# Understanding what is 'special' about the security market line

Quantitative Finance Asked by Andy on November 28, 2020

I am trying to get my head around the CAPM model and all the intricacies of portfolio management. I have written some code to help me visualise what happens to the risk-return characteristics of my portfolio as I vary the weightings amongst three stocks (classic bullet shape).

What I don’t understand is what is special about the security market line.

$$bar{r_i}-r_{f} = beta_{i}(bar{r_{M}}-r_{f})$$

In short, I already know how to calculate $$bar{r_i}$$ (by supposing each stock as a random variable with returns following the normal distribution). Sooooo, great, the security market line gives me a new way of calculating $$bar{r_i}$$ with respect to how it covaries with the market portfolio, why is that special? or any more revealing than simply calculating $$bar{r_i}$$ as mentioned above?

I hope this makes sence.

In CAPM (security market line), the returns are endogenous. It is the result of the equilibrium of the entire market according to the mean-variance criterion, and is not determined by the so-called risk (variance, beta, or covariance). The beta value is calculated from the equilibrium return, using beta value to explain the expected return is a circular argument. In addition, calculating the beta value and then solving the expected return by CAPM is not as easy as taking the expectation of return directly.

In the framework of CAPM equilibrium, risky securities are priced as a whole, and the security returns and the market return are endogenous. Examining the return of individual security in isolation leads to the wrong causal inference that beta determines the expected return.

For the closed-form solution of CAPM formula, see CAPM: Absolute Pricing, or Relative Pricing? or Arbitrage Opportunity, Impossible Frontier, and Logical Circularity in CAPM Equilibrium

Answered by Chen Deng-Ta on November 28, 2020

CAPM is the graphical representation of the security market line. What is special about it is that it can tell you where you expect the return for an asset to be given its level of systematic risk - beta. CAPM in a way measured the price the market would expect for that level of volitility in an asset. For instance a stock is supposed to be a good investment if it has an abnormal return- that is an actual return much higher that the CAPM expected return. That way the asset is actually producing wealth above what the market says it should. CAPM is a good comparison of stock returns and their value when stocks have no dividends and hence the Gordon growth model and others are not helpful in estimating price /worth of the said asset.

Regarding portfolio weighting, to weight a portfolio requires weights and a return like you mentioned. CAPM is good as the higher the expected return of one asset, the higher the maximum portfolio return can be. It gives an estimate of what the market would say a good weighting would be for a number of stocks.

I hope this clarifies some points for you

Answered by JazKaz on November 28, 2020

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