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

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 the zero-beta CAPM. Let γ = E(rzp ), then the theory says that E(Rt − γ) = βE(Rpt − γ) We can estimate the model asset by asset using nonlinear least square (NLS). The formula must be in the form r = γ(1 − β) + βRm . Let g and b be γ and β, we can compare the estimates of γ as follows: > > + + + + + + model > > > > >

...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 investment risk of very risky...

...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 risk as well?...

...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 ... and Johan Lyhagen for their help with...

...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 5-year period...

...CAPM Project
1.
| T-bill | S&P 500 | Microsoft | Dell | Exxon | GM | IBM | Ford |
Average | 0.00351 | 0.00838 | 0.02632 | 0.03673 | 0.01284 | 0.00725 | 0.01069 | 0.00690 |
SD | 0.00154 | 0.03996 | 0.10257 | 0.15161 | 0.04580 | 0.09327 | 0.08761 | 0.09430 |
2.
| T-bill | S&P 500 | Microsoft | Dell | Exxon | GM | IBM | Ford |
T-bill | 1.00000 | 0.06922 | 0.13241 | 0.06114 | 0.03865 | -0.00266 | 0.04134 | -0.02359 |
S&P 500 | | 1.00000 | 0.54399 | 0.43517 | 0.45093 | 0.44741 | 0.54018 | 0.50752 |
Microsoft | | | 1.00000 | 0.52712 | 0.13734 | 0.12264 | 0.46422 | 0.22796 |
Dell | | | | 1.00000 | 0.06558 | 0.17795 | 0.36041 | 0.26893 |
Exxon | | | | | 1.00000 | 0.20574 | 0.25684 | 0.24470 |
GM | | | | | | 1.00000 | 0.27395 | 0.56059 |
IBM | | | | | | | 1.00000 | 0.25477 |
Ford | | | | | | | | 1.00000 |
3.
a) Because T-bills are bonds issued by the U.S. government, they are virtually default free. Therefore, they have very low risk and returns on T-bills do not vary a lot over time and its standard deviation is small.
(b) Because Microsoft, Dell and IBM all belong to the same industry; therefore, events that affect that industry will have effects on these three companies as well. If Dell and IBM’s computers don’t sell well or the demand is low, Microsoft will sell less software. Therefore, all of the three companies tend to move together and the correlation coefficient between returns...

...CAPM
1 Calculate the expected return for A Industries which has a beta of 1.75 when the risk free rate is 0.03 and you expect the market return to be 0.11.
2 Calculate the expected return for B Services which has a beta of 0.83 when the risk free rate is 0.05 and you expect the market return to be 0.12.
3 Calculate the expected return for C Inc. which has a beta of 0.8 when the risk free rate is 0.04 and you expect the market return to be 0.12.
4 Calculate the expected return for D Industries which has a beta of 1.0 when the risk free rate is 0.03 and you expect the market return to be 0.13.
5 Calculate the expected return for E Services which has a beta of 1.5 when the risk free rate is 0.05 and you expect the market return to be 0.11.
6 Calculate the expected return for F Inc. which has a beta of 1.3 when the risk free rate is 0.06 and you expect the market return to be 0.125.
USE THE FOLLOWING INFORMATION FOR THE NEXT FIVE PROBLEMS
Rates of Return
Year RA Computer Market Index
1 13 17
2 9 15
3 -11 6
4 10 8
5 11 10
6 6 12
7 Compute the beta for RA Computer using the historic returns presented above.
8 Compute the correlation coefficient between RA Computer and the Market Index.
9 Compute the intercept of the characteristic line for RA Computer.
10 The equation of the characteristic line for RA is
11 If you expected return on the Market Index to be 12%, what would you expect the return on RA Computer to be?
USE THE...

...Introduction of Ford Motor Company
Ford Motor Company is the world's largest producer of cars and trucks combined. Ford has manufacturing, assembly or sales affiliates in 34 countries. Ford companies employed 337,800 people world-wide in 1996.
Ford has manufacturing facilities in 22 countries on 5 continents, with 87 plants in North America and 41 in Europe. Europe 1995, Ford's combined vehicle market share, at 12.2%, was the highest for eleven years, with three of the eight best-selling cars.
On January 1, 1995, Ford merged its North American Automotive Operations and its European Automotive operations into a single organization, Ford Automotive Operations. Instead of being organized by geographic regions, the Company is now realigned by product line, with five Vehicle Centers, each responsible for one group of products worldwide. At the same time, Ford is reducing the time taken to develop a new vehicle from 48 to 24 months and reducing engines, transmissions, and basic vehicle platforms by 30% worldwide. Ford hopes that by pooling global skills and resources will result in more variations on each vehicle platform, increasing the number of vehicles introduced over the next five years by 50%.
Case Abstract
The case involving the explosion of Ford Pinto's due to a defective fuel system design led to the debate of many issues, most centering around the use by Ford of a cost-benefit analysis and the ethics surrounding its decision not to upgrade the fuel system based...

...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...