You are considering two investments. Let X represent the proportional rate of return on the first investment, and let Y represent the proportional rate of return on the second investment. These are annual rates of return.
X is approximately normally distributed with mean 0.35 and standard deviation 0.3. Y is approximately normally distributed with mean 0.40 and standard deviation 0.5.
These six questions are about the rates of return, X and Y.
1. What is the probability of a negative rate of return on the first investment? 3 decimals.
2. What is the probability of a negative rate of return on the second investment? 3 decimals.
3. If the rates of return on these investments are independent, what is the probability that the rates of return on both investments will be negative? 3 decimals.
4. What is the expected amount by which Y exceeds X? HINT: The amount by which the rate of return on the second investment is higher than the rate of return on the first investment is Y - X. 2 decimals.
5. If the rates of return on these investments are independent, what is the probability that the second investment will have a higher rate of return than the first? HINT: Restate the question in terms of the rate of return on the second investment minus the rate of return on the first investment. 3 decimals.
6. If instead X and Y have a correlation of – 0.5 (a negative correlation), what is the probability that the second investment will have a higher rate of return than the first? HINT: Be careful! You’re given the correlation, not the covariance! 3 decimals.
In: Statistics and Probability
Suppose the price of one typical stock could only increase by 2 or decrease by 1 in one day. From the historical data, we somehow know that this stock goes up with probability 0.7, goes down with probability 0.3. Suppose the initial price is 100. Suppose we want to study the price behavior for that stock for one week(5-weekdays). (Round your answer in 3 decimal Places) This question is just for setting up the model.
what is the probability of the stock price close up at 102 at the end of Monday?
what is the probability of the stock price close up at 99 at the end of Monday?
Which of the following distribution bear the most resemblance to the distribution of stock price on Monday?
what is the probability of the stock price close up at 107 at the end of Friday?
Which of the following distribution bear the most resemblance to the distribution of stock price at the end of Friday?
what is the probability of the stock price close up at 108 at the end of Friday?
what is the probability of the stock price close up at most as 107 (include 107 itself) at the end of Friday?
what is the probability of the stock price close up at least as 108 (include 108 itself) at the end of Friday?
what is the probability of the stock price close up at least as 107 (include 107 itself) at the end of Friday?
what is the probability of the stock price close up at most as 100 (include 100 itself) at the end of Friday?
In: Finance
Question 3
The sales and finance team of a car company is evaluating a new
proposed luxury model of its
brand that will require an investment of $1Billion in a new machine
for car interior decoration.
Demand for the company’s car is expected to begin at 100,000 units
in year 1, with 10% annual
growth thereafter. Production cost will be $35,000 per unit in the
first year, and increase by a rate
of either 3% or 5% per year as a result of wage increase. Selling
price will start at $37,000 and
increase by 4% of the production cost. The model will be phased out
at the end of year 10. In
addition, 0.3%, 2% and 1.5% of before tax profit per year will be
spent on social corporate
responsibility, commercial (including promotions) and recalls
respectively. Assume taxes will be
30% of yearly profit and that inflation will remain at 0% per year
throughout the 10 year of
production. Also assume interest rate is expected to be 3% per year
in the first 5 years and 5% in
the last 5 years.
a. Based on present worth analysis, is the proposed investment
profitable if production cost
increases by a rate of 3% per year as a result of wage increase?
Justify your answer.
b. Based on present worth analysis, is the proposed investment
profitable if production cost
increases by a rate of 5% per year as a result of wage increase?
Justify your answer. (
In: Finance
Consider the following information regarding the performance of a money manager in a recent month. The table represents the actual return of each sector of the manager’s portfolio in column 1, the fraction of the portfolio allocated to each sector in column 2, the benchmark or neutral sector allocations in column 3, and the returns of sector indices in column 4.
| Actual Return | Actual Weight | Benchmark Weight | Index Return | |||||||||
| Equity | 2.1 | % | 0.7 | 0.5 | 2.6% (S&P 500) | |||||||
| Bonds | 1.1 | 0.1 | 0.2 | 1.3 (Barclay’s Aggregate) | ||||||||
| Cash | 0.5 | 0.2 | 0.3 | 0.5 | ||||||||
a-1. What was the manager’s return in the month? (Do not round intermediate calculations. Input all amounts as positive values. Round your answer to 2 decimal places.)
|
a-2. What was her overperformance or underperformance? (Do not round intermediate calculations. Input all amounts as positive values. Round your answer to 2 decimal places.)
|
b. What was the contribution of security selection to relative performance? (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)
|
c. What was the contribution of asset allocation to relative performance? (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)
|
In: Finance
Lafarge is a French industrial company specializing in three major products: cement, construction aggregates, and concrete. Lafarge Zambia operates 2 integrated cement plants (situated in Ndola and Lusaka) with a total production capacity of 1.4 million tonnes per annum. Lafarge Zambia is considering to develop a new plant in the central province of Zambia. The following three options available. These are to open a small plant, a medium-sized plant, or no plant at all. The marketing department has advised that the market for a plant in central province can be good, average, or bad. The probabilities for these three possibilities are 0.2 for a good market, 0.5 for an average market, and 0.3 for a bad market. The net profit or loss figures for the medium-sized and small plant for the various market conditions are given in the following table. Building no plant at all yields no loss and gain.
|
Alternative |
Good market (k) |
Average market (k) |
Bad market (k) |
|
Small plant |
1,350,000 |
450,000 |
-720,000 |
|
Medium-sized plant |
1,800,000 |
630,000 |
-1,080,000 |
|
No plant |
0 |
0 |
0 |
The above information has been given to you as management accountant of Lafarge.
Required
Basing on the minimax regret criterion and the minimum Expected Opportunity loss criterion, which would you recommend? (10 mar
In: Finance
9.1. Obtain the total periodic payments of a loan of 16,000€ and 3 years term, with the following conditions:
a. Adjustable interest rate.
Annual adjustment period: 1 year.
Type of loan: Semi-annually constant principal repayments over 3
years.
Nominal interest rate for the 1st
period: 3%
Interest rates for the remaining periods: the index rate plus 0.5
percentage points.
The index rate take the following values for the other periods:
ir = 0.05 ; ir = 0.045
Find the periodic payments to be made.
b. Monthly constant payments over each adjustment
period.
Annual adjustment period: 1 year.
Nominal interest rate for the 1st period : 5%.
Remaining periods: index rate plus 0.3 percentage points.
The index rates take the following values for each of the
periods:
ir = 0.06 ; ir = 0.04
Find the periodic payments to be made.
c. Adjustable interest rate.
Annual adjustment period: 1 year.
Type of loan: quarterly constant principal repayments over 3
years.
Nominal interest rate for the 1st
period: 7%
Interest rates for the remaining periods: the index rate plus 0.2
percentage points.
The index rates take the following values for the other periods:
ir = 0.035 ; ir = 0.05
Find the periodic payments to be made.
In: Finance
SciTools Incorporated, a company that specializes in scientific instruments, has been invited to make a bid on a government contract. The contract calls for a specific number of these instruments to be delivered during the coming year. The bids must be sealed (so that no company knows what the others are bidding), and the low bid wins the contract. SciTools estimates that it will cost $5000 to prepare a bid and $95,000 to supply the instruments if it wins the contract. On the basis of past contracts of this type, SciTools believes that the possible low bids from the competition, if there is any competition, and the associated probabilities are those shown in the table below. In addition, SciTools believes there is a 30% chance that there will be no competing bids.
| Lowest competing Bid | Probability |
|
Less than $115,000 |
0.2 |
|
Between $115,001 and $120,000 |
0.4 |
|
Between $120,001 and $125,000 |
0.3 |
|
Greater than $125,000 |
0.1 |
Based on the data in the table above, SciTools will limit its choices for bids to $115,000, $120,000, and $125,000.
a) Draw a decision tree for this scenario
b) Solve this decision tree using EMV
c) Draw the risk profiles for all decision strategies
d) Draw the cumulative risk profile for this scenario. Is there dominance?
e) Construct a tornado diagram for this scenario, if we assume the following ranges for the
variables:
a. Probability of no competing bids: 0 to 0.6
b. Cost to supply the instruments: $85,500 to $105,400
c. Bid cost: $4,500 to $5,500
In: Operations Management
|
|||||||||||||||||||||||||||
|
|||||||||||||||||||||||||||
In: Statistics and Probability
The dean of Mihaylo Business School is forecasting total student enrollment for next year based on the following historical data:
Year Total Enrollment
2015 1600
2016 2000
2017 2200
2018 2600
2019 3000
What is 2020's forecast using a 2-period moving average? Select one:
a. 2,800
b. None of the choices
c. 3,000
d. 1,960
e. 2,450
What is the MAPE value based on 2 year moving average?
Select one:
a. None of the choice
b. 0.191
c. 0.178
d. 0.144
e. 0.237
What is the forecasted value of 2020 by using a 3 year weighted
moving average by using weights of 0.6, 0.3 and 0.1.
Select one:
a. 2480
b. 2800
c. 2680
d. None of the choices
e. 2400
a. None of the choice
b. 0.191
c. 0.178
d. 0.144
e. 0.237
What is the MSE value based on exponential smoothing forecast
with smoothing constant of 0.4?
Select one:
a. 1,557,436
b. None of the choices
c. 576
d. 1,297,863
e. 357,985
Compare 2 year moving average and exponential smoothing with
alpha=0.4, which forecasting approach is better? Using MAE as your
forecast accuracy measure.
Select one:
a. Exponential smoothing with alpha=0.4
b. 2 year moving average
In: Statistics and Probability
The dean of Mihaylo Business School is forecasting total student enrollment for next year based on the following historical data: Year Total Enrollment 2015 1600 2016 2000 2017 2200 2018 2600 2019 3000 What is 2020's forecast using a 2-period moving average? Select one: a. 2,800 b. None of the choices c. 3,000 d. 1,960 e. 2,450 What is the MAPE value based on 2 year moving average? Select one: a. None of the choice b. 0.191 c. 0.178 d. 0.144 e. 0.237 What is the forecasted value of 2020 by using a 3 year weighted moving average by using weights of 0.6, 0.3 and 0.1. Select one: a. 2480 b. 2800 c. 2680 d. None of the choices e. 2400 a. None of the choice b. 0.191 c. 0.178 d. 0.144 e. 0.237 What is the MSE value based on exponential smoothing forecast with smoothing constant of 0.4? Select one: a. 1,557,436 b. None of the choices c. 576 d. 1,297,863 e. 357,985 Compare 2 year moving average and exponential smoothing with alpha=0.4, which forecasting approach is better? Using MAE as your forecast accuracy measure. Select one: a. Exponential smoothing with alpha=0.4 b. 2 year moving average
In: Statistics and Probability