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Capital Market Line (CML) vs Security Market Line (SML)

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 Capital Market Line (CML) vs Security Market Line (SML)
S. M. Ikhtiar Alam
The CML is a line that is used to show the rates of return, which
depends on risk-free rates of return and levels of risk for a specific
portfolio. SML, which is also called a Characteristic Line, is a
graphical representation of the market’s risk and return at a given
time.

Security market line (SML) is the representation of the capital asset

pricing model. It displays the expected rate of return of an
individual security as a function of systematic, non-diversifiable
risk. The risk of an individual risky security reflects the volatility of
the return from security rather than the return of the market
portfolio. The risk in these individual risky securities reflects the
systematic risk.

Security Market Line Assumptions

Since the security market line is a representation of the CAPM, the assumptions for CAPM
are also applicable to SML. The most notable factor is CAPM is a one-factor model that
is based only on the level of systematic risk the securities are exposed to.
The more the risk the more are the expected returns that are applicable in CAPM are also
applicable in the case of SML.

• All market investors are risk-averse and they cannot affect the price of a security.

• The investment scope for all investors is the same.

• No short sales take place in the market.

• No taxes or transaction costs are applicable.

 • Only one risk-free asset is there in the portfolio

• There are numerous risky assets.

• All market participants have access to all necessary information.

One of the differences between CML and SML, is how the risk
factors are measured. While standard deviation is the measure of
risk for CML, Beta coefficient determines the risk factors of the
SML.

The CML measures the risk through standard deviation, or through

a total risk factor. On the other hand, the SML measures the risk
through beta, which helps to find the security’s risk contribution
for the portfolio.

While the Capital Market Line graphs define efficient portfolios,

the Security Market Line graphs define both efficient and non-
efficient portfolios.

While calculating the returns, the expected return of the portfolio

for CML is shown along the Y- axis. On the contrary, for SML, the
return of the securities is shown along the Y-axis. The standard
deviation of the portfolio is shown along the X-axis for CML,
whereas, the Beta of security is shown along the X-axis for SML.

Where the market portfolio and risk-free assets are determined by

the CML, all security factors are determined by the SML.
Unlike the Capital Market Line, the Security Market Line shows the
expected returns of individual assets. The CML determines the risk
or return for efficient portfolios, and the SML demonstrates the
risk or return for individual stocks.

The Capital Market Line is considered to be superior when

measuring the risk factors.

Summary:

1. The CML is a line that is used to show the rates of return, which
depends on risk-free rates of return and levels of risk for a specific
portfolio. SML, which is also called a Characteristic Line, is a
graphical representation of the market’s risk and return at a given
time.

2. While standard deviation is the measure of risk in CML, Beta

coefficient determines the risk factors of the SML.

3. While the Capital Market Line graphs define efficient portfolios,

the Security Market Line graphs define both efficient and non-
efficient portfolios.

4. The Capital Market Line is considered to be superior when

measuring the risk factors.
5. Where the market portfolio and risk-free assets are determined
by the Capital Market Line, all security factors are determined by
the SML.

Capital Market Line

The Capital Market Line is a graphical representation of all the
portfolios that optimally combine risk and return. CML is a theoretical
concept that gives optimal combinations of a risk-free asset and the
market portfolio. The CML is superior to Efficient Frontier in the sense
that it combines the risky assets with the risk-free asset.

• The slope of the Capital Market Line (CML) is the Sharpe

Ratio of the market portfolio.
• The efficient frontier represents combinations of risky assets.
• If we draw a line from the risk-free rate of return, which is
tangential to the efficient frontier, we get the Capital Market
Line. The point of tangency is the most efficient portfolio.
 • Moving up the CML will increase the risk of the portfolio, and
moving down will decrease the risk. Subsequently, the return
expectation will also increase or decrease, respectively.

All investors will choose the same market portfolio, given a specific
mix of assets and the associated risk with them.

Capital Market Line Formula

The Capital Market Line (CML) formula can be written as follows:

ERp = Rf + SDp * (ERm – Rf) /SDm

where,

• Expected Return of Portfolio

• Risk-Free Rate
• Standard Deviation of Portfolio
• Expected Return of the Market
• Standard Deviation of Market

We can find the expected return for any level of risk by plugging the
numbers into this equation.

Example of the Capital Market

Line
Suppose that the current risk-free rate is 5%, and the expected
market return is 18%. The standard deviation of the market
portfolio is 10%.

Now let’s take two portfolios, with different Standard Deviations:

• Portfolio A = 5%
• Portfolio B = 15%

Using the Capital Market Line Formula,

Calculation of Expected Return of Portfolio A

• = 5% +5%* (18%-5%)/10%
• ER(A) = 11.5%

Calculation of Expected Return of Portfolio B

• = 5% +15% (18%-5%)/10%
• ER(B) = 24.5%

As we increase the risk in the portfolio (moving up along the Capital

Market Line), the expected return increases. The same is true vice-
versa. But the excess return per unit of risk, which is the Sharpe ratio,
remains the same. It means that the capital market line represents
different combinations of assets for a specific Sharpe ratio.

Capital Market Theory

Capital Market Theory tries to explain the movement of the Capital
Markets over time using one of the many mathematical models. The
most commonly used model in the Capital Market Theory is
the Capital Asset Pricing Model.
Capital Market Theory seeks to price the assets in the market.
Investors or Investment Managers who are trying to measure the risk
and future returns in the market often employ several of the models
under this theory.

Assumptions of the Capital

Market Theory
There are certain assumptions in the Capital Market Theory, which
hold true for the CML also.

• Frictionless Markets – The theory assumes the existence of

frictionless markets. This means that there are no transaction
costs or taxes applicable to such transactions. It assumes that
investors can smoothly conduct transactions in the market
without incurring any additional costs.
• No Limits on Short Selling – Short selling is when you borrow
securities and sell them with an expectation of the securities’
price going down. Capital Market Theory assumes that there are
no limits on the usage of the funds received from short selling.
• Rational Investors – The Capital Market Theory assumes that
investors are rational, and they take a decision after assessing
risk-return. It assumes that the investors are informed and make
decisions after careful analysis.
• Homogenous Expectation – Investors have the same
expectations of future returns in their portfolio. Given the 3 basic
inputs of the portfolio model for calculating future returns, all
investors will come up with the same efficient frontier. Since the
risk-free asset remains the same, the tangency point, which
 represents the Market Portfolio, will be the obvious choice of all
investors.

Limitations
• Assumptions – There are certain assumptions that exist within
the concept of Capital Market Line. However, these assumptions
are often violated in the real world. For example, the markets are
not frictionless. There are certain costs associated with the
transactions. Also, investors are usually not rational. They often
make decisions based on sentiments and emotions.
• Borrowing/Lending at Risk-Free Rate – Theoretically, it is
supposed that investors can borrow and lend without any limits
at the risk-free rate. However, in the real world, investors usually
borrow at a higher rate than the rate at which they are able to
lend. This increases the risk or standard deviation of a leveraged
portfolio.

Conclusion
The Capital Market Line (CML) draws its basis from the capital market
theory as well as the capital asset pricing model. It is a theoretical
representation of different combinations of a risk-free asset and a
market portfolio for a given Sharpe Ratio. As we move up along the
capital market line, the risk in the portfolio increases, and so does the
expected return. If we move down along the CML, the risk decreases
as does the expected return. It is superior to the efficient frontier
because the ef only consists of risky assets/market portfolio. The CML
combines this market portfolio with this market portfolio. We can use
the CML formula to find the expected return for any portfolio given its
standard deviation.
The assumption for the CML is based on the assumptions of the
capital market theory. But these assumptions often don’t hold true in
the real world. The Capital Market Line is often used by analysts to
derive the amount of return that investors would expect to take a
certain amount of risk in the portfolio.
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