Risk Management
Capital Asset Pricing Model (CAPM)
Before starting with CAPM, it is vital to understand the Two Fund Separation Theorem.
Let’s take a look at the above representation and take two scenarios into consideration.
We have a riskfree asset, and the three risky securities. The red line is the efficient frontier with the riskfree asset, the green line is the efficient frontier with only the risky security. Remember that this portfolio denoted tangency, is the only portfolio that belongs simultaneously to the two efficient frontiers. We know that this portfolio, because it also belongs to the green frontier, is only composed of risky assets.
So how are investors going to choose their portfolio if they have access to
the riskfree security?
They're going to choose the portfolio along the green line. Not everyone will choose the same portfolio, because not everyone has the same target of the same tolerance to risk. An individual who is very risk averse will like to have a low level of risk in his portfolio.
So, he will choose to reach maybe a level of standard deviation of 5% and his portfolio will be located on the red line because he will optimally diversify. But his portfolio will be located close to the level of RF.
Another investor who is more tolerant to risk and is seeking a better return might choose a portfolio located to the right of the tangency portfolio, above the tangency portfolio in the red line. What is very important to understand about the composition of these two different portfolios of the risk averse and the very risk Tolerance is that they are actually composed of two funds. We could view each of these portfolios as a combination between only two portfolios. So, the actual choice of portfolio allocation, comes down in this framework to choosing the relative weight of these two portfolios. The risk averse investor who is looking for a low level of risk will have a large proportion in the riskfree asset and a small proportion in the tangency portfolio. The more risk
tolerant investor, will have a large proportion in the tangency portfolio and a small proportion in the riskfree rate.
Capital Market Line
The capital market is a reqpresentaion of all portfolios which combine risk and return.
The tangency point in the above graph is actually the market portfolio as it represents an average of all portfolios exisiting on the line.
Portfolios appearing on the CML optimize the riskreturn tradeoff and maximize performance. CML brings in the addition of riskfree securities.
CML Equation:
Rp = Rf + (RM – Rf) σp
σM
CAPM Equation:
E[Ri] = Rf + β(E[RM] – Rf)

This equation shows a minimum return level represented by Rf which is the riskfree return

Instead of having the level of risk of the asset, we have this measure of nondiversifiable risk, which is the beta. This quantity measures the amount of risk that cannot get away from by just combining the asset with other asset in the economy. Some of the risk of each asset can be diversified away by combination with other financial security. That part is diversifiable.

Beta is measured as covariance between portfolio and market return divided by variance in the market
Security Market Line (SML)
SML is the graphical representation of CAPM showing different levels of systemic risk as plotted against different levels of risk.
Equation:
Rp = Rf + β(RM – Rf)
The security market line is commonly used by money managers and investors to evaluate an investment product that they're thinking of including in a portfolio. The SML is useful in determining whether the security offers a favorable expected return compared to its level of risk.
When a security is plotted on the SML chart, if it appears above the SML, it is considered undervalued because the position on the chart indicates that the security offers a greater return against its inherent risk.
Conversely, if the security plots below the SML, it is considered overvalued in price because the expected return does not overcome the inherent risk.
The SML is frequently used in comparing two similar securities that offer approximately the same return, in order to determine which of them involves the least amount of inherent market risk
relative to the expected return. The SML can also be used to compare securities of equal risk to see which one offers the highest expected return against that level of risk.