Question 1

Ann, a portfolio manager, has two assets under consideration: a "bond" and a "stock."The bond has two possible return values: 5% and 15%. The stock has four possible values of annual return: -8%, 10%, 20% and 30%.

Thejoint distributionofthe returns for the "bond"and"stock"is given in the table below:

"stock"

"bond"

-8%

10%

20%

30%

5%

0.05

0.15

0.15

0.1

15%

0.1

0.2

0.2

0.05

1. Find the expected annual return for the "bond".
2. Find the expected annual return for the "stock".
3. Find the standard deviation of the annual return for the "bond".
4. Find the standard deviation of the annual return for the "stock".
5. Find the covariance between the annual return of the "bond" and the "stock".
6. Find the correlation between the annual return of the "bond" and the "stock".

Ann has five million dollars to invest and she decides to forms a portfolio by investing 3.5 million dollars in "bond" and the rest in "stock".

g. What is the expected return from such a portfolio?

h. Compute the standard deviation of the above portfolio.

i. Using the standard deviation as a measure of financial risk (volatility), how does the risk of the above portfolio compare with the risk of the individual components: "bond" and "stock"?

Question 2

According to IDC, 70% of smartphones in the world use Google's Android operating system in the fourth quarter of 2012. Answers the following questions based on a random sample of 14 smartphones users.

1. What is the probability that exactly 9 people from this sample have a smartphone using the Android operating system?
2. What is the probability that all 14 people from this sample have a smartphone using the Android operating system?
3. What is the probability that 11 or fewer people from this sample have a smartphone using the Android operating system?
4. What are the mean and standard deviation for this distribution?

Question 3

Sara is a salesperson for Camera's Etc. which is a retailer for high-end digital cameras. Historically, Sara has averaged selling 2.1 extended warranties per day for cameras that she sell. Assume the number of camera warranties that Sara sells per day follows the Poisson distribution.

1. What is the probability that Sara will sell five extended warranties tomorrow?
2. What is the probability that Sara will not sell an extended warranty tomorrow?
3. What is the probability that Sara will sell more than two extended warranties tomorrow?
4. What is the standard deviation for this distribution?