1. Medco Construction Company builds medical buildings in lower income, urban areas. It is typically assumed that the construction time in days follows a normal distribution. The mean time for construction of a medical building is 100 days, and the variance is 400. Business has picked up for building such facilities as a result of changes in medical insurance requirements. The financial manager of Medco just signed a contract to complete construction on a building in 90 days. Failure to complete the medical facility in the contracted time (90 days) would result in severe penalties but the financial manager knew that Medco needed this contract in order to not go bankrupt.
a. What is the probability that Medco Construction will be in violation of their construction contract?
b. What is the probability that they will not be in violation?
c. What is the probability that the triplex will take between90 and 100 days?
2. Suppose you have some money to invest, for simplicity assume that it is $1, and you put a fraction w of it into a stock market mutual fund and the rest, (1-w), into a bond mutual fund. Suppose that $1 invested in a stock fund yields Rs after one year and that $1 invested in a bond fund yields Rb .Here we will assume Rs is random (variable) with mean 15 (15%) and standard deviation 22 (22%), and whereRb is random (variable) with mean 8 (8%) and standard deviation 12 (12%). For this problem, the correlation between Rb and Rs is 0.
If you place a fraction w of your money in the stock fund and the rest (1-w) in the bond fund, then the return on your investment (portfolio) is R = wRs + (1-w)Rb.
a. Suppose that w = 1/3. Compute the mean and standard deviation of R.
b. Suppose that w = 1/2. Compute the mean and standard deviation of R.
c. What value of w makes the mean of R as large as possible? What is the standard deviation of R for this value of w?
d. Would a risk-averse individual prefer to invest all of their money in either the stock fund exclusively or in the bong fund exclusively, or divided between the two funds? Use the information in the problem to discuss your answer. You might want to differentiate between relative levels of risk-averseness.
3. REPEAT QUESTION 2a ONLY, BUT FOR THIS Problem YOU WILL ASSUME THAT THE CORRELATION BETWEEN RbAND Rs IS -1.0. Then answer part b* for this problem.
That is,
a. Suppose that w = 1/3. Compute the mean and standard deviation of R.
NEW QUESTION b.:
b. Compare the mean and the standard deviations for 2a (where corr(Rb ,Rs )=0 ) and 3a. (wherecorr(Rb ,Rs )= -1.0), both usingw = 1/3. That is, compare your results from each part of question 2a.with those from question 3a. Discuss briefly your results (what patterns do you notice).
4. Compute the p-value in the following cases:
