SML and CML individual, security, standard, between, include

IAmNeil

Schweser says: (Pg 174, Differences between SML and CML)

When market is in equilibrium, the individual security's risk and return combination lies along the SML but lies below the CML.

Reason being given: the individual security's standard deviations include unsystematic risk that is diversified away in the market portfolio

Can someone tell me how does this reason back the notion that the point will lie below the CML?

scarecrow

it would be inefficient, hence more risk per unit of reward than a diversified portfolio

SFoyil

The SML represents an individuals security's risk and return and only represents unsystematic risk. If your portfolio was comprised of 100% GM stock, you receive no benefits from diversification. Therefore, the SML would plot below the CML.

NO EXCUSES

tianxin

The CML measures total risk, thus the total risk of any individual security is higher than that of a well-diversified portfolio with the same expected return. Therefore, the security is inefficient, and remember that all points below the CML are inefficient portfolios.

Sportsman

I'm thinking that points above mean that those portfolios outperform the market and require active management and accurate forecasts to construct. They are not impossible.

Anyone please confirm that!

kingstongal

In the world of modern portfolio theory, it is impossible to outperform the market on a risk-adjusted basis. That said, anyone is free to disagree with MPT.

iteracom

CML: Slope is sp / sm

SML: Slope is p*sp/sm (beta)

where sp - s.d of portfolio
sm - s.d of market
p - correlation coeff of portfolio with market

Now as p < 1 .. SML will be below CML as they have the same intercept

zhaoyp

Okay folks, see this: CFAI Vol6 Page 579, lines 5 and 6

"The SML is the equation that specifies the required/expected return for a security that is implied by the CML when the market is in equilibrium."

This statement is part of a vignette, and is a TRUE statement as answered in Q 14 later.

Now, doesn't this statement imply, in equilibrium, a security that lies on SML would also lie on CML ?

I answered this question incorrectly, and haven't yet figured why the statement should be TRUE !!!!

giorgio10

SML: Equation is the CAPM equation.
Ri=rf + Betai*(Rm-Rf)

Intercept=rf
rm-rf = Slope
Betai = X point of Intersection.

CML: Equation:
ri = rf + [(rm-rf)/sm] * si

Intercept = rf (same as SML)
Slope = (rm-rf)/sm
sp = X Point of intersection.

If Both SML and CML are equal:
betai = si/sm

betai = cov(i,m)/sm^2

cov(i,m) = corr*si*sm

so corr*si*sm/sm^2 = si/sm
or corr*si/sm = si/sm

so implies corr=1

additionally - the equilibrium portion is true - because both CML and SML depends on investors having homogenous expectations etc.

CP

President1988

rus1bus Wrote:
-------------------------------------------------------
> Okay folks, see this: CFAI Vol6 Page 579, lines 5
> and 6
>
> "The SML is the equation that specifies the
> required/expected return for a security that is
> implied by the CML when the market is in
> equilibrium."
>
> This statement is part of a vignette, and is a
> TRUE statement as answered in Q 14 later.
>
> Now, doesn't this statement imply, in equilibrium,
> a security that lies on SML would also lie on CML
> ?
>
> I answered this question incorrectly, and haven't
> yet figured why the statement should be TRUE !!!!


The SML represents the risk of an individual security or a well diversified portfolio. However, it doesn't explain the risk of an efficient portfolio, which is described by the CML. The CML represents total risk, sigma, which is unsystematic and systematic risk. The SML risk measure is beta, which only represents unsystematic risk. Based on this, a security that lies on the SML could not lie on the CML because you are using two different risk measures.

NO EXCUSES