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.