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 regressions, we find several significant estimation results. Dell has the highest correlation with the index. Also Dell has the highest R Square of 0.44, which means 44% of the variance of Dell’s excess returns is explained by the variation in the excess returns of the index. Other three corporations of R Square are much similar but a little lower than Dell. For another key variable of alpha, which indicates whether the security is a good or bad buy, these four corporations has the different numbers but only Dell has a negative number comparing with other three corporations....

...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...

...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...

...SHARPE’S PORTFOLIO THEORY
This model was developed by William Sharpe. According to Sharp’s model, the theory estimates the expected return and variance of indices which may be one or more and are related to economic activity. This theory has come to be known as Market Model.
Sharpe’s single indexmodel will reduce the market related risk and maximize the returns for a given level of risk. Sharpe’s model will take into consideration the total risk of portfolio. The total risk consists of both systematic and unsystematic risk. The risk may be eliminated by diversification. If the diversification is perfect and unsystematic risk is negligible, then it is very easy to overcome the systematic risk.
Assumptions:
1. The securities returns are related to each other.
2. The expected return and variances of indices are the same.
3. The return on individual securities is determined by unpredictable factors.
The return on security’s increases or decreases is depending upon a great extent in the market index. The movement of security return shows the correlation with the market index. The individual security’s return is determined by the following equation:
Ri = αi + βiI + ei
Where,
Ri = Expected return on security
αi = Alpha coefficient
βi = Beta coefficient
I = the level of market return index
ei = Error (residual risk of a...

...Chapter 8 IndexModels 163 Multiple Choice Questions 1. As diversification increases the total variance of a portfolio approaches ____________. A 0 B 1 C the variance of the market portfolio D infinity E none of the above Answer: C Difficulty: Easy Rationale: As more and more securities are added to the portfolio unsystematic risk decreases and most of the remaining risk is systematic as measured by the variance of the market portfolio. 2. Theindexmodel was first suggested by ____________. A Graham B Markowitz C Miller D Sharpe E none of the above Answer: D Difficulty: Easy Rationale: William Sharpe building on the work of Harry Markowitz developed the indexmodel. 3. A single-indexmodel uses __________ as a proxy for the systematic risk factor. A a market index such as the SampP 500 B the current account deficit C the growth rate in GNP D the unemployment rate E none of the above Answer: A Difficulty: Easy Rationale: The single-indexmodel uses a market index such as the SampP 500 as a proxy for the market and thus for systematic risk. Chapter 8 IndexModels 164 4. The Security Risk Evaluation book published by Merrill Lynch relies on the __________ most recent monthly observations to calculate regression parameters. A 12 B 36 C 60 D 120 E none of the above Answer: C...

...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...

...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...

...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 5-year period (60 observations) monthly returns for 48 industry...

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