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A STUDY ON CAPM & REALISM OF
ITS UNDERLYING ASSUMPTIONS
Adapted from Students Assignment 2011.
Table of Contents
Chapter Particulars Page No.
1 Research Design 4
2 CAPM : An Introduction 5
(i) Assumptions underlying CAPM
(ii) CAPM tools to make investment decisions - Security Market
Line, Efficiency Frontier & Capital Market Line
6
7
3 CAPM Assumptions ; A realistic Approach 9
4Comparison of Expected Returns using CAPM and Actual Returns,
based on Historic Data - and construction of SML for the same11
5 Consideration of taxes in CAPM
6Effect of inclusion of taxes on the SML and comparing with Actual
Returns using graphs21
7 Findings & Interpretations 27
8 Bibliography 28
Research Design
a) Statement of Purpose:
The basic assumption behind the CAPM model are Zero taxes and transaction costs, Homogenity,
Riskfree borrowing and lending. Since these assumptions are unrealistic, we propose to examine how
inclusion of taxes in the model will effect the Security Market Line - a decision making tool.
b) Research objectives:
Adapted from students assignment 2011. Page 2
o To understand the CAPM and related tools(SML/CML).
o Realistic examination of it’s assumption’s.
o Effect of relaxation of the assumptions on the SML and the change in the nature of the curve.
c) Research methodology:
We performed primary as well as secondary research to better understand CAPM and its usefulness in
predicting future security returns. We obtained the opinions of stock market traders on the value of CAPM
in securities analysis, who guided us in our research. We also extensively studied material available on
the internet. This project is a result of all we have understood of the subject from both these sources.
d) Research Scope:
This research gives an overview of the meaning, techniques and usefulness of CAPM. However, in depth
study of possibility of a substitute new model has not been done. Just a few examples have been taken
to understand how it works. More important is if it actually is an effective forecast for prices.
e) Research limitations
Statistical figures may not be accurate as they are estimated and not released by official sources
We've tried to be as extensive in our research as is possible, but, considering that the topic is
controversial, there may be information on the topic that is not available in the public domain.
CAPM : An Introduction
The capital asset pricing model (CAPM) is the standard risk-return model used by most academicians
and practitioners. The underlying concept of CAPM is that investors are rewarded for only that portion of
risk which is not diversifiable. This non-diversifiable risk is termed as beta, to which expected returns are
linked. The objective of the study is to test the validity of this theory in Indian capital market & the stability
of this non diversifiable risk (i.e. systematic risk or beta).
CAPM describes the relationship between risk and expected return and that is used in the pricing of risky
securities. It is based on two parameter portfolio analysis developed by Markowitz (1952). It is the
standard risk return model used by most academicians & practitioners. The underlying concept of CAPM
Adapted from students assignment 2011. Page 3
is that, investors are rewarded for only that portion of risk which is not diversifiable. This non-diversifiable
variance is termed as beta, to which expected returns are linked.
The general idea behind CAPM is that investors need to be compensated in two ways: time value of
money and risk. The time value of money is represented by the risk-free (rf) rate in the formula and
compensates the investors for placing money in any investment over a period of time. The other half of
the formula represents risk and calculates the amount of compensation the investor needs for taking
on additional risk. This is calculated by taking a risk measure (beta) that compares the returns of the
asset to the market over a period of time and to the market premium (Rm-rf).
Assumptions
The set of assumptions employed to develop CAPM can be summarized as follows:
I. Investors are risk averse & they have a preference for expected return & dislike of risk.
II. Investors make investment decision based on expected rate of return & the variance of the
underlying asset return. i.e. assumptions of two-parameter.
III. Investors desire to hold a portfolio that lies along the efficient frontier. (The efficient frontier is also
known as diversification frontier)
Adapted from students assignment 2011. Page 4
IV. There is a risk less asset & investors can lend or borrow at that risk free rate.
V. All the investments are perfectly divisible. That is, the fractional shares for any investment can be
purchased in any moment.
VI. All the investors have the homogeneous expectations regarding investment horizon or holding
period and to forecasted expected return & level of risk on securities. At the same time, there is a
complete agreement among investors as to the return distribution for each security & portfolio.
VII. There are no imperfections in the market that prevent the investors to buying or selling the assets.
More importantly, there are no commissions or taxes involved with the security transaction. That
means, there are no costs involved in diversification & there is no differential tax treatment of
capital gain & ordinary income.
VIII. There is no uncertainty about expected inflation, or alternatively, all security prices are fully reflect
all changes in future inflation expectations.
IX. Capital market is in equilibrium. That is all the investment decisions have been made & there is no
further trading without new information.
CAPM tools to make investment decisions
SECURITY MARKET LINE (SML)
The SML will tell us assets’ required returns, given their level of systematic risk (as measured by
beta).We can compare this to the assets’ expected returns (given our forecasts of future prices and
dividends) to identify undervalued assets and create the appropriate trading strategy.
An asset with an expected return greater than its required return from the SML is undervalued; we
should buy it.
An asset with an expected return less than the required return from the SML is overvalued; we
should sell it (or short sell it if we’re inclined to be aggressive).
An asset with an expected return equal to its required return from the SML is properly valued;
we’re indifferent between buying and selling it.
Adapted from students assignment 2011. Page 5
Example : The following table contains information based on analyst’s forecasts for three stocks. The risk-free
rate is 7 percent and the expected market return is 15 percent. Compute the expected and required return on
each stock, determine whether each stock is undervalued, overvalued, or properly valued, and outline an
appropriate trading strategy.
Stock Price today E(Price) in 1 year E(Divid.) in 1 year Beta
Stock A 25 27 1.00 1.0
Stock B 40 45 2.00 0.8
Stock C 15 17 0.49 1.2
Answer: Expected and required returns are shown in the figure below:
Expected Return Required Return
A (27 -25 +1) / 25 = 12.0% 0.07 + (1.0) (0.15 – 0.07) = 15.0%
B (45 - 40 + 2) / 40 = 17.5% 0.07 + (0.8) (0.15 – 0.07) = 13.4%
C (17 - 15 + 0.49) / 15 =
16.6%
0.07 + (1.2) (0.15 – 0.07) = 16.6%
A is overvalued. It’s expected to earn 12%, but based on its systematic risk it should earn 15%.
B is undervalued. It’s expected to earn 17.5%, but based on systematic risk it should earn 13.4%.
C is properly valued. It is expected to earn 16.6%, & based on systematic risk it should earn 16.6%.
The appropriate trading strategy is: Short sell A, buy B and buy, sell, or ignore C.
EFFICIENCY FRONTIER & CAPITAL MARKET LINE
The efficient frontier consists of the set portfolios that has the maximum expected return for a given risk
level.
Adapted from students assignment 2011. Page 6
SML for stock C
Rf = 7%
R(k) = 16.6%
Beta 1.0
Rm=15%
SML
1.2
R(k) = 7% + 1.2[8%] = 16.6%
E(k)
Rf = 7%
R(k) = 16.6%
Beta 1.0
Rm=15%
SML
1.2
R(k) = 7% + 1.2[8%] = 16.6%
E(k)
B
D
C
30
40
50
60
70
80
B D
standard deviation
exp
ecte
d r
etu
rn
Efficiency frontier
C
For every level of standard deviation along the X axis, the efficient frontier records the portfolio with the
highest expected return (e.g. B & D). No investor would choose Portfolio C because portfolio B has a
higher expected return for the same level of risk. Asset allocation along the efficiency frontier changes to
provide diff risk-return combos. D will correspond to & 70% equity & B 30 % equity. Higher return - higher
risk.
Capital Market Line (CML): is the line of tangency between the RFR point on the vertical axis and the
efficient frontier.
The CML is considered to be superior to the efficient frontier since it takes into account the inclusion of a
risk-free asset in the portfolio. The portfolio at the point of tangency is the market portfolio. Market
portfolio is a portfolio consisting of a weighted sum of every asset in the market, with weights in the
proportions that they exist in the market. The MP is the only risky portfolio anyone would hold and is the
only source of risk. As per risk tolerance, all investors choose a combo of risk free asset and market
portfolio. The capital asset pricing model (CAPM) demonstrates that the market portfolio is essentially the
efficient frontier. This is achieved visually through the security market line (SML).
CAPM Assumptions - A Realistic Approach (Relaxation)Adapted from students assignment 2011. Page 7
M
0
10
20
30
40
50
60
70
80
M
standard deviation
exp
ecte
d r
etu
rn
Efficiencyfrontier
Rf
Capital market Line
With the data presented thus far regarding efficiency of capital markets, the assumptions of the CAPM
can be relaxed on these grounds :
The model assumes that the variance of returns is an adequate measurement of risk. This might be
justified under the assumption of normally distributed returns, but for general return distributions other
risk measures (like coherent risk measures) will likely reflect the investors' preferences more adequately.
Indeed risk in financial investments is not variance in itself, rather it is the probability of losing: it is
asymmetric in nature
1. Differential borrowing and lending rates: There is only one risk free rate in the model. This is an
unrealistic assumption. Investors cannot borrow and lend at the same rate. Two rates mean 2
CMLs (as shown in the graph below). One implication of differential borrowing and lending rates is
that the borrowing portfolio is not as profitable as when it assumed investors could borrow at risk
free rate.
2. Heterogeneous expectations : If all investors have different expectations about risk and return,
each would have a unique CML and/or SML, and the composite graph would be a band of lines
with a breadth determined by the divergence of expectations. The CAPM assumes invests have
the same beliefs about expected returns and risks of available investments. But we know that
there is massive trading of stocks and bonds by investors with different expectations.
3. Differing planning periods : if one investor uses a one-year planning period and another uses a
one-month planning period, then the two investors have different SML.
Adapted from students assignment 2011. Page 8
E(R)
Rb
RFR
Risk (standard deviation )
F
G
K
E(R)
Rb
RFR
Risk (standard deviation )
F
G
K
4. Taxes Exist : Zero taxes. The CAPM assumes investment trading is tax-free and returns are
unaffected by taxes. Yet we know this to be false: (1) many investment transactions are subject to
capital gains taxes, thus adding transaction costs; (2) taxes reduce expected returns for many
investors, thus affecting their pricing of investments; (3) different returns (dividends versus capital
gains, taxable versus tax-deferred) are taxed differently, thus inducing investors to choose
portfolios with tax-favored assets; (4) different investors (individuals versus pension plans) are
taxed differently, thus leading to different pricing of the same assets.
5. Transaction costs Exist: The cost trading the security may offset any potential excess return
resulting from the trade securities will plot close to SML but not exactly on it (shown below).
Transaction costs also limit diversification, because at some point , the additional cost of
diversification would exceed its benefits
6. Non availability of risk free assets : The CAPM assumes the existence of zero-risk securities, of
various maturities and sufficient quantities to allow for portfolio risk adjustments. But we know
even Treasury bills have various risks.
Comparison of SML & Actual Returns Based on Historic Data
In order to understand the deviation between the returns calculated using CAPM and the actual
returns, the following steps have been taken:
Adapted from students assignment 2011. Page 9
E(R)
E(Rm)
i
SML
0.0 1.0
E(Rz)
E(RFR) or
1. Five Stocks have been selected from the Nifty 50 for purpose of analysis
2. Construction of SML:
a) The variables in the CAPM model were collected as follows :
i) Risk Free Rate of Return - This has been obtained using the 10 year Indian
government bond yield for the respective periods.
ii) Beta - Obtained from the NSE website for the respective periods from archives
iii) Estimated Market Rate of Return - This data has been collected from .
b) SML was constructed in the manner described in the previous pages for each period.
3. Actual Returns are computed on the basis of historic prices (obtained from NSE) using the
formula:
AR = P1 - P0
P0
For example if Actual Returns for Jan 2008 are being computed:
P1 = Market Price of Stock in Jan 2008
P0 = Market Price of Stock in Jan 2007
D1 = Dividend during period Jan 2007-08
Actual returns for the periods are specified next to the respective charts.
Stock 1: Suzlon
Year Risk Free rate
Beta Expected Market Rate of Return (NIFTY)
CAPM Return R(k)
Actual Returns
Jan-08 7.72 1.05 -51.83 -54.8172 -96.806Jan-09 5.96 1.53 71.45 106.1597 36.27451Jan-10 7.63 1.5 17.24 22.045 -39.121
Adapted from students assignment 2011. Page 10
Adapted from students assignment 2011. Page 11
-60
-50
-40
-30
-20
-10
0
10
20
0 0.5 1 1.5
Beta
Return
SML
Rf = 7.72
Rm = -51.84
R( k ) = -54.81R(k)
Jan 2008
1.05
-60
-50
-40
-30
-20
-10
0
10
20
0 0.5 1 1.5
Beta
Return
SML
Rf = 7.72
Rm = -51.84
R( k ) = -54.81R(k)
Jan 2008
1.05
0
10
20
30
40
50
60
70
80
90
100
110
120
0 0.5 1 1.5 2
Beta
Return
SML
Rf = 5.96
Rm = 71.45
R( k ) = 106.16
R(k)
1.53
Jan 2009
0
10
20
30
40
50
60
70
80
90
100
110
120
0 0.5 1 1.5 2
Beta
Return
SML
Rf = 5.96
Rm = 71.45
R( k ) = 106.16
R(k)
1.53
Jan 2009
0
3
6
9
12
15
18
21
24
0 0.5 1 1.5 2
Beta
Return
SML
Rf = 7.63
R(k) = 22.045
Rm = 17.24
R(k)
Jan 2010
0
3
6
9
12
15
18
21
24
0 0.5 1 1.5 2
Beta
Return
SML
Rf = 7.63
R(k) = 22.045
Rm = 17.24
R(k)
Jan 2010
Stock 2: ACC
Adapted from students assignment 2011. Page 12
Year Risk Free rate
Beta Expected Market Rate of Return (NIFTY)
CAPM Return R(k)
Actual Returns
Jan-08 7.72 0.89 -51.83 -45.28 -53.2389Jan-09 5.96 0.69 71.45 51.1481 79.32199Jan-10 7.63 0.79 17.24 15.2219 19.67071
-60
-50
-40
-30
-20
-10
0
10
20
0 0.5 1 1.5
Beta
Return
SML
Rm = -51.84
Rf = 7.72
R(k) = -45.28 R(k)
0.89
Jan 2008
-60
-50
-40
-30
-20
-10
0
10
20
0 0.5 1 1.5
Beta
Return
SML
Rm = -51.84
Rf = 7.72
R(k) = -45.28 R(k)
0.89
Jan 2008
0
10
20
30
40
50
60
70
80
0 0.5 1 1.5
Beta
Return
SML
Rm = 71.45
Rf = 5.96
R(k) = 51.15 R(k)
0.69
Jan 2009
0
10
20
30
40
50
60
70
80
0 0.5 1 1.5
Beta
Return
SML
Rm = 71.45
Rf = 5.96
R(k) = 51.15 R(k)
0.69
Jan 2009
Stock 3: Bharti Airtel
Year Risk Free rate
Beta Expected Market Rate of Return (NIFTY)
CAPM Return R(k)
Actual Returns
Jan-08 7.72 0.89 -51.83 -45.2877 -25.9154Jan-09 5.96 0.92 71.45 66.2108 -54.11Jan-10 7.63 0.93 17.24 16.5673 9.3230
Adapted from students assignment 2011. Page 13
0
3
6
9
12
15
18
21
0 0.5 1 1.5
Beta
Return
SML
Rm = 17.24
Rf = 7.63
0.79
R(k) = 15.22R(k)
Jan 2010
0
3
6
9
12
15
18
21
0 0.5 1 1.5
Beta
Return
SML
Rm = 17.24
Rf = 7.63
0.79
R(k) = 15.22R(k)
Jan 2010
Adapted from students assignment 2011. Page 14
-60
-50
-40
-30
-20
-10
0
10
20
0 0.5 1 1.5
Beta
Return
SML
Rf = 7.72
Rm = -51.839
R( k ) = -45.28R(k)
0.89
Jan 2008
-60
-50
-40
-30
-20
-10
0
10
20
0 0.5 1 1.5
Beta
Return
SML
Rf = 7.72
Rm = -51.839
R( k ) = -45.28R(k)
0.89
Jan 2008
0
10
20
30
40
50
60
70
80
0 0.5 1 1.5
Beta
Return
SML
Rf = 5.96
Rm = 71.45
R( k ) = 66.2108 R(k)
0.92
Jan 2009
0
10
20
30
40
50
60
70
80
0 0.5 1 1.5
Beta
Return
SML
Rf = 5.96
Rm = 71.45
R( k ) = 66.2108 R(k)
0.92
Jan 2009
0
3
6
9
12
15
18
21
0 0.5 1 1.5
Beta
Return
SML
Rf = 7.63
Rm = 17.24
R( k ) = 16.56
R(k)
0.93
Jan 2010
0
3
6
9
12
15
18
21
0 0.5 1 1.5
Beta
Return
SML
Rf = 7.63
Rm = 17.24
R( k ) = 16.56
R(k)
0.93
Jan 2010
Stock 4: ITC
Year Risk Free rate
Beta Expected Market Rate of Return (NIFTY)
CAPM Return R(k)
Actual Returns
Jan-08 7.72 0.65 -51.83919271 -30.9935 -21.1519Jan-09 5.96 0.54 71.45 41.3246 46.44125Jan-10 7.63 0.61 17.24 13.4921 -30.7418
Adapted from students assignment 2011. Page 15
-60
-50
-40
-30
-20
-10
0
10
20
0 0.5 1 1.5
Beta
Return
SML
Rf = 7.72
Rm = -51.84
R( k ) = -30.99
R(k)
0.65
Jan 2008
-60
-50
-40
-30
-20
-10
0
10
20
0 0.5 1 1.5
Beta
Return
SML
Rf = 7.72
Rm = -51.84
R( k ) = -30.99
R(k)
0.65
Jan 2008
0
10
20
30
40
50
60
70
80
0 0.5 1 1.5
Beta
Return
SML
Rf = 5.96
Rm = 71.45
R( k ) = 41.32
R(k)
0.54
Jan 2009
0
10
20
30
40
50
60
70
80
0 0.5 1 1.5
Beta
Return
SML
Rf = 5.96
Rm = 71.45
R( k ) = 41.32
R(k)
0.54
Jan 2009
Stock 5: Tata Motors
Year Risk Free rate
Beta Expected Market Rate of Return (NIFTY)
CAPM Return R(k)
Actual Returns
Adapted from students assignment 2011. Page 16
0
3
6
9
12
15
18
21
0 0.5 1 1.5
Beta
Return
SML
Rf = 7.63
Rm = 17.24
R( k ) = 13.49R(k)
0.61
Jan 2010
0
3
6
9
12
15
18
21
0 0.5 1 1.5
Beta
Return
SML
Rf = 7.63
Rm = 17.24
R( k ) = 13.49R(k)
0.61
Jan 2010
Jan-08 7.72 0.83 -51.83 -41. 4.835493Jan-09 5.96 1.04 71.45 74.0696 378.0882Jan-10 7.63 1.23 17.24 19.4503 60.46098
Adapted from students assignment 2011. Page 17
-60
-50
-40
-30
-20
-10
0
10
20
0 0.5 1 1.5
Beta
Return
SML
Rf = 7.72
Rm = -51.84
R( k ) = -41.71 R(k)
0.83
Jan 2008
-60
-50
-40
-30
-20
-10
0
10
20
0 0.5 1 1.5
Beta
Return
SML
Rf = 7.72
Rm = -51.84
R( k ) = -41.71 R(k)
0.83
Jan 2008
0
10
20
30
40
50
60
70
80
0 0.5 1 1.5
Beta
Return
SML
Rf = 5.96
Rm = 71.45
R( k ) = 74.07
R(k)
1.04
Jan 2009
0
10
20
30
40
50
60
70
80
0 0.5 1 1.5
Beta
Return
SML
Rf = 5.96
Rm = 71.45
R( k ) = 74.07
R(k)
1.04
Jan 2009
0
3
6
9
12
15
18
21
0 0.5 1 1.5
Beta
Return
SML
Rf = 7.63
Rm = 17.24
R( k ) = 19.45
R(k)
1.23
Jan 2010
0
3
6
9
12
15
18
21
0 0.5 1 1.5
Beta
Return
SML
Rf = 7.63
Rm = 17.24
R( k ) = 19.45
R(k)
1.23
Jan 2010
INTERPRETATION
As is seen in the charts and table above, there is a vast difference between the Expected returns
calculated using the Capital Asset Pricing Model (CAPM) and the Actual Returns computed as per
historic prices.
One must keep in mind that in the 3 year period selected above - there was a global recession,
following which the Stock Market Indices also took unpredictable paths.
When one uses the CAPM, the Rm is calculated on the basis of historic Indices data and is only an
estimate - and this variable can drastically change the expected returns as per CAPM. This is
because the Beta, being a risk measure, is also calculated using historic Indices data. Thus, the
recession can be considered as one of the reasons for variations.
However, even allowing a margin for the unusual external factors mentioned above, the disparity is
high enough to show that CAPM assumptions are unrealistic and its value as a practical tool must be
questioned. Thus, we proceed to examine how considering taxes in the CAPM formula may impact
the returns.
Considering Taxes & Transaction Costs In CAPM
On including tax in the CAPM formula as follows : Re = Rf (1-t) + B [Rm (1-t)- Rf(1-t)],
The following marginal changes in return are observed:
Adapted from students assignment 2011. Page 18
Year Risk Free rate (Rf)
Beta Expected Market Rate of Return (NIFTY) (Rm)
Tax rate
CAPM Return R(k)
CAPM return with taxes (Re)
Actual Returns (AR)
Difference
SUZLON
Jan-08 7.72 1.05 -51.83 33.99% -54.8172 -36.1848 -96.806 60.6212Jan-09 5.96 1.53 71.45 33.99% 106.1597 70.07602 36.27451 33.80151Jan-10 7.63 1.5 17.24 33.99% 22.045 14.5519 -39.121 53.6729
BHARTI AIRTEL
Jan-08 7.72 0.89 -51.83 33.99% -45.2877 -29.8944 -25.9154 -3.97903Jan-09 5.96 0.92 71.45 33.99% 66.2108 43.70575 -54.11 97.81576Jan-10 7.63 0.93 17.24 33.99% 16.5673 10.93607 9.323097 1.612978
TATA MOTORS
Jan-08 7.72 0.83 -51.83 33.99% -41.7141 -27.5355 4.835493 -32.371Jan-09 5.96 1.04 71.45 33.99% 74.0696 48.89334 378.0882 -329.195Jan-10 7.63 1.23 17.24 33.99% 19.4503 12.83914 60.46098 -47.6218
ITC
Jan-08 7.72 0.65 -51.83 33.99% -30.9935 -20.4588 -21.1519 0.693112Jan-09 5.96 0.54 71.45 33.99% 41.3246 27.27837 46.44125 -19.1629Jan-10 7.63 0.61 17.24 33.99% 13.4921 8.906135 -30.7418 39.64793
ACC
Jan-08 7.72 0.89 -51.83 33.99% -45.2877 -29.8944 -53.2389 23.34455Jan-09 5.96 0.69 71.45 33.99% 51.1481 33.76286 79.32199 -45.5591Jan-10 7.63 0.79 17.24 33.99% 15.2219 10.04798 19.67071 -9.62273
Thus, we observe that the inclusion of taxes in the formula in the formula makes a marginal
difference.
Effect of Inclusion of Taxes on SML & Comparison With Actual
Returns
NOTE : R(k) referred to in these charts is the expected returns calculated as per CAPM on inclusion
of taxes.
Adapted from students assignment 2011. Page 19
Stock 1 : Suzlon
Adapted from students assignment 2011. Page 20
-110
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
20
0 0.5 1 1.5Beta
Return
SML
AR
Rf = 7.72
Rm = -51.84
R( k ) = -36.1848
Jan 2008
1.05
AR = -96.806
-110
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
20
0 0.5 1 1.5Beta
Return
SML
AR
Rf = 7.72
Rm = -51.84
R( k ) = -36.1848
Jan 2008
1.05
AR = -96.806
0
10
20
30
40
50
60
70
80
0 0.5 1 1.5 2
Beta
Return
SML
AR
Rf = 5.96
Rm = 71.45
AR = 36.27451
R(k)= 70.07
1.53
Jan 2009
-42-39-36-33-30-27-24-21-18-15-12
-9-6-30369
12151821
0 0.5 1 1.5 2
Beta
Return
SML
AR
Rf = 7.63
AR = -39.121
Rm = 17.24R(k) =14.5
Jan 2010
-42-39-36-33-30-27-24-21-18-15-12
-9-6-30369
12151821
0 0.5 1 1.5 2
Beta
Return
SML
AR
Rf = 7.63
AR = -39.121
Rm = 17.24R(k) =14.5
Jan 2010
Stock 2: Bharti Airtel
Adapted from students assignment 2011. Page 21
-60
-50
-40
-30
-20
-10
0
10
20
0 0.5 1 1.5
Beta
Return
SML
AR
Rf = 7.72
Rm = -51.839
AR = --25.9154
-29.8944
0.89
Jan 2008
-70-60
-50-40-30-20
-100
1020
30405060
7080
0 0.5 1 1.5
Beta
Return
SML
ARRf = 5.96
Rm = 71.45
AR = -54.11
R(k)= 43.70
0.92
Jan 2009
Stock 3: Tata Motors
Adapted from students assignment 2011. Page 22
0
3
6
9
12
15
18
21
0 0.5 1 1.5
Beta
Return
SML
AR
Rf = 7.63
Rm = 17.24
AR = 9.32
R(k) = 10.93
0.93
Jan 2010
-60
-50
-40
-30
-20
-10
0
10
20
0 0.5 1 1.5
Beta
Return
SML
AR
Rf = 7.72
Rm = -51.84
AR= 4.83
R(k)=-27.5355
0.83
Jan 2008
Stock 4 : ITC
Adapted from students assignment 2011. Page 23
0
50
100
150
200
250
300
350
400
0 0.5 1 1.5
Beta
Return
SML
AR
Rf = 5.96
Rm = 71.45
AR = 378.08
R(k)= 48.89
1.04
Jan 2009
0
10
20
30
40
50
60
70
0 0.5 1 1.5
Beta
Return
SML
AR
Rf = 7.63
Rm = 17.24
R( k ) = 19.45
AR=60.46
1.23
Jan 2010
-60
-50
-40
-30
-20
-10
0
10
20
0 0.5 1 1.5
Beta
Return
SML
AR
Rf = 7.72
Rm = -51.84
AR = -21.1519 R(k)= -20.4588
0.65
-60
-50
-40
-30
-20
-10
0
10
20
0 0.5 1 1.5
Beta
Return
SML
AR
Jan 2008
Stock 5 : ACC
Adapted from students assignment 2011. Page 24
0
10
20
30
40
50
60
70
80
0 0.5 1 1.5
Beta
Return
SML
AR
Rf = 5.96
Rm = 71.45
AR= 46.44
R(k)=27.27
0.54
Jan 2009
-40
-30
-20
-10
0
10
20
0 0.5 1 1.5
Beta
Return
SML
AR
Rf = 7.63
Rm = 17.24
AR = -30.74
R(k)= 8.90
0.61
Jan 2010
-60
-50
-40
-30
-20
-10
0
10
20
0 0.5 1 1.5
Beta
Return
SML
AR
Rm = -51.84
Rf = 7.72
R(k)= -29.8944
0.89
AR = -53.23
Jan 2008
FINDINGS & INTERPRETATIONS
Adapted from students assignment 2011. Page 25
0
10
20
30
40
50
60
70
80
90
0 0.5 1 1.5
Beta
Return
SML
AR
Rm = 71.45
Rf = 5.96
R(k) = 33.76286
0.69
AR = 79.32199
Jan 2009
0
10
20
30
0 0.5 1 1.5
Beta
Return
SML
ARRm = 17.24
Rf = 7.63
0.79
R(k)= 10.04798
AR = 19.67071
Jan 2010
On the premises of data collected, analysed and observed, the Capital Asset Pricing Model proves to
be one that can only generate a trendline i.e. the behaviour of returns at differing degrees of
systematic risk. Capital Asset Pricing Model proves to be ineffective with or without taxes.
The behaviour of the SML which we set out to study, changes drastically on inclusion of taxes in the
model. There is no longer a linear relationship between market return and expected returns as per
CAPM. Rather the nature of the curve itself changes to a non - linear curve showing the non -
correlation of market returns to forecasted returns on inclusion of taxes.
However, even on inclusion of the taxes in the model, the model was ineffective in forecasting the
actual returns for the future periods.
Many reasons can be attributed to the inadequacy of the model. The uncertainty in market
conditions, and hence, difficulty in predicting the expected market return on historic index trends
leads to variation between expected and actual returns. Furthermore, even Beta is computed on the
basis of past historic data, and there is no reliability that if the market moves a certain percentage
points upwards, the stock will also move as a multiple of that movement.
Thus, on closer observation, we see that the assumptions of CAPM are not its only weakness, as was
assumed at the beginning of the Research project.
As a recommendation, we suggest that even if reasonably sound estimate of Market Return can be
made, a study in finding an alternative to use of Beta as the measure of risk and measure of
correlation to the market be made. A detailed analysis of an alternative to correlate the market and
stock be made.
BIBLIOGRAPHYAdapted from students assignment 2011. Page 26
www.nseindia.com : to obtain historic indices, stock prices
www.tradingeconomics.com : to obtain 10 year Indian government bond yield
www.wikipedia.com : to obtain theoretical understanding of CAPM
Adapted from students assignment 2011. Page 27
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