Analytical Methods in Economics and Finance
The capital asset pricing model (CAPM) is an important model in the field of finance/financial economics. It explains variations in the rate of return on a security as a function of the rate of return on a portfolio consisting of all publicly traded stocks, which is known as the market portfolio. Generally, the rate of return on any investment is measured relative to its opportunity cost, which is measured as the return on a risk-free asset. The resulting difference is called the risk premium, since it is the reward or punishment for making a risky investment. The CAPM says that the risk premium on securityj is proportional to the risk premium on the market portfolio. That is,
Where rjand rfare the returns to security j and the risk-free rate, respectively, rm is the return on the market portfolio, and is the j’th security’s “beta” value. A stock’s beta is important to investors because it reveals the stock’s volatility. It measures the sensitivity of security j’s return to variation in the whole stock market. As such, values of beta less than one (1) indicate that the stock is ‘defensive’, since its variation is less than the market’s. A beta greater than one (1) indicates an ‘aggressive stock.’ Investors usually want an estimate of a stock’s beta before purchasing it. The CAPM model shown above is the ‘economic model’ in this case. The ‘econometric model’ is obtained by including an intercept in the model (even though theory says it should be zero) and an error term,
Data:
Please download the required data kept in the file ‘Assignmentdata_T12013’ in excel format from the CloudDeakin site. The file contains data on monthly returns of two firms, viz., Microsoft (MSFT) and Mobil-Exxon (XOM) from January 1998 to December 2008, with 132 observations.These data are reported in the worksheet labelled ‘DataBasic’. On this worksheet, the first column is named “OBS”, under which you will find the observation dates. The second (column B)and the third column (Column C) entitled “MSFT” and “XOM”report returns of Microsoft and Mobil, respectively. The last two columns represent the rate of return on the market portfolio (MKT), and the rate of return on the risk free asset (RISKFREE). Also, note that additional data are provided on worksheet labelled ‘IPINdex&InterestRateData’. These data are explained in part (h) below.
You should use MSExcel for your statistical analysis to answer the following questions.Please make sure you include all your regression output as an appendix to your submission.
(a) Using XOM and MKT data plot the returns for the entire period and comment on the relative fluctuations of these two variables. [2]
(b) Calculate and construct the series of the risk premium on Microsoft and Mobil-Exxon. Also calculate the risk premium on the market portfolio for the entire period.Use the data for “MSFT”, “XOM”, “MARKET” and “RKFREE”. [3]
(c) Present the descriptive statistics of monthly returns of MSFT and XOM. Interpret and compare the measures of central tendency and deviation of the variables. [3]
(d) Estimate the CAPM model for Microsoft and Mobil-Exxon, and comment on their estimated beta values. [4]
(e) Finance theory suggests that the intercept parameter should be zero. Does this seem correct given your estimates? [2]
(f) Suppose a financial consultant believes that Microsoft’s beta value is equal to 1. Test the consultant’s claim of Microsoft’s beta value at 1% level of significance against the alternative that it is less than one. Interpret your result. [2]
(g) Predict the risk premium for Microsoft and Mobil-Exxon given the risk premium for market portfolio of 7%. [2]
(h) Econometricians often find it useful to examine the impact of a number of economic variables such as Industrial Production and Interest rate on the risk premium of a specific security. Incorporating these two explanatory variables, viz. US Industrial production index and US Interest Rates (Federal Funds Rate) in the CAPM, estimate the following model for both Microsoft and Mobil-Exxon:
Where the variables Y and R represent US Industrial Production Index and US Interest Rates, respectively. These data are provided in the worksheet labelled ‘IPIndex&InterestRateData’ in the excel datafile. [4]
(i) Do you think that the risk premium on the market portfolio, Industrial production index and interest rate jointly explain the risk premium for Microsoft and Mobil-Exxon’s securities? Explain your answer. [4]
(j) Test whether industrial production and Interest rate together significantly explain Mobil-Exxon’s risk premium. [2]
(k) Briefly summarize your findings about Microsoft’s and Mobil-Exxon’s stock and their relationship to the stock market. [2]
Notes: This is an individual assignment. All Excel worksheets should be attached at the end of your submitted assignment. These should clearly demonstrate the work undertaken independently by you. Submissions should be made both in hardcopy and online on DSO. On-campus students must submit to the campus specific faculty office while the off campus students submit the assignments as per the information provided in the unit guide and should contact the Division of Student Affairs (DSA).
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