Arbitrage Pricing Theory
The fundamental foundation for the arbitrage pricing theory is the law of one price, which states that 2 identical items will sell for the same price, for if they do not, then a riskless profit could be made by arbitrage—buying the item in the cheaper market then selling it in the more expensive market. This principle also applies to financial instruments, such as stocks and bonds. For instance, if Microsoft stock is selling for $30 on one exchange, but $30.25 on another exchange, then an arbitrageur could simultaneously buy the stock on the cheaper exchange and sell it short on the more expensive exchange for a riskless profit. (The arbitrage is done simultaneously because the price discrepancy must be taken advantage of immediately; otherwise it will probably disappear by the time of settlement.) The arbitrageur would continue doing this until the price discrepancy disappeared, since buying on the cheaper exchange would increase the demand, and therefore the price, on that exchange, while the short selling on the more expensive exchange would increase supply, thereby reducing its price. There is another law of one price used in the arbitrage pricing theory that is slightly different from the above examples. It is predicated on the fact that 2 financial instruments or portfolios—even if they are not identical—should cost the same if their return and risk is identical. The justification for this is that the only reason that a financial instrument is purchased is to earn a return for a certain amount of risk—no other aspect of the financial instrument matters. Hence, the law of one price requires that any 2 financial instruments or portfolios that have the same return-risk profile should sell for the same price. If this is not true, then a profit could be made by selling short the security or portfolio with the lower return, and buying the higher return portfolio. The simplest form of the APT is the one macroeconomic factor model for the...
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