securities, derivatives or futures that are not following a constant pattern with the assumption that prices of instruments will always move in a definite pattern in the near future.

The next step is to long the undervalued security and short the overvalued one. Suppose there are two stocks A and B- say A underperforming B – arbitrageurs will buy or long A and sell or short B.

The arbitrage strategy expects that eventually the two stocks will return to the constant pattern. The understanding of advance software programming and stock market is important to capitalize on gains and to generates potential pairs stocks.

The arbitrageurs should compare price, size, price-earnings ratio (P/E ratio), price-book ratio (P/B ratio), total sales, debt levels, and dividends for a set of stocks.

The arbitrageurs should consider stocks in each pair from same sector and invest an equal amount of money in each stock. If you create a portfolio with 50-60 pairs, than 20% of the pairs should represent same sector. Suppose you have a portfolio with 50-60 pairs, at least 10-12 pairs should represent same sector and no more than 20% of money should be allocated to each sector. The diversification across pairs can help reduce the risk for your overall portfolio.

Types of Statistical Arbitrage

1. Volatility ArbitrageVolatility Arbitrage (or vol arb) is a type of statistical arbitrage that is implemented through a delta neutral  portfolio of an option and its underlier. The aim is take advantage of differences between the option’s implied volatility, and a forecast of the underlier’s future realized volatility.

According to Wikipedia: “The traders attempt to buy volatility when it is low and sell volatility when it is high.  If a trader buys options as part of a delta-neutral portfolio, he is said to be long volatility. If he sells options, he is said to be short volatility.  As the trading is done delta-neutral portfolio, buying an option suggest that the underlier’s future realized volatility will be high, while selling an option suggest that future realized volatility will be low.

Assume a call option is trading at \$1.90 with the underlier’s price at \$45.50 and is yielding an implied volatility of 17.5%. A short time later, the same option might trade at \$2.50 with the underlier’s price at \$46.36 and be yielding an implied volatility of 16.5%. Even though the option’s price is higher at the second measurement, the option is still considered cheaper because the implied volatility is lower. This is because the trader can sell stock needed to hedge the long call at a higher price.”

2. Liquidation Arbitrage: Liquidation arbitrage is a strategy to exploit the difference between a company’s current value and its estimated liquidation value.

3. Risk Arbitrage or Merger ArbitrageAn arbitrage strategy in which  arbitrageur exploit the discrepancy between the market prices of the stocks of two firms being merged. It usually involves buying the stock  of the acquiree firm and simultaneously selling the stock of the acquirer firm. When the merger occurs, the stock of the acquirer firm decreases slightly, and the stock of the acquiree firm increases significantly.

Suppose company A is trading at \$40 a share. Then company X announces that they plan to buy it, in which case holders of stock get \$80. Then the stock jumps to \$70. It does not go to \$80 since there is some chance the deal will not go through. Here the odds are 25% that it does not (assuming the stock is worth \$40 in that case). The convergence trade is that the deal will go through and the stock really is worth \$80. Here the person playing gains \$10 if he is right, but loses \$30 if he is wrong.

There are two types of merger, a cash merger and a stock merger.

1. Cash mergerIn a cash merger, an acquirer proposes to purchase the shares of the target for a certain price in cash. Until the acquisition is completed, the stock of the target typically trades below the purchase price. An arbitrageur buys the stock of the target and makes a gain if the acquirer ultimately buys the stock.

2. Stock Merger: In a stock merger, the acquirer proposes to buy the target by exchanging its own stock for the stock of the target. An arbitrageur may then short sell the acquirer and buy the stock of the target. This process is called “setting a spread.” After the merger is completed, the target’s stock will be converted into stock of the acquirer based on the exchange ratio determined by the merger agreement. The arbitrageur delivers the converted stock into his short position to complete the arbitrage.

## Arbitopedia

[library term=”Arbitrage”]

## What is Arbitrage

Arbitrage is a trade of taking profit of a price difference between two or more markets. The definition can be simplified as to buy an asset at a low price then immediately selling it on a different market for a higher price.

1. Buy in one country and sell in other: The arbitrageurs constantly visit different places where discounted goods are likely to found.It is important to identify the goods that can be sold at maximum profit elsewhere. This type of arbitrage relies on the buying and selling at the same time. The arbitrageurs need to act immediately whenever an imbalance happens in the market. Suppose the price of a laptop in San Francisco for \$300. The same laptop in New York is \$400. Anyone who lives in San Francisco could buy for \$300 and sell in New York for \$400 with a profit of \$100. You can also sell the laptop at ebay or to someone you know in New York. Considering the transaction charges, you can still manage to get a good profit. As the supply of laptops in New York increases, the price of the laptop will decrease, and as the supply of San Francisco decreases, the price of the laptop will increase. After some time, the price of the item will almost be same. The arbitrage opportunity ends here. The arbitrage is very common in Europe as free trade exists between all countries of European Union.

## Interest Rate Arbitrage

Interest Rate Arbitrage Opportunity

Interest rate arbitrage opportunity is a strategy of buying a currency from one bank at its low rate and simultaneously selling to another bank at its high rate.  If forward contract is included in the financial instrument then it is called covered interest arbitrage, otherwise uncovered interest arbitrage. Developed countries have low interest rate, but developing countries such as India and Brazil provide you high-interest rate. You can take the benefit of the interest rate difference between the US (2.5%) and developing markets like India (7%) and Brazil (10%) while keeping in mind that Interest Rate Arbitrage involves a number of risks such as transaction costs, tax policy, supply or demand inelasticity and foreign exchange controls.

Check for arbitrage opportunity

Forward Rate/Spot Rate = (1 + Interest Rate of Base country)/ (1 + Interest Rate of Foreign country)

1. Rb = Interest rate in Base Country

2. Rf = Interest rate in Foreign Country

3. F= Forward Exchange Rate

4. S= Spot Exchange Rate

LHS = F / S
RHS = (1+Rb)/(1+Rf)

Case 0: LHS = RHS. There is no arbitrage opportunity.

Case 1: LHS > RHS.

There is inconsistency between interest rates and forward rates, and thus arbitrage opportunity. In this case, borrow base currency, convert at spot, invest in foreign and convert back to base at forward.

Case 2: LHS < RHS.

There is mismatch between interest rates and forward rates, and thus arbitrage opportunity. In this case, borrow foreign, convert at spot, invest in base and convert back to foreign at forward.

Rf = 0.06

Rb = 0.035

F = \$1.325/€

S = \$1.345/€

F/S =  \$1.325/€  / \$1.345/€ = 0.98513
(1+Rb) / (1+Rf) = 1.035 / 1.06= 0.98

There is inconsistency between interest rates and forward rates, and thus arbitrage opportunity.

## Sports Arbs

Sports Arbitrage or Sporting Arbitrage
Sport arbitrage or Sporting Arbitrage  is a way of trading which uses difference in odds in several bookmakers, and guarantee you profit with 100% RISK FREE.
Why Sports Arbitrage Opportunity occur?

Sports Arbitrage Opportunities means taking advantage of discrepancies in odds between online bookmakers. The discrepancy happens due to large number of bookmakers and excess number of outcomes for different events. There are more than 250 bookmakers in the internet. Leading bookmakers offer  odds, while other bookmakers, who don’t have a thorough knowledge of every sport, will follow the odds of leading bookmakers. It took time to match their odds with the leading bookmakers, and the mismatch between the odds of the bookmakers creates the arbitrage opportunity.

Lets take a look at this following tennis game:

To calculate sporting arbitrage opportunity you want to understand that the odd 1.36 means that placing a money for \$1 gives you \$1.36 in case of a Simon win.  Now, lets calculate the cost of each odd.

Simon= 1/1.36=.735

Ebden=1/4.33=.231

Total Cost= \$.966

This calculation tells us that we will need \$0.966 to be sure to get \$1. If the result of the calculation is below 1 (0.966 < 1), then you have an arbitrage opportunity.

## Sports Arbitrage

Sports Arbitrage, Sports arbitraging, or Sporting Arbitrage is a way of trading which uses difference in odds in several bookmakers, and guarantee you profit with 100% RISK FREE. Today there are many bookmakers online, and each one posts different odds to the same game.

Sport arbitrage happens when different bookies publish different odds of some sporting event. We can pick the best odd we find on each outcome and place the money in a different bookie, so we back all the event’s outcomes and guarantee a profit no matter what the outcome is. Sports Arbitrage helps you win for sure without risking your money and regardless of the outcome of the event.

Sports Arbitrage or Sporting Arbitrage Example

Lets take a look at this following tennis game:

3.494% profits means that if you invest 1000\$ you will get back 1034.94\$.

34.94\$ profit risk free!!

Lets see how we do this:

To calculate sporting arbitrage you want to understand that the odd 1.36 means that placing a money for \$1 gives you \$1.36 in case of a Simon win.  Now, lets calculate the cost of each odd.

Simon= 1/1.36=.735

Ebden=1/4.33=.231

Total Cost= \$.966

Total Profit= \$1 – \$.966=\$.034

This calculation tells us that we will need \$0.966 to be sure to get \$1. If the result of the calculation is below 1 (0.966 < 1), then you have an arbitrage opportunity. if you do the math without rounding, the profit is 0.03494 or 3.494 percent.

We can use the Arbitrage Calculator and find the amount to invest on each outcome. If we invest 760.98\$ on Simon we will get 1034.94\$ back, and if we invest 239.02\$ on Ebden we will also get 1034.94\$ back.

Important points to remember for Sports Arbitrage

1.Odds: Odds are defined as the chance or probability of a certain outcome in an event. The odds allow you to calculate how much money you will win if you put your money in an event.  The three main types of odds are Decimal, Fractional and American.

Decimal odds are the most popular odds currently in use. They are offered mainly in Europe and also known as European odds.
Formula for calculating decimal odds = (odds * stake) – stake.
A 9.0 odd can be calculated as (9.0 * \$10 stake) – £10 stake  = \$80.
It means that every one dollar you stake you will receive 9 dollars back.

Fractional odds explained that for every 1\$ you win then 9\$ you will lose. A 9/1 fractional odd can be calculated as  1 / (9 + 1) = 0.10.
It means you have a 10% chance of winning and an 90% chance of losing.

American odds are indicated with a + sign and a -sign. The positive sign (+) show the amount you would win for a 100 stake. The negative sign (-) show how much you need to stake to win 100.

2. Bookmakers: A bookmaker, mediator or a person that put money on sporting and other events at agreed odds. Bookies offer best odds opportunities in a wide range of sports, including horse racing, cricket, auto racing, tennis, football, basketball, and many more.

3. Type of Events: There are several types of straight sport events you will come across when placing money online or offline.

Football:

1. Full Time Result: To predict whether the result will be win, lose or draw. It is also called as 1 X 2. The 1 marks the home win, the X marks the draw and the 2 marks the away win.

2. Asian Handicap(AH): Asian Handicap gives a possibility for one of only two winning outcomes. Asian Handicap gives a weaker team a handicap start and removes the possibility of the draw. There are two types of handicap named single handicap and double handicap.

3. Total Goals: To predict whether the total number of goals are more or less than the number of goals quoted. Bookmakers usually propose Over/Under at 2.5 goals. A Under event is won if 2 goals maximum are scored and lost if 3 or more are scored during the match.

Read Full Time Result, Accumulator, Asian Handicap, Score, Half Time/Full Time.

Other Sports:

1. Horse Racing

2. Cricket

3. Tennis

5. Football

## Forex Arbitrage

Forex arbitrage is a forex trading strategy that is used by forex traders to exploit the price differences between two brokers or market in order to earn great profit with minimal risk.

Suppose in one market the EUR/USD is quoted at 1.3002/1.3004, and at the same time in another market the following quotes for the same currency pair: 1.3006/1.3008. If you buy at one market, and simultaneously sell at another market, you will profit 2 pips just from the difference in the quotes.

There are two types of forex arbitrage, Multiple Broker Forex arbitrage and Market Forex arbitrage.

1. Multiple Broker Forex Arbitrage: When two or more different brokerages are trading the currency during different prices, leading to an arbitrage opportunity to purchase from the only one with the lower price and sell to the one together with the higher price.

To calculate the odds related to the arbitrage, you need good Forex Arbitrage calculator. It shows you opportunities of low-risk or risk-free trades on Forex.

2. Multiple Forex Arbitrage: Multiple Forex Arbitrage or Triangular arbitrage is the process of exchanging the initial currency for a second currency, then converting second currency for a third currency, and finally third currency exchanging back to the original currency. The triangular arbitrage only last for short span of time. The understanding of advance software programming and forex market is important to capitalize on gains in one currency versus another currency. Arbitrageurs doesn’t actually buy or sell any physical currency, but rather buys or sells a cross rate from one currency to another.

Triangular Arbitrage Opportunity

Suppose you have \$1000 and you are provided with the following exchange rates:

1.EUR/USD = 1.3765

2. EUR/GBP = .8254

3. USD/GBP = .6011

Calculating EUR/GBP= EUR/USD * USD/GBP= .8274, while the actual rate of EUR/GBP= .8254. We can see the exchange rate mismatch and an opportunity for a triangular arbitrage. We need to capitalize the opportunity asap before the discrepancy is corrected.

Triangular Arbitrage Example

As an example, suppose you have following currency U.S. dollar (USD), British pound (GBP), and Euro (EUR). The currency pairs are EUR/USD, EUR/GBP and USD/GBP.

1. EUR/USD = 1.3765

2. EUR/GBP = .8254

3. USD/GBP = .6011

The currency pairs are:

1. EUR/USD is 1.3765, which means that you will have to spend about 1.3765 in Euro to buy 1 USD.

2. USD/GBP = .6011, which means that for 1 USD, you can buy about .6011 in GBP.

3. EUR/GBP = .8254, which means that you can buy 1 Great Britain Pound for about .8254 Euro.

EUR/GBP= EUR/USD * USD/GBP= .8274, while the actual rate of EUR/GBP= .8254.

Calculate the Arbitrage:

The currency is traded in units is called lots. Standard lots are blocks of 100,000, while mini-lots are blocks of 10,000. Suppose we have 100,000 USD.

Buy Euros: 100,000 x 1.3765 = 137,650 euros
Convert the Euros in Pounds (GBP): 137,650/.8254 = 166,768 pounds (GBP)
Sell pounds (GBP) for dollars (USD): 166,768 x .6011 = 100,244 USD

Profit: Final Trading Value – Investment Value

= 100,244 – 100,000 = 244 USD

## Dividend Arbitrage

Dividend Arbitrage is buying a stock before the ex-dividend date and selling an equivalent amount of the underlying’s stock futures or buy a put after the ex-dividend date.The strategy is used by arbitrageurs to purchase put options and proportionate number of stock before the ex-dividend date. The next step is to wait till the dividends are paid, and then exercise the put after collecting the dividend. The profit is the difference between dividends received and total value of put options bought.

The stock that pays the dividend would rise before the dividend is paid, and then declines overnight as the stock goes ex-dividend date. The arbitrageurs will not benefit by just buying the stock for a dividend because you lose in stock price what you gain in dividend payment. Be sure to buy the puts with extrinsic value lower than the dividends receivable.

Dividend Arbitrage Example

Suppose a company ABC is trading at \$30 and announced a dividend to investors with a value of \$1 per share in one week’s time. A put contract of the company is trading at \$2.25 with one month expiry at a strike price of \$32.

The trader purchases 100 shares at the price of \$3000 and a contract for \$225. The net investment is \$3225. In a week, the dividend of \$100 is paid. Trader will exercise the put option at \$3200. The total earning will be \$3300, for a profit of \$75.

1. Stock Price: \$30
2. Dividend: \$1
2. Strike Price: \$32
3. Put Contract Price: \$2.25
4. Dividend Expiry Date: 7 days

Total Investment: \$30 * 100 shares + \$225 (a put option contract)
= \$3225
Total Earning= \$100 (total dividend) + \$3200 (selling put option)
= \$3300

Profit= Earning -Investment= \$75

Important points to remember for Dividend Arbitrage:

1. Strike or Exercise Price: The strike price of an option will give the buyer the right to buy or to sell a specific amount of stock for a predetermined price.

2. Call Option: A Call Option is security that gives the owner the right to buy a stock, bond, commodity, index or other instrument at a specified price by a specified time period.

3. Put Option: An Put Option is security that gives the owner the right to sell a specified amount of an underlying security at a specified price by a specified time period.

4. Ex-dividend Date: The ex-dividend date is the date up to which you need to hold the stock in order to be entitled to receive the dividend. Ex-dividend is the time period between the announcement and payment of a dividend.

4. Option Contract: The contract gives to the option holder the right to buy or sell a particular asset at a specified price by a specified time period. Options contracts are used in securities, commodities, and future market. One option contract represents one hundred shares in the underlying stock.

5. Intrinsic Value: Intrinsic value is define as exercising the option at its strike price and then liquidating the stock position at the current market price of the stock.
Intrinsic Value = Market Price – Strike Price

6. Extrinsic Value: Extrinsic value is the value of the option before it expires. Extrinsic value depends on the strike price, time, volatility, and demand.
Extrinsic Value = Option Value – Intrinsic Value

7. Expiry: The last date on which an option contract can be exercised.

8. Assignment: A notice by an option writer to sell the security in the case of a call option, or to buy the security in the case of a put option at a specified price by a specified time period.

9. Dividend: A dividend is the share of the profit that a company decides to distribute to its shareholders in proportion to their holdings. The dividend can be in form of cash, stock, property, interim and others.

10. Option Premium: The premium is defined as the price that we pay for the purchase of the option contract or the amount of money which we receive when we sell the option contract.
Option Premium= intrinsic value + extrinsic value

## Covered Interest Arbitrage

Covered Interest Arbitrage

Covered Interest Strategy is an arbitrage strategy in which an investor purchases a base currency denominated investment at its spot rate and hedges the resulting foreign exchange risk by performing a forward contract sale in the financial instrument sales proceeds back into the investor’s base currency. The trade make use of a inconsistencies between interest rates and forward rates to make a riskless profit.

Covered Interest Arbitrage Opportunity

The arbitrage is only possible in two cases:

1. If the interest rate differential between two countries is less than the difference between the spot and forward exchange rate.

2. If the interest differential is greater than the difference between the spot and forward exchange rate.

1. Rb = Interest rate in Base Country

2. Rf = Interest rate in Foreign Country

3. F= Forward Exchange Rate

4. S= Spot Exchange Rate

LHS = F / S
RHS = (1+Rb)/(1+Rf)

Case 0: LHS = RHS. There is no arbitrage opportunity.

Case 1: LHS > RHS.

There is inconsistency between interest rates and forward rates, and thus arbitrage opportunity. In this case, borrow base currency, convert at spot, invest in foreign and convert back to base at forward.

Case 2: LHS < RHS.

There is mismatch between interest rates and forward rates, and thus arbitrage opportunity. In this case, borrow foreign, convert at spot, invest in base and convert back to foreign at forward.

Covered Interest Arbitrage Example

Let us consider a investor who borrow 100,000 GBP at the spot exchange rate of \$1.345/€  would exchange at  \$134,500. The interest rate of 3.5% per annum would result in a future value of \$139207.5.

In foreign investment,  the interest rate of 6% per annum would result in a future value of \$106000. The investment of 106,000 GBP at the forward exchange rate of \$1.325/€  would exchange at  \$140450.

Repay the loan amount of \$139,207 and get \$1242.5 profit.

Check for arbitrage opportunity

Rf = 0.06
Rb = 0.035
F = \$1.325/€
S = \$1.345/€

F/S =  \$1.325/€  / \$1.345/€ = 0.98513
(1+Rb) / (1+Rf) = 1.035 / 1.06= 0.98

There is inconsistency between interest rates and forward rates, and thus arbitrage opportunity.

Uncovered Interest Arbitrage

The Uncovered Interest Strategy is an arbitrage strategy in which an investor purchases a base currency denominated investment at lower interest rate and convert to a foreign currency that offers a higher rate of interest but hedging of the resulting foreign exchange risk is not covered by performing a forward contract sale in the financial instrument.

Uncovered Interest Arbitrage Example

Let us consider a investor who borrow 100,000 GBP at the spot exchange rate of \$1.345/€  would exchange at  \$134,500. The interest rate of 3.5% per annum would result in a future value of \$139207.5.

Let us consider two cases

1. In foreign investment,  the interest rate of 6% per annum would result in a future value of \$106000. The investment of 106,000 GBP at the exchange rate of \$1.325/€  would exchange at  \$140450. Repay the loan amount of \$139,207 and get \$1242.5 profit.

2. Now the exchange rate of \$1.305/€  would exchange at  \$138,330. Repay the loan amount of \$139,207  with a loss of \$877.

The above example showed that there is no guaranteed profit in uncovered interest arbitrage.

Important points to remember

1. Spot Foreign Exchange RateThe spot rate is the current price of the foreign exchange contract at which a buyer and a seller agree on the specified time and place.

2. Forward Exchange ContractA  forward contract refers to buy or sell currency contract at a future date.

3. Base Currency or Domestic CurrencyThe currency of the domestic country in which a trader or investor is buying or sellingThe base currency, or domestic currency, is the first in a currency pair, the second currency is the quoted currency. A currency pair is a quotation featuring two different currencies. For example, in a currency exchange of USD/JPY, the base currency is the U.S. dollar and Japanese Yen is the quoted currency.

4. Carry Trade: A carry trade is a strategy in which an investor borrows money at a low interest rate in order to invest in an security that provides a higher interest.

5. Hedging: Hedging is a strategy to reduce the risk of price fluctuations in an asset that may be incurred by an investment.

Adsense Arbitrage or Pay Per Click (PPC) Arbitrage is to pay low price for a keyword in an advertising program like Google AdWords, Yahoo Search Marketing, or Bing Ads and direct visitors to a page where you can write articles that has higher payout (e.g., insurance, car, betting, health, medicine, loans, etc.).

For example, Suppose you spend \$1 for a keyword advertising your website. The keyword direct anyone clicking on them to a Web page that is optimized for a more expensive keyword that is five dollars per click. You get a 70% of the adwords price, \$1.4 for every click. The profit will be \$.40 per click.

Suppose you spend \$100 in one month, and earn \$140 in ad clicks, you make \$40 monthly, presuming you get 100% clicks. You can get profit till you achieve 80% CTR; otherwise you are going to lose money.

 Total Users Cost per click Total Visitors Ads per Click Income Profit 100 \$1 100 \$1.4 \$140 \$40 100 \$1 90 \$1.4 \$126 \$26 100 \$1 80 \$1.4 \$112 \$12 100 \$1 70 \$1.4 \$98 -\$2

Important points to remember for Adsense Arbitrage/ PPC Arbitrage:

Content: The content published on the site should be useful, unique, and original without excessive advertising, and should have higher payout. Google use to prohibit those arbitrage sites who have scrapped content from other sites, gibberish content that makes no sense or seems auto-generated, duplicate content, or contents unrelated to the topic or business model. The CTR on content websites is generally 30%. Suppose you are buying traffic for 5 cents per click, and you get 100 visitors. The amount spent is \$5. The 30% CTR means 30 clicks. The EPC (Earning per Click) is \$.80. With 30 clicks, the income is around \$24. The good quality content would increase the relevancy of ads and hence help the website to get high paying ads.