Last month\u2019s column introduced the concept of arbitrage in which an asset is bought and sold near-simultaneously (the duration for which the asset is held can widely range, depending on the market perspective) in two different markets with the profit derived from the price differential.\u00a0 Arbitrage functions to equalize price gradients across the market landscape, indirectly communicating information between buyers and sellers, thereby leading to a more efficient economy.\u00a0 \u00a0Of course, the parties engaged in arbitrage don\u2019t set out to perform a useful service, they want to get incredibly rich, but seeking profit for themselves produces, essentially as a by-product, a societal good.\u00a0 Basically, their savviness in producing a profit ensures that they will look for arbitrage opportunities with a diligence and innovativeness that someone simply hired for the job would never match.<\/p>\n
The place where this \u2018goodness\u2019 is most fully on display is the financial market where likely billions are made in arbitrage each day and where the erasure of gradients across the economy serve the most people.\u00a0 It is within this context, that this month\u2019s column explores the concept of how to price a security or capital instrument so as to maximize profit and minimize risk.<\/p>\n
To this end, this analysis will briefly explore two models: the Capital Asset Pricing Model<\/a> (CAPM) and the Arbitrage Pricing Theory<\/a> (APT).<\/p>\n Because a security\u2019s price is essentially negotiated between the buyer and the seller at the time of the transaction and is not set by some outside force (e.g. Fred\u2019s or Joe\u2019s market in last month\u2019s banana example), it is distinctly possible for an arbitrage opportunity to fail to net a profit.\u00a0 In other words, despite the classical analysis to the contrary, arbitrage activities have risk.\u00a0 How much should an investor be willing to pay to buy the asset and how much he can reliably sell it for become incredibly important.<\/p>\n In some sense CAPM is a special case of APT and, as a result both models share similar mechanics and strategies for minimizing risk while maximizing profit.\u00a0 Let\u2019s deal with the mechanics first.<\/p>\n In a financial arbitrage, the party engaged in the arbitrage (called an arbitrageur) first identifies a mispriced asset.\u00a0 If the asset is too expensive, he sells it and uses the proceeds to buy another assets.\u00a0 If the asset is too cheap, he sells something else and uses the proceeds to buy the cheaper security.\u00a0 In both cases, a sense of relative pricing attaches when deciding which asset goes where.\u00a0\u00a0 In an ideal situation, both assets will be mispriced but it is likely that the arbitrageur has to settle for just one.\u00a0 The purchased asset is then held for some time until it is relatively overpriced, at which point it provides the working fund for the next transaction.\u00a0 It is important to understand that the sells that the arbitrageur enacts are typically short sells.<\/p>\n The strategy clearly centers around the identification of a mispriced asset relative to the market as a whole but since the asset is held for some time, called the period, the key feature is comparing the rate of return of the asset relative to other assets.\u00a0 The measure of relative fitness is based on the response of the asset\u2019s price to a host of systemic, macroeconomic risks, such as inflation, unemployment, and so on.\u00a0 For each of these risk factors the risk-free rate of return of the asset is modified by a set of linear corrections.\u00a0 In the abstract, this modification results from the following equation (adapted from Arbitrage Pricing Theory (APT)<\/a> by Adam Hayes)<\/p>\n where:<\/p>\n As in most things, it is much easier to understand this model with a concrete example (derived from Hayes\u2019s article).\u00a0 Consider an asset that depends on the following four macroeconomic factors (i.e\u00a0 i<\/em> = 4):<\/p>\n Historic data are typically analyzed, according to the available literature, via a linear regression.\u00a0 This process not only identifies the preceding four factors as the most important it also gives values for the sensitivity factor \u00a0and the premiums for each.\u00a0 Assuming a free rate of return \u00a0= 3%, the data conveniently present themselves in the following table:<\/p>\n
\n  = Rfree<\/sub>\u00a0+ \u03b21<\/sub> RP1<\/sub> + \u03b22<\/sub> RP2<\/sub> + ...<\/div>\n\n
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