# гЂгяТлЮФЭј

### СЊЯЕЗНЪН

##### SUMMATIVE ASSIGNMENT

ТлЮФзїепЃКСєбЇЩњТлЮФТлЮФЪєадЃКзївЕ AssignmentЕЧГіЪБМфЃК2010-06-01БрМ­ЃКanneЕуЛїТЪЃК2168

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SUMMATIVE ASSIGNMENT
Question 1
a) The probability that a person has a certain disease is 0.03. Medical diagnostic tests are available to determine whether the person actually has the disease. If the disease is actually present, the probability that the medical diagnostic test will give a positive result (indicating that the disease is present) is 0.90. If the disease is not present, the probability of a positive test result (indicating that the disease is present) is 0.02. Suppose that the medical diagnostic test has given a positive result (indicating that the disease is present). What is the probability that the disease is actually present? What is the probability of a positive test result?
(8 marks)
b) A study showed that in 2004 only 24 percent of UK income earners aged 15 and older invested directly in stocks. If a random sample of 20 UK income earners aged 15 and older is selected, what is the probability that:
i) all 20 invest in stocks?
ii) no more than 15 invest in stocks?
iii) more than 10 invest in stocks?
iv) what assumptions did you have to make to answer i) ЈC iii)?
(7 marks)
c) A random sample of 172 accounting students was asked to rate on a scale from one (not important) to five (extremely important) starting salary as a job characteristic. The sample mean rating was 3.31 and the sample standard deviation was 0.70. Test at the 1 percent significance level the null hypothesis that the population mean rating is at most 3.0 against the alternative that it is bigger than 3.0
(5 marks)
Question 2
In the file QUESTION2.xls each of you has been allocated the monthly time series of the closing prices of the DataStream-calculated Swiss market index (SMI) as well as one of its current constituent stocks for the January 2000 ЈC December 2007 period (96 monthly observations).
a) Obtain descriptive statistics on the time series of log-differenced returns for both the SMI as well as the selected stock and comment on them.
(5 marks)
b) Using the single-factor Capital Asset Pricing Model
Ri,t = a + ІТ(Rm,t ЈC Rf,t) + ІХi,t,
where Ri,t  is the return on the selected stock, Rf,t  is the 3-month Swiss interbank rate and Rm,t  is the return on the SMI:
i) obtain estimates for the a and ІТ coefficients; discuss and interpret these results
ii) provide a definition of multicollinearity, heteroscedasticity and autocorrelation biases, their sources and implications and propose possible remedies for them
iii) investigate whether any of the above biases are present in your model, using suitable econometric tests where appropriate. If any of the above biases appear in your model try to correct for it using one of the remedies you discussed in ii)
(20 marks)
c) We now extend the Capital Asset Pricing Model by including the Size (SML), Book-To-Market (HML) and Momentum (MOM) variables in its construction according to Carhart (1997), such that it now becomes:
Ri,t = a + ІТ(Rm,t ЈC Rf,t) + ІУSMLi,t + ІФHMLi,t +ІЫMOMi,t + ui,t
On the basis of the above information:
a) obtain estimates for the a, ІТ, ІУ, ІФ and ІЫ coefficients; discuss and interpret these results
b) evaluate whether any of the aforementioned three biases (multicollinearity, heteroscedasticity, autocorrelation) appear in your results. If so, apply relevant remedial measures you presented in b)БОТлЮФгЩгЂгяТлЮФЭјЬсЙЉећРэЃЌЬсЙЉТлЮФДњаДЃЌгЂгяТлЮФДњаДЃЌДњаДТлЮФЃЌДњаДгЂгяТлЮФЃЌДњаДСєбЇЩњТлЮФЃЌДњаДгЂЮФТлЮФЃЌСєбЇЩњТлЮФДњаДЯрЙиКЫаФЙиМќДЪЫбЫїЁЃ

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