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Finance

Customer Question

This is due on september 5th at 1pm eastern time


Q1:  Index Models:


Download 61 months (December 2007 to December 2012) of monthly data for the S&P 500 index (symbol = ^GSPC). Download 61 months (December 2007 to December 2012) of Apple Inc. data and 61 months (December 2007 to December 2012) of Exxon Mobil Corporation data. Download 60 months (January 2008 to December 2012) of the 13 week T-bill rate (symbol = ^IRX). Be sure to use end-of-month data! Construct the following on a spreadsheet:


1. Calculate 60 months of returns for the S&P 500 index, Apple and Exxon. Use January 2008 to December 2012. Note this means you need price data for December 2007.  On the answer sheet report the average monthly returns for the S&P 500 index, Apple and Exxon, as well as the average monthly risk-free rate.


2. Calculate excess returns for the S&P 500 index, Apple and Exxon. Note you must divide the annualized risk-free rate (^IRX) by 1200 to approximate the monthly rate in in decimal form.  On the answer sheet report the average monthly excess returns for the S&P 500 index, Apple and Exxon.


3. Regress excess Apple returns on the excess S&P 500 index returns and report, on the answer sheet, α, β, the r-square and whether α and β are different from zero at the 5% level of significance. Briefly explain your inference.


4. Use equation 8.10 to decompose total risk for Apple into systematic risk and firm-specific risk. That is, calculate total risk, systematic risk and firm-specific risk for Apple.


5. Regress excess Exxon returns on the excess S&P 500 index returns and report, on the answer sheet, α, β, the r-square and whether α, β are different from zero at the 5% level of significance.  Briefly explain your inference.


6. Use equation 8.10 to decompose total risk for Exxon into systematic risk and firm-specific risk. That is, calculate total risk, systematic risk and firm-specific risk for Exxon.


7. Use equation 8.10 to estimate the covariance and correlation of Apple and Exxon excess returns.



Q2:  CAPM and APT:


1.  The expected rate of return on the market portfolio is 9% and the risk–free rate of return is 3%.  The standard deviation of the market portfolio is 22%.  What is the representative investor’s average degree of risk aversion?


 


2.  Stock A has a beta of 1.25 and a standard deviation of return of 32%.  Stock B has a beta of 1.95 and a standard deviation of return of 40%.  Assume that you form a portfolio that is 60% invested in Stock A and 40% invested in Stock B.  Using the information in question 1, according to CAPM, what is the expected rate of return on your portfolio?


 


3.  Using the information in questions 1 and 2, what is your best estimate of the correlation between stocks A and B?


 


4.  Your forecasting model projects an expected return of 10% for Stock A and an expected return of 17% for Stock B.  Using the information in questions 1 and 2 and your forecasted expected returns, what is your best estimate of the alpha of your portfolio when using CAPM to determine a fair level of expected return?


 


5.  A different analyst uses a two–factor APT model to evaluate expected returns and risk.  The risk premiums on the factor 1 and factor 2 portfolios are 5% and 4%, respectively, while the risk–free rate of return remains at 3%.  According to this APT analyst, your portfolio formed in question 2 has a beta on factor 1 of 1.7 and a beta on factor 2 of 2.5.  According to APT, what is the expected return on your portfolio if no arbitrage opportunities exist?


 


6.  Now assume that your forecasting model of question 4 accurately projects the expected return of Stocks A and B and therefore your portfolio, and that the APT model of question 5 describes the fair rate of return for your portfolio.  Do any arbitrage opportunities exist?  If yes, would you invest long or short in your portfolio constructed in question 2?


Submitted: 1 year ago.
Category: Multiple Problems
Expert:  F. Naz replied 1 year ago.
It will be my pleasure to do the assignment, please provide equation 8.1. Please also mention your deadline, thanks.
Customer: replied 1 year ago.
The deadline is September 5th at 5pm
The equation is in the book:Investments - 9.Edition - 2011
Bodie, Zvi; Kane, Alex; Marcus, Alan J.
McGraw-Hill
ISBN: 9780073530703
chapter 8 (formula 8.1)
I will only have access to the book tonight!
Expert:  F. Naz replied 1 year ago.
I do not have access to book if you could provide it, thanks.
Customer: replied 1 year ago.

 


Normality of Returns and Systematic Risk


We can always decompose the rate of return on any security,


i,


into the sum of its expected


plus unanticipated components:




ri=E(ri)+ei (8.1)




where the unexpected return,



e i , has a mean of zero and a standard deviation of  i


that


measures the uncertainty about the security return.



When security returns can be well approximated by normal distributions that are correlated



across securities, we say that they are




joint normally distributed.


This assumption


alone implies that, at any time, security returns are driven by one or more common variables.



When more than one variable drives normally distributed security returns, these



returns are said to have a




multivariate normal distribution.


We begin with the simpler


case where only one variable drives the joint normally distributed returns, resulting in a



single-factor security market. Extension to the multivariate case is straightforward and is



discussed in later chapters.



Suppose the common factor,




m,


that drives innovations in security returns is some


macroconomic variable that affects all firms. Then we can decompose the sources of



uncertainty into uncertainty about the economy as a whole, which is captured by




m,


and


uncertainty about the firm in particular, which is captured by




e i


. In this case, we amend


Equation 8.1 to accommodate two sources of variation in return:



ri=E(ri)+m+ei (8.2)

Customer: replied 1 year ago.

Attachment: 2013-09-03_225125_quantitative_problem_set_3_answer_sheet.xlsx

the answers need to be in the attached file and I also need a excel document with all detailed calculations.


Thank you

Expert:  F. Naz replied 1 year ago.

Sorry I have gone through and unable to do this, I am opting out so other experts may help you, take care.

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