Difference Between CAPM and APT
CAPM vs APT
For shareholders, investors and for financial experts, it is prudent to know the expected returns of a stock before investing. There are various statistical models that compare different stocks on the basis of their annualized yield to enable investors to choose stocks in a more careful manner. CAPM and APT are two such valuation tools. Before we try to find out the differences between APT and CAPM, let us take a closer look at the two theories. APT stands for Arbitrage Pricing Theory that has become very popular among investors because of its ability to make a fair assessment of pricing of different stocks. The basic assumption of APT is that the value of a stock is driven by a number of factors. First there are macro factors that are applicable to all companies and then there are company specific factors. The equation that is used to find the expected rate of return of a stock is as follows. r= rf+ b1f1 + b2f2 + b3f3 + …..

Here r is the expected return on security, f is different factors affecting the price of the security, and b is the measure of relationship between the price of security and the factor. Interestingly, this is the same formula that is used to calculate the rate of return with CAPM, which stands for Capital Asset Pricing Model. However, the difference lies in the use of a single non company factor and a single measure of relationship between price of asset and the factor in the case of CAPM whereas there are many factors and also different measures of relationships between price of asset and different factors in APT. Another difference is that in APT, the performance of the asset is taken to be independent from the market and its price is assumed to be driven by non company and company specific factors. However, one drawback of APT is that there is no attempt to find out these factors, and in fact one has to himself find out empirically different factors in case of every company that he is...

...consumption and in disposable income. (See for example Ericsson and Karlsson, (2003)
“Choosing factors in a multi-factor pricing model”, Stockholm School of Economics,
http://econpapers.hhs.se/paper/hhshastef/0524.html.)
When there are n risky assets indexed by 1 = 1, 2 . . . , n (stocks say), then there are
n equations for the model, one for each asset;
ri = ai + b1,i f1 + · · · + bk,i fk + ei ,
i = 1, . . . , n.
The factors are the same for each asset (that is what makes them correlated), but it
is assumed that the error terms are uncorrelated between assets, E(ei ej ) = 0, i = j.
If we form a portfolio of the n assets, deﬁned by the weights (α1 , . . . , αn ), then in
fact this portfolio is itself determined by a factor model, that is, the rate of return
r = n αi ri of the portfolio satisﬁes (2) with
i=1
n
αi ai
a =
i=1
n
bj =
αi bj,i
i=1
n
e =
αi ei .
i=1
1.2
Single-factor models: CAPM revisited
The simplest case is when there is only one factor being considered;
ri = ai + bi f + ei .
All the mean-variance parameters can be computed directly in terms of the model
parameters:
r i = ai + b i f
2
2
2
σi = b2 σf + σei
i
2
σij = bi bj σf .
Unlike the original Markowitz framework, where 2n + n(n − 1)/2 parameters must be
2
estimated, here we need only estimate 3n + 2 parameters; the 2n of ai , bi , one f , one σf ,
2
and n of σei , a signiﬁcant savings of work.
2
2
Note...

...Model commonly known as CAPM defines the relationship between risk and the return for individual securities. CAPM was first published by William Sharpe in 1964. CAPM extended “Harry Markowitz’s portfolio theory” to include the notions of specific and systematic risk. CAPM is a very useful tool that has enabled financial analysts or the independent investors to evaluate the risk of a specific investment while at the same time setting a specific rate of return with respect to the amount of the risk of a portfolio or an individual investment. The CAPM method takes into consideration the factor of time and does not get wrapped up over by the systematic risk factors, which are rarely controlled. In this research paper, I will look at the implications of CAPM in the light of the recent development. I will start by attempting to explain and discuss the various assumptions of the CAPM. Secondly, I will discuss the main theories and moreover, the whole debate that is surrounding this area more specifically through the various critics of the CAPM assumptions.
When Sharpe (1964) and Lintner (1965) proposed CAPM, it was majorly seen as the leading tool in measuring and determining whether an investment will yield negative or positive return. The model attempts to expound the relationship between expected reward/return and the...

...CAPMCAPM provides a framework for measuring the systematic risk of an individual security and relate it to the systematic risk of a well-diversified portfolio. The risk of individual securities is measured by β (beta). Thus, the equation for security market line (SML) is:
E(Rj) = Rf + [E(Rm) – Rf] βj
(Equation 1)
Where E(Rj) is the expected return on security j, Rf the risk-free rate of interest, Rm the expected return on the market portfolio and βj the undiversifiable risk of security j. βj can be measured as follows:
βj = Cov (Rj, Rm)
Var (Rm)
= σj σm Cor jm
σ2 m
= σj Cor jm
σm
(Equation 2)
In terms of Equation 2, the undiversifiable (systematic) risk (βj) of a security is the product of its standard deviation (σj) and its correlation with the market portfolio divided by the market portfolio’s standard deviation. It can be noted that if a security is perfectly positively correlated with the market portfolio, then CML totally coincides with SML.
Equation 1 shows that the expected rate of return on a security is equal to a risk-free rate plus the risk-premium. The risk-premium equals to the differencebetween the expected market return and the risk-free rate multiplied by the security’s beta. The risk premium varies directly with systematic risk measured by beta.
The figure above illustrates the security market line. For a given amount of...

...Yurop Shrestha
Economics Thesis
CAPM vs. APT: An Empirical Analysis
Introduction
The Capital Asset Pricing Model (CAPM), was first developed by William Sharpe (1964), and later extended and clarified by John Lintner (1965) and Fischer Black (1972). Four decades after the birth of this model, CAPM is still accepted as an appropriate technique for evaluating financial assets and retains an important place in both academic scholars and finance practitioners. It is used to estimate cost of capital for firms, evaluating the performance of managed portfolios and also to determine asset prices. Since the inception of this model there have been numerous researches and empirical testing to assess the strength and the validity of the model. Several variations of the models have been developed since then (Wei 1988, Stein, Fama & French 1993, Merton 1973).
The Arbitrage Pricing Theory of Capital Asset Pricing formulated by Stephen Ross (1976) and Richard Roll (1980) offers a testable alternative to the CAPM. Both of these asset pricing theories have gone through intense empirical and theoretical scrutiny with multiple researches supporting or refuting both the models. The purpose of this paper is to empirically investigate the two competing theories in light of the US Stock Market in relatively stable economic times.
The first section will look at the logic and theoretical aspects of the competing...

...Capital asset pricing model (CAPM)
Using the Capital Asset Pricing Model, we need to keep three things in mind. 1 there is a basic reward for waiting, the risk free rate. 2 the greater the risk, the greater the expected reward. 3 there is a consisted trade off between risk and reward.
In finance, It is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk. The CAPM says that the expected return of a security or a portfolio equals the rate on a risk-free security plus a risk premium. If this expected return does not meet or beat the required return, then the investment should not be undertaken. The security market line plots the results of the CAPM for all different risks (betas - a model that calculates the expected return of an asset based on its beta and expected market returns.)
Using the CAPM model and the following assumptions, we can compute the expected return of a stock in this CAPM example: if the risk-free rate is 3%, the beta (risk measure) of the stock is 2 and the expected market return over the period is 10%, the stock is expected to return 17%=(3%+2(10%-3%)).
Risk of a Portfolio
We all know that investments have risk, so it’s safe to assume that all stocks have risk as well? But did you know that there are different types of...

...Is CAPM Beta Dead or Alive? Depends on How you Measure It
Jiri Novak*
* Uppsala University, Sweden E-mail: jiri.novak@fek.uu.se October 2007 Abstract: The CAPM beta is arguably the most common risk factor used in estimating expected stock returns. Despite of its popularity several past studies documented weak (if any) association betweenCAPM beta and realized stock returns, which led several researchers to proclaim beta “dead”. This paper shows that the explanatory power of CAPM beta is highly dependent on the way it is estimated. While the conventional beta proxy is indeed largely unrelated to realized stock returns (in fact the relationship is slightly negative), using forward looking beta and eliminating unrealistic assumptions about expected market returns turns it (highly) significant. In addition, this study shows that complementary empirical factors – size and ratio of book-to-market value of equity – that are sometimes presented as potential remedies to beta’s deficiencies do not seem to outperform beta. This suggests they are not good risk proxies on the Swedish stock market, which casts doubt on the universal applicability of the 3-factor model. Keywords: asset pricing, CAPM, beta, factor pricing models, 3-factor model, market efficiency, Sweden, Scandinavia JEL classification: G12, G14 Acknowledgements: I would like to thank Dalibor Petr, Tomas ... and Johan Lyhagen for...

...the systematic variance as diversification increases, which means diversifying across industries offer benefit over diversifying within a given industry. Second, using the figures estimated to testify that the CAPM works in practice.
The capital asset pricing model (CAPM) provides us with an insight into the relationship between the risk of an asset and its expected return. This relationship serves two significant functions. First, it provides a benchmark rate of return for evaluating possible investments. Second, the model helps us to make an educated guess as to the expected return on asset that have not yet been traded in the marketplace. Although the CAPM is widely used because of the insight it offers, it does not fully withstand empirical tests. CAPM is a one-period model that treats a security’s beta as a constant, but beta can be changed in respond to firms investment in new industry, change in capital structure and so on. If betas change over time, simple historical estimates of beta are not likely to be accurate. Mismeasuring of betas will not reflect stocks’ systematic risk, so in this case the CAPM does not compute the risk premium correctly. Furthermore, the systematic risk, the source of risk premiums, cannot be confined to a single factor. While the CAPM derived from a single-index market cannot provide any insight on this.
The data we used provides us with...

...ECON 405: Quantitative Finance
CAPM and APT
In this document, I use the package ”gmm”. You can get it the usual way through R or though the development website RForge for a more recent version. For the latter, you can install it by typing the following in R: > install.packages("gmm", repos="http://R-Forge.R-project.org") The data I use come with the package and can be extracted as follows: > > > > library(gmm) data(Finance) R > > > >
Rm F) 0.70956 0.70956 0.70956 0.70956
They use a particular test for multivariate linear models. If we look at the p-values, it says that we don’t reject the hypothesis that all αi are zero. We can therefore reestimate the model without the intercept: > res2 res2
Call: lm(formula = Z ~ Zm - 1) Coefficients: WMK UIS Zm 0.4770 1.3438 ZOOM Zm 0.7240
ORB 1.0524
MAT 0.7084
ABAX 0.7218
T 0.8037
EMR 0.9395
JCS 0.4137
VOXX 1.3517
We can then look at the systematic and non systematic risk of each asset: > > > > + + sigm > > > > > > > a > >
b > > > > > D Chisq) 1 2 10 8.2292 0.6065
2
Zero-beta CAPM (Black)
The zero-beta CAPM is based on the properties of the portfolio frontier. One of them tells us that for each eﬃcient portfolio rp of risky assets, there exists a portfolio on the lower part of the portfolio frontier, rzp , which is uncorrelated with it. Its β deﬁned as Cov(rp , rzp )/V ar(rp ) is therefore 0. That’s why the model is called...

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