Comparison Analysis of Capital Market Line and Security Market Line, Minimum Variance Portfolio and Capital Asset Pricing Model

This article provides a detailed comparison analysis of Capital Market Line and Security Market Line, Minimum Variance Portfolio and Capital Asset Pricing Model. It explains the concept of Minimum Variance Portfolio and Capital Asset Pricing Model. The article also provides an example of building a minimum variance portfolio and computation of expected return under CAPM. The relevance of CAPM over other models has also been discussed.

FIN200 Assignment, Trimester 2 2018
1. Introduction
Security Market Line
Security Market Line1 is representation in visual form of Capital Asset Pricing Model
(CAPM). This line depicts the relationship between the expected return of an asset or
security with its Beta coefficient (a measure of systematic risk of such security). In layman
terms, it depicts risk return relationship for a given beta or return risk relationship for a
given expected return.
The formula for the Security Market Line in terms of CAPM equation has been depicted
here-in-below:
Expected Return= Risk Free Rate of Return + Beta coefficient of Security ( Risk
Premium) ;
Whereby formula for Risk Premium is Market Rate of Return – Risk Free rate of Return.
Capital Market Line
Capital Market Line (CML)2 is a graph that depicts relationship between expected return
of a portfolio encompassing all possible proportions between the market portfolio and risk
free asset. Also the expected return represents the return of market as a whole. The
formula for generation of expected return of a portfolio is shown here-in-below:
Expected Return of a Portfolio= Proportion of Market Portfolio * Expected Return of
Market Portfolio* (1- Proportion of Market Portfolio)* Risk Free Rate.
Further under CML, the return of a non-leveraged portfolio can be less or equal to market
portfolio. However, the return of a leveraged portfolio can exceed the return of market
portfolio.
2. Comparison Analysis of Difference
(a) Capital Market Line is a graphical representation of Capital Asset Pricing Model
which depicts relationship between the expected return of a portfolio (not an individual
security) and their total risk (risk of portfolio). Further, under Security Market Line
relationship is presented between the required of an individual security and its non-
diversifiable risk (not total risk only systematic risk).3
1 http://financialmanagementpro.com/security-market-line-sml/
2 http://financialmanagementpro.com/capital-market-line-cml/
3 https://www.managementnote.com/difference-between-cml-and-sml/

(b) The risk under Capital Market line is measured through computation of standard
deviation of the portfolio encompassing both diversifiable risk and non- diversifiable4
risk. Under Security Market Line, the measurement of Risk is Beta which represent
systematic risk of an individual security.
(c) Under the Capital Market Line graph, only efficient portfolio is defined and is thus
called efficient frontier. Under the Security Market Line both efficient and non-
efficient portfolios are defined;
(d) The Y axis under the Capital Market Line depicts the expected return of a portfolio
while X axis represents the total risk or Standard deviation while under Security
Market Line Y axis represent return of a security and X axis show the level of risk of
such security represented by Beta. The same has been represented here-in-below:
Capital Market Line
4 Non-diversifiable risk is the risk that cannot be eliminated by diversifying and is ingrained to investment.

(e) When 5the market portfolio and risk free assets are required to be determined CML is used
while when all security factors need to be determined Security market Line is used.
(f) Further, Capital Market Line shows relation between return that an individual can earn by
investing in risk free asset and thereby increasing risk gradually while in case of Security
Market Line, the risk level is shown for a given level of return.6
(g) Let us further analyse the same by taking an example7:
Let us assume that the risk free rate of return is 5%;
Return on Australian ASX 200 is 10%
Then Risk premium is 5%.
Further let the total risk of portfolio be 8% and non-diversifiable risk of security be 0.25.
Further market Standard deviation is 8%
Then According to SML rate of return is =5% +0.25*5%=6.25%.
Then According to CML rate of return is =5% +[(5%/8%]*10%=11.25%
3. Minimum Variance Portfolio
5 http://www.differencebetween.net/business/difference-between-cml-and-sml/
6 https://www.differencebetween.com/difference-between-capital-market-line-and-vs-security-market-line/
7 http://financialmanagementpro.com/capital-market-line-cml/

Let us first understand the meaning of minimum variance portfolio which is a well-
diversified portfolio that is composed of assets that are risky on an individual basis but
when they from a part of portfolio their overall risk is reduced8 with a given level of
anticipated return. It is one of the significant portfolio optimising tool which maximises
return and minimizes risk9 which is generally the goal of rationale investor.
Building of Minimum variance portfolio
For building a minimum variance portfolio, an investor needs to make a combination of
difference securities with different level of risk generally low level or securities with low
correlation with each other. Further, with low correlation is the most common method of
building minimum variance portfolio.
In short, minimum variance portfolio is a diversified portfolio with securities having a low
or negative correlation for a given level of return with an intention to reduce risk.
Let us take an example to understand the concept more clearly:
Suppose an individual has portfolio consisting of 100% shares and return of 15% and risk
of 18% while other individual has return of 7% and risk of 10% by investing in bonds and
a third individual has return of 11% by investing in international market of 13%.. The
Minimum variance portfolio can be achieved by creating an optimum combination of all
three portfolio in such a manner that the return on such investment shall exceed 11% and
the risk of such investment shall be lower than 13%. Let us assume that combination is
30% of shares, 30% of Bond and 40% of international market. This represents the
minimum variance portfolio.
Let us10 take another example under which there are only 5 stocks in the investment
horizon and the weight, rate of return over 9 years have been tabulated here-in-below:
8 http://www.businessdictionary.com/definition/minimum-variance-portfolio.html
9 https://www.thebalance.com/minimum-variance-portfolio-overview-4155796
10 https://www.myaccountingcourse.com/accounting-dictionary/minimum-variance-portfolio

Weights 15% 20% 12% 36% 17%
Year Stock A Stock B Stock C Stock D Stock E
1 21.46% 12.53% 20.32% 7.48% 15.65%
2 -6.54% -1.49% 4.95% 4.16% 1.21%
3 6.05% 0.02% 0.72% 9.97% 1.37%
4 -3.78% -3.41% 10.82% -1.47% 2.92%
5 -0.16% -6.22% 1.93% 1.17% -3.49%
6 -3.33% 1.08% -3.93% -5.06% -9.49%
7 -9.95% -11.81% -8.48% -0.37% 7.80%
8 -5.34% -11.45% -18.64% -19.69% -10.37%
9 16.75% 15.65% 26.64% 13.19% 13.18%
Average 1.68% -0.81% 3.81% 1.04% 2.09%
Standard Deviation 10.88% 9.51% 14.02% 9.71% 9.10%
Annual Return 22.19% -9.25% 56.72% 13.27% 28.11%
Further annual return has been computed by taking the formula (1+ average return)*time-1
Also the correlation and covariance between the stocks presented here-in-below:
Correlation A B C D E
A 1 0.71 0.7 0.5 0.67
B 0.71 1 0.69 0.56 0.55
C 0.7 0.69 1 0.62 0.63
D 0.5 0.56 0.62 1 0.6
E 0.67 0.55 0.63 0.6 1
Covariance A B C D E
A 0.0105 0.0028 0.0039 0.002 0.0025
B 0.0028 0.008 0.0034 0.002 0.0018
C 0.0039 0.0034 0.0175 0.003 0.0028
D 0.002 0.002 0.003 0.0084 0.002
E 0.0025 0.0018 0.0028 0.002 0.0074
Thus optimised portfolio is presented here-in-below

Optimised Porfolio
A B C D E
Weight 15% 20% 12% 36% 17%
15% 0.0002 0.0001 0.0001 0.0003 0.0001
20% 0.0001 0.0003 0.0001 0.0001 0.0001
12% 0.0001 0.0001 0.0003 0.0001 0.0001
36% 0.0000 0.0001 0.0001 0.0011 0.0001
17% 0.0001 0.0001 0.0001 0.0001 0.0002
Total 0.0005 0.0007 0.0005 0.0016 0.0006
Variance 0.40%
Standard Deviation 6.29%
Return 17.84%
On the basis of above, one may see that return has increased and risk has minimised.
The graph of minimum variance portfolio is presented here- in- below;
The importance of Minimum Variance Portfolio has been detailed here-in-below:
(a) Reduces risk to a minimum level;
(b) Provides healthy return on investment at lower risk;

(c) Eliminates or minimises diversifiable risk;
4. Capital Asset Pricing Model
Capital11 Asset Pricing Model is a financial model that depicts relationship between
systematic risk i.e. Beta and expected rate of return. It is an additive model. The formula
for computation of expected return has been depicted here-in-below:
RT
The Computation under CAPM is based on two notions:
(a) Time value of Money;
(b) Risk
The other models that are common for computation of expected return include dividend
discount Model, weighted Average Cost of Capital and others.
Relevance of Capital Asset Pricing Model over other models
The first and foremost significance and relevance of CAPM is on account of its ease of
computation. The formula for computation is simple and represents only two portions time
value of money represented by Risk free rate and risk represented by Beta and market
premium. Further, the method can be easily stress tested to compute a wide array of
values of outcome to provide confidence and range to investor of possible rate of return.
The assumption of investor holding a diversified portfolio is in alignment with market
portfolio and minimum variance portfolio and thus useful. Further, due to diversification
only systematic risk i.e. Beta shall be taken into consideration.
Further, CAPM takes into account Systematic which is not considered under other models
like Dividend Discount Model. This is a significant part of investment analysis and can
never be overlooked while making an investment in security.
In addition12, business and financial risk variability compatibility is present under CAPM
which is missed out under Weighted Average Cost of Capital method. Thus if the current
11 https://www.investopedia.com/terms/c/capm.asp
12 https://www.investopedia.com/articles/investing/021015/advantages-and-disadvantages-capm-model.asp

mix of debt equity is not in alignment with the proposed project, then even CAPM can be
used for computation of return.
The model of CAPM is theoretically derived and has been subject to many back testing. It
has been established based on frequent empirical research and testing.13
The model further considers a wider picture taking market as a whole rather than being
confined to the company as done under other models. The model considers market rate of
return which is missing in other models and thus predict a more realistic and accurate
model. Further, research and studies have predicted a very high rate of success of CAPM
compared to other models for computation of expected return.
Further, one more advantage of using CAPM is that it provides rate of discount for
appraising a project which is absent under WACC method. Thus, it is more convenient
compared to WACC.
In addition, CAPM model can be used for computation of expected return even if the
company is paying dividend or not which is absent under dividend discount model which
is dependent on dividend for computation of return.14
Thus, on the basis of above it can be understood that CAPM simplify and ease the work of
financial investor and decision makers. The decision makers can use this model in
conjunction with traditional techniques and a healthy judgement to predict pragmatic and
useful estimates of expected return15.
13 https://www.accaglobal.com/in/en/student/exam-support-resources/fundamentals-exams-study-
resources/f9/technical-articles/CAPM-theory.html
14 https://budgeting.thenest.com/capm-vs-ddm-24472.html
15 https://hbr.org/1982/01/does-the-capital-asset-pricing-model-work