More on pricing

To summarize my earlier post on asset pricing, in the absence of arbitrage opportunities assets are random variables and prices are expectations. The probabilities are normalized prices, not probabilities of random events, and the expectation is not a risk expectation but a market expectation. I called an asset with vanishing market variance a benchmark, and questioned whether such an asset can actually exist.

Apparently, in the literature what I am calling market expectation is usually called "risk-neutral pricing with respect to normalized price probabilities". Note the underlying confusion of applying the concept of risk aversion to normalized prices, as opposed to the probabilities of actual events.

Now, since the price is not related to actual risk but is just an abstract mathematical expectation, benchmarks cannot be argued away on the grounds that risk-free assets are implausible. Mathematically, one would consider a finite collection of assets, estimate their "market covariance" matrix and, if the latter were singular, the associated portfolio would be a benchmark. The problem is how one can estimate the market variance from a time series of market expectations. Some sort of underlying model is required that reproduces the observed expectation dynamics, and that can then be used to reconstruct the underlying variances.

The fraud that is the central bank

Let's see if I got this right...

• Money is created by the central bank by lending it to the private banks at interest.
• The state treasury then funds government projects by borrowing money from the banks in the form of bond issues.
• The interest rate that the treasury pays for bonds is always higher than the interest rate at which the central bank lends money to the private banks.

In this way, the private banks get to milk the treasury for free through the central bank. Notice that both the treasury and the central bank are branches of government. Independent central banks are still part of the government, they are just independent from the executive. In this way, modern separation of powers is into four branches: executive, legislative, judiciary and monetary.

The inescapable conclusion is, though, that the idea of a central bank independent of the state's treasury is a fraud designed to allow private banks to rob the country of its resources at an exponential rate.

Why doesn't the government just create the money it needs to fund its own projects? It already has the authority (delegated to the central bank) to create money, and this would allow the government to fund its projects more cheaply since the current system is equivalent to the government creating money to fund its projects and then subsidizing the private banks proportionally to the money created.

Check out this newsletter on debt-free money.

A formalization of the asset pricing problem

Updated October 6

We assume that there is a given collection of assets. A linear combination of assets is a portfolio. Negative coefficients in a portfolio represent short-selling or borrowing of the corresponding asset. More general functions of assets are called derivative assets. An asset is positive if it is always possible to sell it for a positive price. The problem is to find a fair price P for all assets. The fair price must be linear (the price of a portfolio is the linear combination of the component asset prices) and positive (a positive asset must have a positive price) in order to avoid the possibility of arbitrage (getting something for nothing).

What I just described is the algebraic axiomatization of probability theory. This means that assets are random variables, and the price is an expectation. In other words, assets are characterized by the probability distributions of their values, whose expectation is their fair price. This is not to say that the expected value is calculated with respect to the probabilities of actual events in the future (or not necessarily). It could also be some sort of market expectation of the value of the asset. I used to think that the price was the risk expectation (i.e., with respect to uncertainty of future value), and that zero-price-variance assets are risk-free assets. That seems not to be the case necessarily, and I quickly got confused trying to follow its logical consequences. In particular, it seems that identifying the market expectation with the risk expectation leads to a contradiction with the Capital Asset Pricing Model.

I am thus going to adopt the interpretation that the price is some sort of market average of perceived value. Then, if an asset x existed such that P(x²)=P(x)², this would mean that there is only one possible price for the asset that anyone will pay. I'll call such an asset a benchmark. It is questionable whether such an asset exists. Back in the time of standard-backed currencies it might have made sense to say that gold was a benchmark, but in a world of freely floating fiat currencies I don't think there are any benchmarks left. Anyway, in a real market with imperfect information or bounded rationality there can't be any benchmarks either.