标题: SML and CML [打印本页] 作者: IAmNeil 时间: 2011-7-11 19:42 标题: SML and CML
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?作者: scarecrow 时间: 2011-7-11 19:42
it would be inefficient, hence more risk per unit of reward than a diversified portfolio作者: SFoyil 时间: 2011-7-11 19:42
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作者: tianxin 时间: 2011-7-11 19:42
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.作者: Sportsman 时间: 2011-7-11 19:43
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.
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.作者: iteracom 时间: 2011-7-11 19:43
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作者: zhaoyp 时间: 2011-7-11 19:43
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 !!!!作者: giorgio10 时间: 2011-7-11 19:43
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作者: President1988 时间: 2011-7-11 19:43
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作者: yalo 时间: 2011-7-11 19:43
Twice now i have seen beta referred to as unsystematic in this thread, which is incorrect.
