Arbitrage: The Gem of Economy

 

The term “arbitrage” is popular in finance largely in the meaning of taking a risk-free benefit from two different prices of a utile object. Somehow in economics, the term is almost unheard of. Instead, people are said to go for it, when a marginal benefit (MB) outweighs the marginal cost (MC); where, the MC means “foregoing the next best of all.”

             We, the nameless, are particularly serious about the last point. For instance, the MC of “liquidity preference” is: the most desperate real want (M∙U in dimensions) of all we can get hold of in return for getting rid of the money (U∙m) in hands.

             According to the general theory, we are in the right mind, as opposed to the left, all through the “run” from “short” to “long.” Few of us would as the lost opportunity name “the composite rate of interest” as in The General Theory (J.M. Keynes); nor “the singular rate of fed funds” as in the IS-LM model “speculated” by so many celebs (e.g. Gregory Mankiw, Macroeconomics). Shh! both cases are for the “short run” aka moment (T⁰, with no regard at all to the time dimension).

 

Arbitrage as MIA. The Harvard economist names “Rational people think at the margin” as Principle 3 of Economics. To paraphrase his principle: ①We cannot have a cake and eat it too; ②The MB of having a cake comes at the MC of not eating the cake; ③In this case, we choose between the present (“eating”) and the short future (“saving”).

             All in all, the choice is always and everywhere between the first best and the second best. That’s nothing other than the marginality in action (MIA).

             Wise men in finance say “riskless” or “risk-free” but cannot and don’t mean it. The only thing all of us can say risk-free is: We couldn’t and didn’t exist (0) prenuptial, do exist on earth (1) in the short to long run, and will eventually rest in peaceful equilibrium (0). As long we are on the run, the risk is a matter of degree; the 010 is a surefire bet, but all the other digits of three or more are more or less risky. (Not go digital just to be on the safe side?)

             In sum, arbitrage in Finance is the same as MIA in Economics. From now on, we choose the term “arbitrage” at the MC of abandoning MIA.

 

Arbitrage. The noun “arbitrage” means “the margin thinking in action” of a few words. One word is preferable to a few; that’s the economy, after all.

             There are three dimensions where arbitrage is useful and used:

1)     Interspatial (L^-2, possible L^-1 or L^-3);

2)     Inter-substitutive (M^-1∙U^-1);

3)     Intertemporal (T^-1)

Hasta mañana for more on this!

The impact of arbitrage. Imagine perfect information which is by design “symmetric.”  Which would we choose between a high and a low offers in price? Which would we choose between a high or a low bids in price. What if we can buy the product at a certain price and resell it as a slightly higher price?  

             After all kinds of arbitrage, we shall have the one price of the product. That would be called “the equilibrium price” of the “Pareto optimal,” a Utilitarian state. As such, at the center of economy and economics is the gem called “arbitrage.” A caveat: The optimum is no more realistic that a metaphor is. A dream is a dream, but can nevertheless work as gravity or a locomotive.

             Ideally, all across the nation all through the year, there would be the general equilibrium in all the national markets. No wonder, we when in macroeconomics observe so many general equilibrium models (GEMs) at the core of which is arbitrage, the gem of GEMs. But for the thorn: So many locomotives (read: trends) of the national economy will run on as many railways, which are never ever in sync, harmony or stability, way far from equilibrium,

             Watch out for blocks, bumps, hills, rocks, mountains, curves … and crosses! In long run of the accounting year (1), we will not (0) hear the shout of victory until  crossing…. Seeking is free but the looked-for benefit takes the MC. And, that’s the way it is.

 

Arbitrage only in finance so far. Management of a portfolio of assets is generally conducted with financial instruments. The purpose there-behind is, of course, in conveniently abandoning, or saving in vernacular, transaction costs in trading real assets. Probably, this type of saving, or evaporating into the thick air, is popularly meant in macroeconomics: Saving equals discarding (cf. “paradox of thrift” or “secular stagnation”)!

             Portfolio management is all about arbitrage of choosing the best at the present moment at the cost of dispensing with the so-far best. We just keep trying to choose the best of expectation, which is rational but more volatile by the order of magnitude than the economy is cyclical. Human “expectation” is in singular while animal “spirits” are in droves.

             The very reason why arbitrage is so popular in finance is that “financial instruments” are as convenient for trade of assets as “money” is for trade of products. Both help save transaction costs to a substantial-yet-limited extent. Nothing comes for free; nothing is complete, either.

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