# 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

## Related Questions

### Do corporate events happen intraday?

1  Asked on January 6, 2022

### Physical commodity trading quantitative risk return model

5  Asked on January 4, 2022

### Calculating M in Kelly portfolio optimization

1  Asked on January 4, 2022 by odufrkeqea

1  Asked on January 2, 2022

### What can I do with AIG+

2  Asked on January 2, 2022

### How can we estimate new stock price after a large purchase?

4  Asked on January 2, 2022

### Testing the significance of active trading strategies other than stocks

1  Asked on December 31, 2021

### Simulation scheme for SABR beside the standard Euler discretization

1  Asked on December 31, 2021

### Leverage and Tracking difference

1  Asked on December 28, 2021

### Power Options & Forwards on Stock Squared

1  Asked on December 28, 2021

### Can “Turbo warrants” be priced using the Black & Scholes model?

1  Asked on December 28, 2021

### Definition of sharpe ratio maximising and variance minimising portfolios

1  Asked on December 26, 2021 by weaklearner

### How to make futuresHelpers in Quantlib work with monday settlement day not IMM?

2  Asked on December 26, 2021 by richard-lin

### Three questions regarding local volatility implementation (based on the Andreasen, Huge article “Volatility interpolation”)

1  Asked on December 24, 2021 by jesper-tidblom

### Relationship between Data Size and Arima Prediction Interval Width?

1  Asked on December 21, 2021 by ericcheng

### I just got Matlab, what are some options that I should model in a jump diffusion

2  Asked on December 21, 2021

### Overnight Index Swaps (OIS) vs. Fed Funds Futures

2  Asked on December 19, 2021 by mild_thornberry

### Why is the Schöbel-Zhu model affine?

0  Asked on December 19, 2021 by frimousse

### Cross Currency Swap – is par basis supposed to change while OIS discounting rate is changing?

2  Asked on December 17, 2021 by pqsn

Get help from others!