Risk management
Homework 1
1) Suppose the returns for two different investment opportunities are as follows. (20 points)
Asset A Asset B
Probability Return Probability Return
0.1 40% 0.2 30%
0.2 30% 0.1 25%
0.3 10% 0.3 20%
0.2 -10% 0.3 0%
0.2 -20% 0.1 -20%
A) What are the expected return and the standard deviation of returns for each asset?
B) Suppose that the correlation between the returns is 0.30. What is the expected return and standard
deviation of return from a portfolio where money is divided equally between the investments?
2) The Texas Department of Insurance publishes data on all the insurance claims closed during a given year.
For the thirteen years from 1990 to 2002 the following table lists the percentage of medical malpractice
claims closed in each year for which the injury actually occurred in the same year.
Year % of injuries in the year that are closed in that year
1990 0.32
1991 1.33
1992 0.86
1993 0.54
1994 0.69
1995 0.74
1996 0.76
1997 1.39
1998 1.43
1999 0.55
2000 0.66
2001 0.72
a) Calculate the mean and standard deviation of % of injuries in the year that are closed in that year
in Texas over the five-year period 1990–1994.
b) Calculate the mean and standard deviation of % of injuries in the year that are closed in that year
in Texas over the five-year period 1995–2001.
c) Looking at your results from (a) and (b), do you think there is any evidence to support the conclusion that % of injuries in the year that are closed in that year are changing in the first and second
five year periods?
3) Select one subject area or company (for example e-commerce, education or coal mining,…) and identify
possible risk exposures associated with the given subject area. Explain the types of exposures. Give some
examples to perils and hazards for the company.
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