Homework 5 due Mar 11 Thursday K Foster, Options & Futures, Eco 275, CCNY, Spring 2010

 

You are encouraged to form study groups to work on these problems.  However each student must hand in a separate assignment: the group can work together to discuss the papers and comment on drafts, but each study group member must write it up herself/himself.  When emailing assignments, please include your name and the assignment number as part of the filename.

Please write the names of your study group members at the beginning of your homework to acknowledge their contributions.

1. Create a vector of 100 standard normal random numbers; find its mean and standard error.  Do this 1000 times, recording the means and standard errors each time.  Plot a histogram of the results.  Does it look like a normal distribution?  (Should it?)  Explain.
2. Consider hypothesis testing with the random draws from the previous question.  Suppose you have a new sample with an average of 0.01.  How many of the 1000 random draws have a larger mean (in absolute value)?  This is a bootstrap p-value.  Compare this with a p-value that you would look up in a table; discuss how they relate.
3. Starting from the program you created above, create a vector of 100 random numbers from 5 different distributions (use Matlab's canned random numbers and/or experiment with functions of these); find the means and standard errors.  Do each 1000 times.  Plot histograms of each.  Do they look like normal distributions?  Discuss.  Can you break it and find something clearly non-normal?
4. For each of the five different distributions, get a bootstrap p-value for a new sample with average of 0.01.  Discuss the relationship to the Law of Large Numbers.
5. Please complete Assignment Question 10.19 in Hull.
6. Please complete Assignment Question 10.21 in Hull.
7. Please complete Assignment Question 10.23 in Hull.
8. I am considering an investment in the country of Cunystan, which uses currency called the "zing".  Since my home country offers interest rates of just 1.5%, I am looking to get higher returns.  You are my portfolio manager, whose expertise I depend upon.  The currency markets allow investors to buy and sell zing at a spot rate of $1 to 70 zing, and buy and sell forward (in one year) at a rate of $1 to 75 zing.  Cunystan government bonds pay a riskless interest rate of 4% in one year (the zero rate, assuming discrete semiannual compounding).  What investment strategy would you recommend, in this situation?