a)
To determine: The probability of earning more than 10 percent on long-term corporate bonds.
Introduction:
The
Standard deviation refers to the variation in the actual observations from the average.
Z-Score helps to know how many numbers of standard deviations is the raw score or outcome away from the average or mean.
a)
Answer to Problem 28QP
The probability of earning more than 10 percent on long-term corporate bonds is 33.41 percent.
Explanation of Solution
Given information:
Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the text).
Determine the probability of having a return greater than 10 percent on long-term government bonds:
Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.
The common steps to be followed to use the “NORM.DIST” function in Excel:
Step 1:
Open an Excel worksheet.
Step 2:
Place the cursor in cell A1.
Step 3:
Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.
After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.
Step 4:
Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having more than 10 percent returns. Hence, “X” equals 10 percent. The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.
Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:
The probability of 0.665882 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10 percent return. The area to the right of Z is the probability of getting a return of 10 percent or more.
The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.665882. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10 percent return or more is 0.334118 or 33.4118 percent
To determine: The probability of earning less than 0 percent on long-term corporate bonds
Answer to Problem 28QP
The probability of earning less than 0 percent on long-term corporate bonds is 0.223058 or 0.223058 percent
Explanation of Solution
Given information:
Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the text).
Determine the probability of having a return less than 0 percent on long-term government bonds:
Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.
The common steps to be followed to use the “NORM.DIST” function in Excel:
Step 1:
Open an Excel worksheet.
Step 2:
Place the cursor in cell A1.
Step 3:
Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.
After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.
Step 4:
Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (0 percent) return or less. Hence, “X” equals (0 percent). The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.
Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:
The probability of 0.223058 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (0 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning less than 0 percent is 0.223058 or 0.223058 percent.
b)
To determine: The probability of earning more than 10 percent on Treasury bills
b)
Answer to Problem 28QP
The probability of earning more than 10 percent on Treasury bills is 0.018006785 or 1.80 percent.
Explanation of Solution
Given information:
Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the textbook).
Determine the probability of having a return greater than 10 percent on Treasury bills:
Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.
The common steps to be followed to use the “NORM.DIST” function in Excel:
Step 1:
Open an Excel worksheet.
Step 2:
Place the cursor in cell A1.
Step 3:
Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.
After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.
Step 4:
Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having more than 10 percent returns. Hence, “X” equals 10 percent. The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.
Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:
The probability of 0.981993215 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10 percent return. The area to the right of Z is the probability of getting a return of 10 percent or more.
The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.981993215. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10 percent return or more is 0.018006785 or 1.80 percent
To determine: The probability of earning less than 0 percent on Treasury bills.
Answer to Problem 28QP
The probability of earning less than 0 percent on Treasury bills is 0.129442113 or 12.94 percent.
Explanation of Solution
Given information:
Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the text).
Determine the probability of having a return less than 0 percent on Treasury bills:
Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.
The common steps to be followed to use the “NORM.DIST” function in Excel:
Step 1:
Open an Excel worksheet.
Step 2:
Place the cursor in cell A1.
Step 3:
Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.
After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.
Step 4:
Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (0 percent) return or less. Hence, “X” equals (0 percent). The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.
Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:
The probability of 0.129442113 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (0 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning less than 0 percent is 0.129442113 or 12.94 percent.
c)
To determine: The probability of earning (4.18 percent) on long-term corporate bonds.
c)
Answer to Problem 28QP
The probability of earning (4.18 percent) on long-term corporate bonds is 0.1039 or 10.39 percent.
Explanation of Solution
Given information:
Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the textbook).
Determine the probability of having (4.18 percent) on long-term government bonds:
Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.
The common steps to be followed to use the “NORM.DIST” function in Excel:
Step 1:
Open an Excel worksheet.
Step 2:
Place the cursor in cell A1.
Step 3:
Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.
After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.
Step 4:
Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (4.18 percent) return or less. Hence, “X” equals (4.18 percent). The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.
Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:
The probability of 0.103921 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (4.18 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning (4.18 percent) is 0.1039 or 10.39 percent.
To determine: The probability of earning 10.56 percent on Treasury bills.
Answer to Problem 28QP
The probability of earning 10.56 percent on Treasury bills is 0.011380598 or 1.14 percent
Explanation of Solution
Given information:
Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the text).
Determine the probability of having a return of 10.56 percent on Treasury bills:
Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.
The common steps to be followed to use the “NORM.DIST” function in Excel:
Step 1:
Open an Excel worksheet.
Step 2:
Place the cursor in cell A1.
Step 3:
Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.
After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.
Step 4:
Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having 10.56 percent returns. Hence, “X” equals 10.56 percent. The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.
Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:
The probability of 0.988619402 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10.56 percent return. The area to the right of Z is the probability of getting a return of 10.56 percent or more.
The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.988619402. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10.56 percent return or more is 0.011380598 or 1.14 percent
Want to see more full solutions like this?
Chapter 10 Solutions
Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
- On how far do you endorse this issue? Analyze the situation critically using official statistics and the literature.arrow_forwardIs globalization a real catalyst for enhancing international business? It is said that relevance of globalization and regionalism in the current situation is dying down. More specifically, concerned has been raised from different walks of life about Nepal’s inability of reaping benefits of joining SAFTA, BIMSTEC and WTO.arrow_forwardIn the derivation of the option pricing formula, we required that a delta-hedged position earn the risk-free rate of return. A different approach to pricing an option is to impose the condition that the actual expected return on the option must equal the equilibrium expected return. Suppose the risk premium on the stock is 0.03, the price of the underlying stock is 111, the call option price is 4.63, and the delta of the call option is 0.4. Determine the risk premium on the option.arrow_forward
- General Financearrow_forwardAssume an investor buys a share of stock for $18 at t = 0 and at the end of the next year (t = 1) , he buys 12 shares with a unit price of $9 per share. At the end of Year 2 (t = 2) , the investor sells all shares for $40 per share. At the end of each year in the holding period, the stock paid a $5.00 per share dividend. What is the annual time-weighted rate of return?arrow_forwardPlease don't use Ai solutionarrow_forward
- A flowchart that depicts the relationships among the input, processing, and output of an AIS is A. a system flowchart. B. a program flowchart. C. an internal control flowchart. D. a document flowchart.arrow_forwardA flowchart that depicts the relationships among the input, processing, and output of an AIS is A. a system flowchart. B. a program flowchart. C. an internal control flowchart. D. a document flowchart.arrow_forwardPlease write proposal which needs On the basis of which you will be writing APR. Write review of at least one article on the study area (Not title) of your interest, which can be finance related study area. Go through the 1. Study area selection (Topic Selection) 2. Review of Literature and development of research of framework 3. Topic Selection 4. Further review of literature and refinement of research fraework 5. Problem definition and research question…arrow_forward
- Let it denote the effective annual return achieved on an equity fund achieved between time (t-1) and time t. Annual log-returns on the fund, denoted by In(1+i̟²), are assumed to form a series of independent and identically distributed Normal random variables with parameters µ = 7% and σ = 10%. An investor has a liability of £20,000 payable at time 10. Calculate the amount of money that should be invested now so that the probability that the investor will be unable to meet the liability as it falls due is only 5%. Express your answer to the NEAREST INTEGER and do NOT include a "£" sign. Note: From standard Normal tables, we have (-1.645) = 0.05.arrow_forwardFor this question, use this data: myFunc = function (x, y = 2) {z = 7 Z+x^2+y } What is the output of myFunc(2)? O 13. O An error, y is undefined. O Nothing, we have to assign it as a vari O 9.arrow_forwarda medical test has some probability of being positive if the patient has the disease (hasPos) and another probability of testing positive if the person does not have the disease (notHasPos). a random member of the entire population has a real problem of having the disease (actual incidence). Based on the attached information what does the result of the function?arrow_forward
- Intermediate Financial Management (MindTap Course...FinanceISBN:9781337395083Author:Eugene F. Brigham, Phillip R. DavesPublisher:Cengage Learning