directions: Learning how to read mathematical equations and understanding the ma
ID: 3303127 • Letter: D
Question
directions: Learning how to read mathematical equations and understanding the mathematical notation in those equations is CRITICAL for your success in this course. In this assignment, you will learn how to read and “speak” math and improve your math literacy.
Third: Create and complete the chart below. Use the equation editor or insert a symbol to enter the mathematical notation for each variable and write a sentence appropriately using the notation. I have provided an example in the first row for the summation notation.
Item
Notation
What does it measure/ mean
Sentence
Summation notation
This symbol means the addition of a sequence of numbers. The number of values to be added is n, this means if there were four numbers in the sequence (1, 5, 7, 8) then n=4 because x1=1; x2=5; x3=7; and x4=8.
Weight of an individual stock in a portfolio
Expected return on a single stock/ asset
Expected return on the portfolio
Holding period return on a single stock
Probability of a single outcome
Observed return on a single stock
Standard deviation of a specific asset
Number of observed outcomes
Fourth: Using the Equation editor of Word, present the mathematical equation for each of the following and “translate” each into English.
For example:
Translation: The average return for an individual stock is the sum of all the observed returns (ki) in the sample for a given stock divided by the size of the sample (n).
Expected return of a single stock =
Standard deviation of a single stock =
Expected return on a portfolio =
Fifth: Use summation notation to condense the equations presented in your e-text for the following equations:
Expected return on an individual stock =
Sixth: (1) read each word problem, (2) use the equation editor to write the equation used to solve the problem, (3) identify the values for each formula component, and (4) solve the problem.
John is watching an old game show on television in which the contestant chooses a prize behind curtain one or curtain two. Behind curtain one is a gag gift worth $150 and behind the other is a round-the-world trip worth $7,200. There is a 75% probability of choosing curtain one. What is the expected return of the choice?
Pamela 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 if the economy stays healthy, then her investment will generate a 30% return; however, if the economy softens her predicted return will be 10%. The return will be -25% if the economy slips into a recession. If the probabilities of a health, soft, and recessionary state are 40%, 50%, and 10%, respectively, what is the expected return AND standard deviationof the return on Pamela’s investment?
Item
Notation
What does it measure/ mean
Sentence
Summation notation
This symbol means the addition of a sequence of numbers. The number of values to be added is n, this means if there were four numbers in the sequence (1, 5, 7, 8) then n=4 because x1=1; x2=5; x3=7; and x4=8.
The average of four numbers is calculated by divided by 4.
Weight of an individual stock in a portfolio
Expected return on a single stock/ asset
Expected return on the portfolio
Holding period return on a single stock
Probability of a single outcome
Observed return on a single stock
Standard deviation of a specific asset
Number of observed outcomes
Explanation / Answer
Weight of individual stock in a portfolio
Percentage of the investment that is done in that particular stock as compared to the total portfolio value
Amazon forms 30% of my portfolio weight
Expected return on a single stock
The amount of gain or loss that you make over and above your investment in a stock
The expected return on my portfolio is 30% till June 2018
Holding period return on a single stock
The return generated on a stock investment during the period you are invested in that stock
I have earned 20% holding returns on ASPS this year whereas the stock moved 40% this year.
Probability of a single outcome
The likelihood of the happening of that event. Say probability of getting a head on tossing an unbiased coin is 50%
There is 90% probability for a rain tonight
Observed return on a single stock
The realized return on a stock during a certain period
Standard deviation of a specific asset
The deviation from the mean return over a certain period of time
The standard deviation of Amazon’s returns is 14%
Number of observed outcomes
Number of times the event occurred
Number 6 appeared on the dice 5 times out of the 20 times it was rolled.
Weight of individual stock in a portfolio
Percentage of the investment that is done in that particular stock as compared to the total portfolio value
Amazon forms 30% of my portfolio weight
Expected return on a single stock
The amount of gain or loss that you make over and above your investment in a stock
The expected return on my portfolio is 30% till June 2018
Holding period return on a single stock
The return generated on a stock investment during the period you are invested in that stock
I have earned 20% holding returns on ASPS this year whereas the stock moved 40% this year.
Probability of a single outcome
The likelihood of the happening of that event. Say probability of getting a head on tossing an unbiased coin is 50%
There is 90% probability for a rain tonight
Observed return on a single stock
The realized return on a stock during a certain period
Standard deviation of a specific asset
The deviation from the mean return over a certain period of time
The standard deviation of Amazon’s returns is 14%
Number of observed outcomes
Number of times the event occurred
Number 6 appeared on the dice 5 times out of the 20 times it was rolled.
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