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 risk-free asset, and the three risky securities. The red line is the efficient frontier with the  risk-free 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 risk-free 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 risk-free 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  risk-free 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 risk-return trade-off and maximize performance. CML  brings in the addition of risk-free 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 risk-free return 

• Instead of having the level of risk of the asset, we have this measure of non-diversifiable 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.