Realistic Arbitrage Example

The basis for arbitrage situations revolves around price inequalities. The banana example considered a locational price differential. Another situation may be an undervalued or overvalued market price. When we explore valuing web sites later in the book we will use fundamental analysis to determine a theoretical value for a website. A profit strategy we will explore is that of purchasing undervalued sites, re-pricing them to the correct value, and then reselling them. You can start to see how knowledge plays such an important role in being able to take advantage of a market. If a website owner is not knowledgeable in the world of business valuation, he or she may offer their website at an undervalued price, opening the door for you or others in "the know" to profit from the situation.

If you are comfortable with your understanding of arbitrage at this point or do not feel the need to go through a detailed real world example, you can skip to the next section of this chapter - Online Advertising and Arbitrage, The "Click Thru Value Chain" and commoditizing the market.

The basic principle for the pricing of a public company's stock is a mathematical formula that, among other things, computes the present value of the future earnings stream of the company. The math and associated assumptions take into consideration various risks associated with the stream and other variables such as potential market-wide impacts.

Consider the S&P 500, which represents a basket of stocks. If an arbitrageur observes the S&P 500 priced at 441.5 in early November and at the same time sees the December S&P 500 futures contract priced at 444. The futures contract expires in 40 days so if the trader buys the futures contract today, he will effectively be purchasing shares of the S&P 40 days into the future at a locked in price of 444. If the S&P is at 445 in 40 days when the trader takes delivery, he basically made a dollar off each share because he will take delivery of shares that he paid 444 for and immediately resell in the market at 445. The situation can go the other way as well if the S&P is below 444 in 40 days, the trader will lose [444-(S&P Market Price)] at the time of delivery. The game here is knowing where the S&P will be in 40 days, which is basically impossible. However, if the trader is armed with some knowledge and notices that the price of the futures

contract is theoretically overvalued, he can lock in a profit using an arbitrage strategy. The trader notices that the theoretical value of the S&P 500 is 441.25, so the futures contract is overpriced. Here's a quick rundown of the math for those who like the quant stuff, but is not necessary to understand: [spot S&P price of 441.15e raised to ((the risk free interest rate minus the dividend yield in the S&P)*(40 days over 365 days in a year). If the risk free rate is .32 and the dividend yield is .03 then the math will give the result of 441.25.

On the day of the observation the trader will buy the S&P stocks. Now, much like I mentioned above about the banana man not just making one trip but as many as he can, the trader will buy as much as he can. Let’s say the trader buys $20 million worth of S&P stock. At the same time he will sell short the S&P futures contract. Selling short is simply a market transaction where you sell something you don’t have, being forced to buy it back at a later date. Most anyone can call their broker and sell shares of stock they don’t have. The idea is that the price of the stock will drop and you will buy it back, or "close out" your position, at a lower price. Essentially you've bought low and sold high, or rather sold high and bought low. So, the trader shorts 91 contracts (he wants to get as close to his $20 million stock purchase as possible:

444*91*500=$20,202,000) at the same time he buys $20 million of stock. When the futures contracts expire, the trader will sell the stock and close out the futures position. No matter where the S&P ends up this trader has locked in an arbitrage

profit. Consider the S&P500 being at 439 on the date of expiration. The trader will receive $19,902,527 from the sale of stock ((439/441.5)*($20million)). He originally invested $20 million, but the effective cost of that investment must consider the time value of money so the effective investment for 40 days at 3.2 percent interest is $20,004,384 (see theoretical S&P value above). The trader lost $20,004,384 - $19,902,527 = $101,857 on the sale of stock. On the futures position, he sold at 444 and bought at 439, so multiplying that out by 500*20 million shows a profit of $227,500. Combined, the arbitrage transaction allowed the trader to lock in a profit of $227,500 - $101,857 = $125,643.

The important point above is that the trader noticed a profit situation through proper analysis. He was able to perform the analysis because he had the knowledge to do so. Observe, identify, and pull the trigger.

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