Pur Autre Vie

I'm not wrong, I'm just an asshole

Monday, February 23, 2015

Economics: The Logic of the Financial Markets

This is part of a series of posts on economics.  Unlike my typical posts, these posts are dynamic—I'm going to come back and edit them as my thoughts develop.  I am basically "thinking out loud."  I am trying to fit things together in a modular way, so that each piece stands on its own analytically.  But no promises.

Now I want to take a closer look at the logic behind the financial markets.  Remember that we have individuals who want to maximize their utility, which they achieve by consuming goods and services.  And recall that many (maybe all) people experience diminishing marginal utility from consumption, meaning that the first dollar the person spends in any time period is more valuable than the second dollar, and so on.  This has two implications:  first, it means that people can sometimes increase their utility by shifting their consumption over time, and second, it means that people have different levels of tolerance for risk.  People with sharply diminishing marginal utility are more risk-averse than others.

Moreover, people discount future consumption using their consumption discount rate, which varies from person to person.  Finally, let's assume that people's wages are not constant over time.  People are sometimes unemployed, and almost everyone wants to retire at some point.

Putting these things together, it's easy to see that there will be demand for at least three things that can be provided by the financial markets.  First, sometimes people will benefit by borrowing money at one point in time and repaying it at a later point in time with interest.  This could be done for many reasons.  Someone who anticipates higher wealth in the future might want to "shift consumption back in time" in order to take advantage of the higher marginal utility of consumption in the present.  Someone with a high consumption discount rate might want to do the same thing, but this time in order to take advantage of the lower discount applied to present consumption than the one applied to future consumption.  Finally, someone might have an investment opportunity—a good or service in the non-financial markets that will yield a rate of return more than sufficient to repay the interest on the loan.  (An example would be borrowing to buy equipment for your business, which will hopefully generate enough income in the future to repay the loan with money to spare.  Another example—hopefully!—would be a student loan.)

The second demand that can be satisfied by the financial markets is the desire to shift money in the other direction—to save money today in order to consume it (plus interest) tomorrow.  This is just the reverse of the situation in the previous paragraph.  Of course, when you shift consumption into the future, you are always pushing against the consumption discount rate (no one discounts present consumption more than future consumption).  But if the interest rate is higher than your discount rate, then you could shift consumption to the future to take advantage of the disparity.

It could also be advantageous to shift spending power to the future if the individual has enough to consume today and wants to make sure she will have enough to consume in the future.  This is especially true if she anticipates the possibility of unemployment or retirement.  Just note that this would not be true if the individual did not experience diminishing marginal utility of consumption—in that case, the inability to consume in the future would not matter, because the individual could obtain the same (or higher) aggregate utility by consuming today.

The third and final demand that can be satisfied by the financial markets is the demand to shift risk among individuals.  A risk-averse individual can improve her utility by entering into insurance-like contracts that are "statistically unfair."  To see how this works, imagine an individual who owns an asset that will, at time t = 1, be worth either $1,000 or $0, with equal probability.  Imagine that this individual has a marginal utility of consumption of 1/2, meaning that this person's utility from consumption follows this function:

U = C1/2

For the sake of simplicity, assume that this individual does not discount future income at all (this is just so that we can leave out some math).  And finally, assume that the individual's only source of wealth at time t = 1 will be the asset.  She will sell the asset (if it is worth anything) and consume the proceeds.

What is her expected utility?  It is:

U = (0.5)($0)1/2 + (0.5)($1,000)1/2

That is, there is a 1/2 probability that she will have a utility of 0 and a 1/2 probability that she will have a utility of (1,000)1/2 or ~31.62, for an expected utility of ~15.81.

Now what if someone offers to pay her $400 at time t = 1 in exchange for the proceeds of the asset (regardless of its value)?  (We will assume this is a credible promise—she can rely on receiving $400 if she takes the deal.  We might address counterparty risk later.)  This is a statistically unfair exchange because the expected monetary value of the asset is $500.  But should she take the offer?  Well, here is her expected utility:

U = ($400)1/2 = 20

So if she keeps the asset, her expected utility is about 15.81, but if she takes the $400 instead, her expected utility is 20.  Of course in reality she should try to get a higher price, but any price above $250 will increase her utility relative to no deal at all.

All right, so, if the financial markets are working properly, what should we observe?  We should see people with higher consumption discount rates borrowing from people with lower consumption discount rates.  We should see people with high current incomes saving money in anticipation of unemployment or retirement.  We should see anyone with a real-world (non-financial) investment opportunity borrowing money to finance it, as long as the interest rate is below the rate of return on the project.  On the other hand, we should not observe anyone investing in a project if a higher rate of return is available in the financial markets (taking risk into account).  We should see risk-averse people buying insurance (whether or not it is formally labeled "insurance") from people or institutions that are less risk-averse.


Blogger Khushboo Gupta said...

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4:21 AM  

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