interesting question regarding CML and SML

I have a question regarding CML and SML, (schweser notes, book 5 page, 242)

for a Market portfolio in SML (CAPM), beta is equal to 1 (systematic risk),

however, for a Market portfolio in CML, the tangent point to efficient frontier, standard deviation(total risk) is only 20% (less than 1),

why systematic risk is bigger than total risk? Do we get the same market return rate by using SML and CML? thanks.

Two things:

  1. Standard deviation does not equal Beta.

  2. SML(CAPM) plots expected return based on a securities relation to the overall market. On the other hand, the portfolio that is tangent and lies on the efficient frontier in the CML doesn’t necessarily consist of stocks that represent the overall market.

Standard deviation does not equal Beta. Correct, but why TOTAL risk is less than systematic risk?

I think you misunderstand that first sentence: standard deviation (of returns) and beta measure very different things; the numbers aren’t comparable.

It’s like asking why my house is bigger than yours (because my address has 5 digits and yours has 4).

I appologize, I tried looking at the page you listed in the Schweser book to get a better understanding of the problem. Although I don’t see anywhere where it talks about total risk and systematic risk. Could you point me out to the paragraph? I might be blind haha

book 5, page 243, question 3, although it doesn’t ask you that, but just my curiosity

Beta measures the slope of a regression line; the units on the axes don’t matter.

In that problem the reason why the portfolio has a beta of less than 1 is because the portfolio includes treasuries which are risk free securities. Risk free securities do not have exposure to systematic risk and therefore the portfolio beta is reduced.

For the portfolio to have a Beta of 1, 100% of the portfolio needs to made up of the market.

sorry, i think on the CML line, the tangent point to the efficient frontier does not include risk free security(treasury bond), just the systmatic risk of market portfolio only

None of this is true.

βport = ρ(mkt,port) × (σport/σmkt)

Thus, beta can equal 1 by having a very volatile portfolio which has a low correlation of returns with the market. And beta can be less than one even for a very volatile portfolio (with no risk-free asset) which has a low correlation of returns with the market.

Not sure if this answers your question or not, but since they are going 40% into bonds, that leaves 60% for the market portfolio. Since you are less than 100% of the market portfolio your portfolio’s systematic risk will be less than that of a portfolio that entirely consists of the market.

Thats the best answer I can give as I’m not 100% sure on what you are asking haha. Sorry