CML vs SML? Market price risk and systematic risk

[rodra333]

Hi everyone,
I have read a couple of time the topic on Portfolio Mgmt.
After reading it it seems to me than since in both “models” homogeneus expectations is assume both of them should bear the same risk. However, in the CML equation we count for total risk and in the SML only for systematic risk.
As I see it, is that also the CML equation should only count for systematic risk.
Can anyone please help me.
Thank you.

 

[CMLSML]

The risk is the same, but the units of measurement is different.

 

[rodra333]

How should I interpret that? Units of measurement?

 

[Harrogath]

rodra333 wrote:
How should I interpret that? Units of measurement?

CML and SML are practically the same.
The CML describes the whole possibilities to build a portfolio between the risk-free asset and the optimal risky portfolio. If you check the book, the slope of the CML is the standard deviation of the risky portfolio divided by the market standard deviation (of returns). Knowing this, you can see a similar expression for the BETA. Why? Remember that due the diversification process the standard deviation of the risky portfolio represents only the systematic risk of it, NOT TOTAL RISK. So, this SDp is exactly like the standard deviation of the market (SDm).
As they are equal, this ratio would be 1 right?, so our “beta” is 1 too. You must know that in CAPM model, the market portfolio has a beta of 1. This is the beautiful match.
Remember too that Total Risk = systematic risk + unsystematic risk. But only the systematic risk has payout, this means that an investor must only expect returns over systematic risk, not from the unsystematic risk because this has been totally diversified by holding the optimal risky portfolio.
Here the SML appears.
The SML only considers systematic risk in the X axis (you know why now) represented by the BETA of the security. In this case, the beta is calculated with the covariance of the security returns and the market returns devided by the market variance of returns. This will give you a beta <1 , =1 or >1 which represents the sensibility of the returns of this security compared with the market returns. If it is less than 1, the security sensibility is less than the market movements, and higher when beta >1.
Summing up, you can learn now that this both lines CML and SML represent practically the same risk but with different approaches.
Regards

 

[S2000magician]

To be clear:

• For a diversified portfolio with no unsystematic risk, the relationship of that portfolio to the CML and the SML will be essentially identical.
• For a security or portfolio with significant unsystematic risk, the relationship of that security/portfolio to the CML and the SML could be very different.

 

[Harrogath]

Exactly. The theory assume we build a well-diversified portfolio, so unsystematic risk erased. The problem is when we get a security with high unsystematic risk. In this case, only the SML or CAPM is suitable for analysis.

 

[CMLSML]

S2000magician wrote:
To be clear:

• For a security or portfolio with significant unsystematic risk, the relationship of that security/portfolio to the CML and the SML could be very different.

What???

 

[S2000magician]

CMLSML wrote:

S2000magician wrote:To be clear:

• For a security or portfolio with significant unsystematic risk, the relationship of that security/portfolio to the CML and the SML could be very different.

What???

Surely you’re aware that you can have a stock with β = 1.0 and twice the volatility of returns of the market.

 

[Harrogath]

CMLSML wrote:

S2000magician wrote:
To be clear:

• For a security or portfolio with significant unsystematic risk, the relationship of that security/portfolio to the CML and the SML could be very different.

What???

The slope of the CML is 1 which could be the beta = 1 of the SML enviroment. Thats the case when CML and SML are the same. Only for a well-diversified portfolio of course.

 

[S2000magician]

Harrogath wrote:

CMLSML wrote:

S2000magician wrote:
To be clear:

• For a security or portfolio with significant unsystematic risk, the relationship of that security/portfolio to the CML and the SML could be very different.

What???

The slope of the CML is 1 which could be the beta = 1 of the SML enviroment. Thats the case when CML and SML are the same. Only for a well-diversified portfolio of course.

The slope of the CML is MRP/σmkt, and the slope of the SML is MRP. Neither has a slope of 1 except by sheer coincidence.

 

[rodra333]

[/quote]
, the slope of the CML is the standard deviation of the risky portfolio divided by the market standard deviation (of returns). Knowing this, you can see a similar expression for the BETA. Why? Remember that due the diversification process the standard deviation of the risky portfolio represents only the systematic risk of it, NOT TOTAL RISK. So, this SDp is exactly like the standard deviation of the market (SDm).
the slope of the CML is STND of the risky portfolio divided by STND of market returns. I thought it was Market risk premium divided by STND of market returns?

 

[rodra333]

Harrogath you stated “the slope of the CML is STND of the risky portfolio divided by STND of market returns”.
I thought it was Market risk premium divided by STND of market returns?
:S???

 

[Harrogath]

rodra333 wrote:
Harrogath you stated “the slope of the CML is STND of the risky portfolio divided by STND of market returns”.
I thought it was Market risk premium divided by STND of market returns?
:S???

Yes, I know, it is some confusing. Im bad telling that the slope of the CML is what I said. Indeed you are right.
The CML is a line tangent to the efficient frontier of portofolios and securities. And the SML is a regression line between expected returns and systematic risk (Beta), so those “models” are totally different right? But in some point they are the same in risk terms… which is I wanted to explain.
S2000magician has clarified the point that they are the same in risk terms only by pure coincidence.

 

[S2000magician]

rodra333 wrote:the slope of the CML is STND of the risky portfolio divided by STND of market returns. I thought it was Market risk premium divided by STND of market returns?

That’s what I wrote:

S2000magician wrote:The slope of the CML is MRP/σmkt … .