CAPM - Equilibrium Theory

[dennis_cmpe]

In the study notes for CAPM Equilibrium Theory:

1) All assets must be held in portfolios, including the risky asset portfolio.

Sounds simple, but I'm not getting the importance of it. What does this mean? Why is this important?

 

[David Harper CFA FRM]

Dennis,

The theoretical significance is that is paves the way for the capital market line (CML). It is an implication (not a premise of) the assumptions underyling the CAPM (assigned Chapter 4, Noel Amenc). If you consider the CAPM assumptions--they are really unrealistic so it is just setting up they theory--a key idea is that all investors have the exact same information about the same set of assets and they also use the same risk/return perspective. In short, the investors are clones of each other therefore they must reach the same conclusion. This homogeneity ensures inclusion of all risky assets: if a stock is avoided, then all will avoid it, and it's price goes to zero. But it is very attractive at zero, so in unison, the investor will like it even at some low price. I can't say i personally find this implication of equilibrium particularly important, but it's on the way to the more important CAPM idea that a security's return/risk owe not to its individual characteristics (e.g., standard deviation) but rather its risk contribution (i.e., beta) to the market portfolio.

David

 

[saurabhpal49]

Hi david,
I have some doubts regarding CAPM
>In capm there is homogenous expection, so why would some one be willing to sell market portfolio as all
investors want market portfolio?

>Could you please explain the below paragraph:
"The expected payoff of any asset remains constant under CAPM assumptions, such that when its price falls, its expected return increases. So, the expected return is at a point where supply is equal to demand in equilibrium"

>E(Rm)-Rf= risk aversion *6^2m

Why does increase in risk aversion increase the risk premium,
It should decreases as investor is unwilling to take more risk

Thanks

 

[David Harper CFA FRM]

Hi @saurabhpal49 There is a lot of theory underlying CAPM (although I've trained it for years, I can't pretend to be a deep expert, I am more like a shallow expert; the Elton book is basically about CAPM theory).

• Homogenous expectations refers to the assumption that all market participants have the same view with respect to the limited inputs that matter in the restricted CAPM universe, which are: returns (or, equivalently prices), variances, and correlations. This is the meaning of "mean-variance:" they agree on means, variances and (related) the correlation (or, related, covariance) matrix. In my view, homogenous expectations leads all investors to the same optimal market portfolio (the portfolio of risky assets with the highest sharpe ratio). Ff you are interested, it so happens that literally yesterday I recorded/published a video to our youtube channel that is called "Capital market line (CML) versus security market line (SML), FRM T1-8" which includes a visualization of achieving the Market Portfolio (aka, mean-variance efficient portfolio, it is called by Ang) http://trtl.bz/2yPLQsa. My view is that, under the theory, homogeneous expectations leads all (equally-informed) investors to hold the same most-efficient Market Portfolio which itself is only the risky assets (the purple triangle in my video, snapshot below) such that, to your point, investors do not want to sell this portfolio. Rather, they are deciding only how to allocate between the Market Portfolio and the risk free asset (ie, where on the blue line will they locate?).
• Your second point is why investors would buy/sell individual securities. He is referring to (eg) the asset's future cash flow. If (eg) we all homogeneously agree that asset AA with a beta of 1.5 will pay future cash of $10.00 but its current price is $9.50, then it is currently priced too high b/c the expected return is only 10/9.50 - 1 = 5.3%. If the Rf rate = 3.0%, it will be sold until its price is down to $8.93 because that is a price that is in equilibrium with its expected return of 12.0%. The idea is the current price adjusts according to an expected return, per PV = future cash/(1+ discount rate).

Equilibrium: The equilibrium concept is extremely important. Equilibrium occurs when investor demand for assets is exactly equal to supply. The market is the factor in equilibrium because in CAPM land, everyone holds the MVE portfolio (except for those who are infinitely risk averse). If everyone’s optimal risky portfolio (which is the MVE) assigns zero weight to a certain asset, say AA stock, then this cannot be an equilibrium. Someone must hold AA so that supply equals demand. If no one wants to hold AA, then AA must be overpriced and the expected return of AA is too low. The price of AA falls. The expected payoff of AA stays constant under CAPM assumptions, so that as the price of AA falls, the expected return of AA increases. AA’s price falls until investors want to hold exactly the number of AA shares outstanding. Then, the expected return is such that supply is equal to demand in equilibrium. Since all investors hold the MVE portfolio, the MVE portfolio becomes the market portfolio, and the market consists of each asset in terms of market capitalization weights.

Equilibrium ensures that the factor—the market portfolio—will have a risk premium and that this risk premium will not disappear. The market factor is systematic and affects all assets. The market risk premium is a function of the underlying investors’ risk aversions and utilities. That is, the risk premium of the market factor reflects the full setup of all people in the economy. The factors that we introduce later—tradeable factors like value-growth investing and volatility investing or macro factors like inflation and economic growth—will also carry risk premiums based on investor characteristics, the asset universe, and the production capabilities of the economy. They will disappear only if the economy totally changes. Equilibrium factor risk premiums will not disappear because clever hedge funds go and trade them—these types of investment strategies are not factors. Investors cannot arbitrage away the market factor and all other systematic factors.

• The market risk premium is compensation for enduring the factor risk of what happens in "bad times." Imagine the bad times are a 30% drop in your equity portfolio. Maybe if you are only moderately risk averse, you require an excess market return of +4% on your equity portfolio. This long run excess return is your "payment" in exchange for your assumption of the very plausible risk of that you will lose money in the short run. As your risk aversion goes up, this means you are more and more fearful of the short-term drop, and consequently you require additional risk premium, maybe your price increases to +6% etc. I hope that's helpful!

 

[MisterDiaz]

The risk premium is the return investors should demand given that they are assuming some degree of risk. If your level of risk aversion goes up (IE you're less willing to assume risk), the amount of return you would demand for assuming said risk should increase as well.