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大概题目如下
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Economics 300 Homework#3 Due in class 7/13
#1 50 points
There are two purposes to this homework: to introduce amodel in which the intercept is important and not an artefact; and to use astatistical test for a non-statistical hypothesis.
The validity of the famous Capital Asset Pricing Model can be tested statistically with the following model:
freturn = β0+ β1mreturn
wherefreturn is the stock's excess return and mreturn is themarket's excess return. The excess return is over and above the risk free rateof return, often taken to be the 3-month Treasury bill rate return. You do not needto know how those rates are calculated.
Implications from the theoretical CAPM model.
If the CAPM is valid (true)then β0 = 0.
If β0≠0, then the CAPM is notvalid (false).
These implications are notstatistical.
Note that if β0 = 0 nothing is implied about the CAPM. If β0= 0, the CAPM may be valid or may not be valid.
Testing whether β0 = 0 is a statistical test ofthe CAPM.
- If β0≠0,we can reject the CAPM (a statistical rejection does not imply the CAPM isfalse or true).
- If β0= 0 then we do not know if the CAPM is valid or not (statistically accepting β0= 0 does not imply anything about the CAPM).
With a statistical test we can not prove truth or untruth.Wecan accept or reject. Using the words accept and reject implies we meanstatistically accept or statistically reject.
If we accept the statisticalhypothesis β0 = 0, we might say we havestatistically failed to reject the CAPM because the only way tostatisticallyreject the CAPM is β0≠0. Theusage here seems appropriate. We also have statisticallyfailed to accept the CAPM!Failed toreject is notapplied to a statistical hypothesis nor is failedto accept. The CAPM implies β0= 0. If we accept the statistical hypothesis that β0 = 0we have not rejected the CAPM but neither have weconfirmed it – we have only accepted one of its conclusions. This is a sense inwhich the wording 'fail to reject' or 'fail to accept' applies.
The statistical hypothesis is the classical 7assumptionsAND β0 = 0, thestatistical hypothesis we accept or we reject.
Use the data in http://econ413.wustl.edu/adata/capm.wf1.The data has 192 observations over time foreach of 2 firms. It is arranged so thatthere are a total of 384 observations and this data set is aTimeSeries/CrossSection. It is not arranged as a Panel data set.
Attach your EVIEWSoutput
a) If you assume the CAPM is valid, then you can test thevalidity of the modelby testing β0in the regression:
freturn = β0 + β1mreturn
[url=](In Eviews[/url]LS freturn C mreturn)[AW1]
Why can you statistically testthe validity of the CAPM?
b) Determine whether you accept or reject the statisticalhypothesis β0=0.
Doyou fail to accept or fail to reject that the CAPM is valid?
Include your output and stateexactly what the tested hypothesis is, and why that tested hypothesis isaccepted or rejected. (Note that the tested hypothesis is accepted or rejected– “fail to accept” or “fail to reject”cannot be used with a statistical test).
c) If you reject the maintained aboutβ0, whatcan you say about the validity of the CAPM?
d) If you accept the maintained about β0, whatcan you say about the validity of the CAPM?
#2 50 points (based on Studenmund #5 pages 111-112)
Edward Saunders published an article that tested thepossibility that the stock market is affected by the weather on Wall Street.Using daily data from 28 years, he estimated an equation with the followingsignificant variables (standard errors in parentheses):
a) Which of the Classical Assumptions would be violated ifyou decided to add a dummy variable to the equation, call it TWTF, that wasequal to 1 if the ith day was a Tuesday, Wednesday, Thursday, or Friday, andequal to 0 otherwise? (HINT: The stock market is not open on weekends.HINT: ShowM + TWTF = C=1 for all observations.)
b) Carefully state the meaning of the coefficients of M.
c) The variable C (terribly named due to the ambiguitywith the intercept C – Saunders likely did not use Eviews!) is a measure of thepercentage of cloud cover from sunrise to sunset on the ith day and reflectsthe fact that approximately 85 percent of all New York’s rain falls on dayswith 100 per-cent cloud cover.
Is C a dummy variable?
What assumptions (or conclusions) did the author have to make to use thisvariable?
(Hint: C can take three values, -1,0 and 1. Using the estimated coefficient, what are the three different effects onDJ)
What constraints does it place on the MODEL?
(We will discuss this at length in dummy variables)
d) Saunders concludes that these findings cast doubt onthe hypothesis that security markets are entirely rational. Based just on thesmall portion of the author’s work that we include in this question, would youagree or disagree? Why?
#3 48 points(based on #11 page 154-155)
Thomas Bruggink and David Rose estimated a regression forthe annual team revenue for Major League Baseball franchises:
a) The authors originally expected a negative coefficientfor S.
Their explanation for the unexpected positivesign was that teams in older stadiums have greater revenue because they’rebetter known and have more faithful fans. That is an explanation (excuse) and not a proof?
Do you think they should have changed their expected sign?What if the Tstatistic was 12 rather than 1?
b) Assume that your team is in last place with P = 350.According to this regression equation, would it be profitable to pay $ 7million a year to a free agent who would raise the team’s winning rate P to500? Be specific.
c) R, P, M, S, and T are horrible names for variables.Make better names for those variables.
[AW1]Dowe need to put this?
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