Questions
You have the following information on 2 risky securities: a and b. Assume that the Risk-Free...

You have the following information on 2 risky securities: a and b.

Assume that the Risk-Free rate of interest is 2.0% per year. Please show all work.

Scenario Probability Return for Security a Return for Security b
Excellent 25.00% -10.00% 10.00%
Good 25.00% 5.00% 40.00%
Average 25.00% 15.00% -24.00%
Bad 25.00% 25.00% 18.00%

a) Find the Expected Return for the Minimum Variance Portfolio (M*) and The Standard Deviation of the Minimum Variance Portfolio (M*).

b) Find the Weight of Security i in the Optimal Portfolio (P*) and The Weight of Security j in the Optimal Portfolio (P*).

c) Find the Expected Return of the Optimal Portfolio (P*) and The Standard Deviation of the Optimal Portfolio (P*).

d) The Sharpe Ratio of Optimal Portfolio (P*) or the Highest Sharpe Ratio

In: Finance

A pension fund manager is considering three mutual funds. The first is a stock fund, the...

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a rate of 3%. The probability distribution of the funds is as follows:

Expected Return

Standard Deviation

Stock Fund

20%

40%

Bond Fund

10%

15%

Risk-free

3%

Correlation

20%
  1. Find the investment proportions in the minimum variance portfolio (MVP) of the two risk asset (5 points)
  2. Find the expected return and standard deviation for the minimum variance portfolio (5 points)
  3. What portion of your wealth should go to S and B respectively to achieve the tangent portfolio (i.e., the portfolio with the highest Sharpe ratio) (5 points)

In: Finance

On a planet far far away from Earth, IQ of the ruling species is normally distributed...

On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 103 and a standard deviation of 17. Suppose one individual is randomly chosen. Let X = IQ of an individual.

a. What is the distribution of X? X ~ N(,)

b. Find the probability that a randomly selected person's IQ is over 85.  Round your answer to 4 decimal places.

c. A school offers special services for all children in the bottom 7% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places.

d. Find the Inter Quartile Range (IQR) for IQ scores. Round your answers to 2 decimal places.
Q1:
Q3:
IQR:

In: Statistics and Probability

On a planet far far away from Earth, IQ of the ruling species is normally distributed...

On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 100 and a standard deviation of 16. Suppose one individual is randomly chosen. Let X = IQ of an individual.

a. What is the distribution of X? X ~ N( ,

b. Find the probability that a randomly selected person's IQ is over 116. Round your answer to 4 decimal places.

c. A school offers special services for all children in the bottom 3% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places.

d. Find the Inter Quartile Range (IQR) for IQ scores. Round your answers to 2 decimal places. Q1: Q3: IQR:

In: Statistics and Probability

Q2) A pension fund manager is considering three mutual funds. The first is a stock fund,...

Q2) A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a rate of 3%. The probability distribution of the funds is as follows:

Expected Return

Standard Deviation

Stock Fund

20%

40%

Bond Fund

10%

15%

Risk-free

3%

Correlation

20%
  1. Find the investment proportions in the minimum variance portfolio (MVP) of the two risk asset (5 points)
  2. Find the expected return and standard deviation for the minimum variance portfolio (5 points)
  3. What portion of your wealth should go to S and B respectively to achieve the tangent portfolio (i.e., the portfolio with the highest Sharpe ratio) (5 points)

In: Finance

A pension fund manager is considering three mutual funds. The first is a stock fund, the...

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a rate of 3%. The probability distribution of the funds is as follows:

Expected Return

Standard Deviation

Stock Fund

20%

40%

Bond Fund

10%

15%

Risk-free

3%

Correlation

20%
  1. Find the investment proportions in the minimum variance portfolio (MVP) of the two risk asset (5 points)
  2. Find the expected return and standard deviation for the minimum variance portfolio (5 points)
  3. What portion of your wealth should go to S and B respectively to achieve the tangent portfolio (i.e., the portfolio with the highest Sharpe ratio) (5 points)

In: Finance

On a planet far far away from Earth, IQ of the ruling species is normally distributed...

On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 105 and a standard deviation of 14. Suppose one individual is randomly chosen. Let X = IQ of an individual.

a. What is the distribution of X? X ~ N(,)

b. Find the probability that a randomly selected person's IQ is over 97. Round your answer to 4 decimal places.

c. A school offers special services for all children in the bottom 4% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places.

d. Find the Inter Quartile Range (IQR) for IQ scores. Round your answers to 2 decimal places.

Q1:

Q3:

IQR:

In: Math

On a planet far far away from Earth, IQ of the ruling species is normally distributed...

On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 119 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual. a. What is the distribution of X? X ~ N( 119 , 15 ) b. Find the probability that a randomly selected person's IQ is over 113. Round your answer to 4 decimal places. c. A school offers special services for all children in the bottom 2% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places. d. Find the Inter Quartile Range (IQR) for IQ scores. Round your answers to 2 decimal places. Q1: Q3: IQR:

In: Math

A manager of a holiday specialty store must determine how many temporary workers to hire for...

A manager of a holiday specialty store must determine how many temporary workers to hire for the holiday season. Estimated revenues (thousands of dollars) are based on poor, good, and excellent economic conditions and whether one, two or three workers are hired as follows:

Economic Condition
Workers Hired Excellent Good Poor
One 50 50 50
Two 100 60 20
Three 150 70

-10

22. If a Maximax strategy is used, how many workers should be hired?

a. one

b. two

c. three

d. either one or two

e. either two or three

23. If a Maximin strategy is used, how many workers should be hired?

a. one

b. two

c. three

d. either one or two

e. either two or three

24. If an Equally Likely strategy is used, how many workers should be hired?

a. one

b. two

c. three

d. either one or two

e. either two or three

25. If it’s determined that there’s a 20% chance of excellent, 30% chance of good, and 50% chance of poor economic conditions, what’s the expected value of alternative #2--hiring two workers?

a. $16000

b. $26000

c. $46000

d. $48000

e. $50000

26. A Risk Taker (decision maker) would choose the project with

       a. The highest Coefficient of Variation

       b. The highest Expected Value

       c. The highest Standard Deviation

      d. The lowest Coefficient of Variation

      e. The lowest Standard Deviation

27. A Risk Averse (decision maker) would choose the project with

       a. The highest Coefficient of Variation

       b. The highest Expected Value

       c. The highest Standard Deviation

      d. The lowest Coefficient of Variation

      e. The lowest Standard Deviation

28. A Risk Neutral (decision maker) would choose the project with

       a. The highest Coefficient of Variation

       b. The highest Expected Value

       c. The highest Standard Deviation

      d. The lowest Coefficient of Variation

      e. The lowest Standard Deviation

In: Operations Management

1.Two dice are tossed 432 times. How many times would you expect to get a sum...

1.Two dice are tossed 432 times. How many times would you expect to get a sum of 5?
———-
2.Sam is applying for a single year life insurance policy worth $35,750.00. If the actuarial tables determine that she will survive the next year with probability 0.996, what is her expected value for the life insurance policy if the premium is $433.00 ?

————-
3.A raffle is being held at a benefit concert. The prizes are awarded as follows: 1 grand prize of
$6,200.00, 3 prizes of $1,000.00, 4 prize of $92.00, and 12 prizes of $25.00.

————
4.Find the expected value for the random variable:

X 1 3 4 6
P(X) 0.21 0.12 0.23 0.44

————
5.Suppose that from a standard deck, you draw three cards without replacement. What is the expected number of aces that you will draw?

———-
6.Consider 3 trials, each having the same probability of success. Let
X
X
denote the total number of successes in these trials. If E[X]=0.6, find each of the following.
(a) The largest possible value of P{X=3}:
P{X=3}≤

(b) The smallest possible value of P{X=3}:
P{X=3}≥

In this case, give possible values for the remaining probabilities:
P{X=0}=

P{X=1}=

P{X=2}=

————-
7.It is reasonable to model the number of winter storms in a season as with a Poisson random variable. Suppose that in a good year the average number of storms is 5, and that in a bad year the average is 8. If the probability that next year will be a good year is 0.3 and the probability that it will be bad is 0.7, find the expected value and variance in the number of storms that will occur.
expected value =
variance =

———-
8.In a popular tale of wizards and witches, a group of them finds themselves in a room with doors which change position, making it impossible to determine which door is which when the room is entered or reentered. Suppose that there are 4 doors in the room. One door leads out of the building after 3 hours of travel. The second and third doors return to the room after 5 and 5.5 hours of travel, respectively. The fourth door leads to a dead end, the end of which is a 2.5 hour trip from the door.

If the probabilities with which the group selects the four doors are 0.2, 0.1, 0.1, and 0.6, respectively, what is the expected number of hours before the group exits the building?

E[Number of hours]=

———-
9.For a group of 100 people, assuming that each person is equally likely to have a birthday on each of 365 days in the year, compute
(a) The expected number of days of the year that are birthdays of exactly 4 people:
E[days with 4 birthdays]=

(b) The expected number of distinct birthdays:
E[distinct birthdays]=

————
10.Consider 35 independent flips of a coin having probability 0.5 of landing on heads. We say that a changeover occurs when an outcome is different from the one preceding it. Find the expected number of changeovers.
E[changeovers]=

In: Statistics and Probability