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Bonus AM: Variable Identification

Bonus AM: Variable Identification

To be successful in chapter 5 (Risk and Reward) and moving forward, you must understand the

mathematical notation used in equations and be able to identify the elements from the word problems.

For the following word problems, write the equation for what you are solving for (e.g. standard

deviation, expected return, holding period return, etc). Match the mathematical notation of the

equation to the values in the word problem. Then solve the problem.

If you choose to complete this assignment, this assignment grade will replace your current lowest

assignment grade (any assignments that were in violation of the academic integrity policy cannot be

replaced). If the grade that you earn on this assignment is lower than your current lowest assignment

grade, the grade will not be recorded. For example,

There is a 30% chance the total return on Dell Stock will be -3.45%, a 30% chance it will be 5.17%, a 30%

chance it will be 12.07% and a 10% chance it will be 24.14%. Calculate the expected return.

Equation:

Matching: Pr1=30%, Pr2=30%, Pr3=30%, Pr4=10%

K1=-3.45%, k2=5.17%, k3=12.07%, k4=24.14% Solution: E(k)=0.30(-0.0345)+0.30(0.0517)+0.30(0.1207)+0.10(0.2414) = 0.0655 = 6.55% Problem 1:

Bailey has a probability distribution for four states of the economy: fast growth, slow growth, recession,

and depression. The probability for each is 15%, 60%, 20%, and 5%, respectively. Bailey has also

calculated the return a firm would earn under each state as 25%, 15%, -5%, and -20% for fast, slow,

recession, and depression, respectively. What is the firm?s expected return?

Problem 2:

Mackey Motors will return a 40% return in a boom economy, a 10% return in a normal economy, and 25% return in a recession. If there is a 30% chance of a boom economy, 50% chance of normal growth,

and 20% chance of a recession, what?s the standard deviation of returns?

Problem 3:

If you are a baseball player about to be drafted by the New York Yankees and your signing bonus is

determined solely by whether you get a hit or not in your last collegiate at-bat. If you get a hit, your

signing bonus will be $800,000. On the other hand, if you do not get a hit your bonus will be $400,000. You believe that there is a 32.5% chance that you will get a hit and a 67.5% chance that you will not.

What do expect your signing bonus to be?

Problem 4:

You are considering a new radio advertising program for your pizza restaurant. You estimate that there

is a 30% chance that 35 people will visit, a 45% chance that 50 people will visit, and 25% chance that 60

people will visit. How many new customers do you expect to respond to the radio ad?

Problem 5

John is watching an old game show on rerun television called Let?s Make a Deal in which you have to

choose a prize behind one of two curtains. Behind one of the curtains is a gag prize worth $150, and

behind the other is a round-the-world trip worth $7,200. The game show has placed a subliminal

message on the curtain containing the gag prize, which makes the probability of choosing the gag prize

equal to 75%.

What is the expected value of the selection?

What is the standard deviation of that selection?

Problem 6

You have chosen biology as your college major because you would like to be a medical doctor. However,

you find that the probability of being accepted into medical school is about 10%. If you are accepted into

medical school, then your starting salary when you graduate will be $300,000 per year. However, if you

are not accepted (90%), then you would choose to work in a zoo, where you will earn $40,000 per year.

Without considering the additional educational years or the time value of money, what is your expected

starting salary?

What is the standard deviation of that starting salary?

Problem 7

Kate recently invested in real estate with the intention of selling the property one year from today. She

has modeled the returns on that investment based on three economic scenarios. She believes that if the

economy stays healthy, then her investment will generate a 30% return. However, if the economy

softens, as predicted, the return will be 10%, while the return will be a -25% if the economy slips into a

recession. If the probabilities of the healthy, soft, and recessionary states are 0.4, 0.5, and 0.1,

respectively, then what are the expected return for Kate?s investment?

What is the standard deviation for Kate?s investment?

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This question was answered on: * Feb 21, 2020 *

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