CAPM is a model which enables investors to determine the expected return from a risky security. It observes the relationship between the risk of an asset (Mobil Oil) and its return. The model uses Beta as the main measure of risk. This model works under the following situations: • In a perfectively competitive market where they are many price-takers’ investors, who have a small market share each. • Investors behaviour is myopic

• Also investments included in the model are publicly traded financial assets such as bonds and stocks. Investors borrow or lend at a risk free rate. Investors have no transactions cost and do not pay taxes on returns • All investors in the market are rational mean variance optimisers. • Finally, investors have homogenous expectations which imply that they analyse securities in the same way, share the same economic view of the world, therefore they share identical estimates of probability distributions of cash flows.

Beta shows the relationship between the expected return of a stock and the return of the financial market as a whole. In relation to this project, it measures the elasticity of Mobil’s Oil returns in relation to the market index. It is calculated as:

Beta (Mobil) = Covariance (Return of Mobil oil, Return of Market) / Variance (Return of Market).

Using Linear least squares, the estimated beta is the same as that calculated using Regression analysis on Excel. Estimated Beta is 0.714 which implies that the total return of Mobil Oil’s stock is likely to move up and down 71.4% of the time when the market changes. As 0.714 < 1, Mobil Oil’s stock is less volatile than the overall Market Portfolio.

Due to CAPM being a simplified model, Beta has to be tested to see if this Beta value for Mobil Oil (0.714) is accurate. By this, I tested if there is a relationship between Mobil’s Oil Return and the Market. H0: hypothesised slope=0. An alternative hypothesis is that there is a relationship between Mobil...

...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 difference between 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 systematic risk (β), SML shows the...

...Pricing 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...

...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 CAPMmodel 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...

...The CAPM and the Index Model report
Introduction
In this report, our group considers four large U.S. corporations, which are Apple, Dell, Nike and Home depot. By using the CAPM and the index model to analyze these four stocks and diversification, we collect data source over the period January 2008 to December 2012 from yahoo finance and process it to show a brief summary below:
Over the period January 2008 to December 2012, we calculate the returns for each corporation each month by using the monthly price of each corporation. After using the same method to calculate the market return and T-bill return, we find that the monthly average return for the market index is 0.10%, which is higher than the monthly average return for T-bills of 0.03%. Comparing with four large U.S. corporations, only Dell has a negative monthly average return. Also comparing each corporation with the market return, we can see that when the market moves, all four corporations tend to move in the same direction, but Apple and Dell have greater amounts while Nike and Home Depot have lower amounts. That means both Apple and Dell have a higher volatility than the market; however, Nike and Home Depot have a lower volatility than the market. By using the index model regression, also we can prove this conclusion by comparing the Beta. In addition, according to the four index model...

...Introduction
Capital asset pricing has always been an active area in the finance literature. Capital Asset Pricing Model (CAPM) is one of the economic models used to determine the market price for risk and the appropriate measure of risk for a single asset. The CAPM shows that the equilibrium rates of return on all risky assets are function of their covariance with the market portfolio. This theory helps us understand why expected returns change through time. Furthermore, this model is developed in a hypothetical world with many assumptions.
The Sharp-Lintner-Black CAPM states that the expected return of any capital asset is proportional to its systematic risk measured by the beta. (Iqbal and Brooks, 2007). Based on some simplifying assumptions the CAPM is expressed as a linear function of a risk free rate, beta and the expected risk premium. An important quantity required for decisions on evaluating public and private funded projects is an appropriate cost of capital. This discount rate is often estimated by a model of expected return. The CAPM has been extensively employed for estimating cost of capital and evaluating the performance of managed funds.
Various studies had been performed by various researchers on the capital asset pricing model in different type of markets across the countries around the world. Some of the...

...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 between CAPM 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...

...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...

...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...

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