Hi afterwork,

"Equilibrium" is deep at the heart of the theory, by which I mean to suggest I am not highly qualified to summarize it safely

I will tell you how I interpret it very simply, at the risk of exaggeration. In CAPM, equilibrium implies that in the efficient market buyers and sellers will trade the asset such that its price will adjust to equal its expected (forecast) price discounted to account for its risk (beta). For example, if stock will have a (consensus) expected price of $10 at the end of the single period, then under CAPM assumptions, all investors will "conspire" to produce a price today of $10*exp[-(Rf + beta*ERP)]. In this way, the rigid (unrealistic) CAPM assumptions create an artificial environment under which conditions imply prices adjust, and the prices adjust to inform a CONSENSUS expected return. This is why, in my videos, I always say I think the assumptions of investors' HOMOGENOUS EXPECTATIONS (i.e., that all investors have the same identical view on asset means and variances) is the most critical: first, because it's unrealistic; second, because it is the key to the "equilibrium" the produces an expected return (again, a function of a market-cleared price) which is only a function of beta (systematic risk).

In CAPM, equilibrium is just an instance (example or class) of a more general equilibrium concept which, I think, can be viewed as models that have a self-contained mechanism to "clear" a price (or return); e.g., in economics, supply and demand "clears" to find an "equilibrium" price/quantity due to tensions ... there is a balance in the model.

The new Tuckman (P2 FRM on fixed income) differentiates between

*equilibrium* interest rate models versus

*arbitrage-free* rate models, where the equilibrium models have a "self-contained" method to producing the interest rate evolution which does not necessarily match the observed interest rate term structure.

The notes of course summarize Elton's

*Modern Portfolio Theory and Investment Analysis*, and the actual text devotes much space to equilibrium theory. I would naively reduce most of it to something like:

**equilibrium in CAPM and non-standard CAPM is when we can maintain, under the *unrealistic* assumptions, a model that "clears" (via risk/return tensions or imbalances) into a set of consensus and "balanced" returns** (again, prices that inform returns!) as a function of risk.

But, I sort of prefer the clarity of the following from Amenc Chapter 4, selected mine:

"[4.1.1.2] Equilibrium Theory: Up until now we have only considered the case of an isolated investor. By now assuming that all investors have the same expectations concerning assets, they all then have the same return, variance and covariance values and construct the same efficient frontier of risky assets. In the presence of a risk-free asset, the reasoning employed for one investor is applied to all investors. The latter therefore all choose to divide their investment between the risk-free asset and the same risky asset portfolio M.

Now, for the market to be at equilibrium, all the available assets must be held in portfolios. The risky asset portfolioM, in which all investors choose to have a share, must therefore contain all the assets traded on the market in proportion to their stock market capitalisation. This portfolio is therefore the market portfolio. This result comes from Fama (1970).

In the presence of a risky asset, the efficient frontier that is common to all investors is the straight line of the following equation [CML line]. This line links the risk and return of efficient portfolios linearly. It is known as the capital market line. These results, associated with the notion of equilibrium, will now allow us to establish a relationship for individual securities.

[4.1.2.4] Market efficiency and market equilibrium: An equilibrium model can only exist in the context of market efficiency. Studying market efficiency enables the way in which prices of financial assets evolve towards their equilibrium value to be analysed. Let us first of all define market efficiency and its different forms

... There are several degrees of market efficiency. Efficiency is said to be weak if the information only includes past prices; efficiency is semi-strong if the information also includes public

information; efficiency is strong if all information, public and private, is included in the present prices of assets. Markets tend to respect the weak or semi-strong form of efficiency, but the CAPM’s assumption of perfect markets refers in fact to the strong form.

The demonstration of the CAPM is based on the efficiency of the market portfolio at equilibrium. This efficiency is a consequence of the assumption that all investors make the same forecasts concerning the assets. They all construct the same efficient frontier of risky assets and choose to invest only in the efficient portfolios on this frontier. Since the market is the aggregation of the individual investors’ portfolios, i.e. a set of efficient portfolios, the market portfolio is efficient. In the absence of this assumption of homogeneous investor forecasts, we are no longer assured of the efficiency of the market portfolio, and consequently of the validity of the equilibrium model. The theory of market efficiency is therefore closely linked to that of the CAPM. It is not possible to test the validity of one without the other. This problem constitutes an important point in Roll’s criticism of the model. "

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