Project 2 Questions Summer 2023
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Feb 20, 2024
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FIN 5935 – PROJECT 2 (12 Questions)
SUMMER 2023
1.
The Excel file Stock Price Data
contains monthly price data for eight (8) stocks.
a.
Compute the monthly returns (using continuous returns) for each of the stocks.
b.
Compute the Matrix of Excess Returns for these stocks.
c.
Use the Matrix of Excess Returns to compute the Sample Variance-Covariance Matrix for
these stocks.
d.
Use the Sample Variance-Covariance Matrix for these stocks to compute the Global Minimum Variance Portfolio (GMVP).
e.
Compute the expected return and standard deviation for this GMVP.
2.
The Excel file Portfolio Bond Immunization Data contains information about three bonds. Coupons are paid annually. Use this data to:
a.
Compute the amount to be invested to meet the future liability noted in the data. This future liability is due in 12 years.
b.
Find a combination of Bond 1 and Bond 2 having a target duration of 12 years.
c.
Find a combination of Bond 1 and Bond 3 having a target duration of 12 years.
d.
Perform an analysis using a data table and an accompanying graph to determine which of the following options (i.e., a portfolio consisting of Bond 1 and Bond 2, a portfolio consisting of Bond 1 and Bond 3, or a portfolio consisting of Bond 1) would be preferred to attempt to immunize this obligation.
i.
Construct a data table by varying the yield to maturity that shows the value of each option at the end of 12 years. Use yield to maturity values ranging from 0% to 15% in 1% increments. ii.
Based on your data table, construct a graph that demonstrates the performance
of these 3 options.
iii.
Analyze each option’s performance in attempting to achieve immunization.
3.
The Excel file Portfolio Manager Annual Returns
contains returns realized last year by clients of two different portfolio managers. Based on this information what is the probability that Portfolio Manager A’s clients
will realize a higher annual return in the upcoming year than Portfolio Manager B’s clients
? Use a resampling procedure with 80 simulations.
4.
A stock is selling today for $125. The stock has an annual volatility of 45 percent and the annual T-bill rate is 12 percent.
a.
Calculate the fair price for a 15 month European call option with an exercise price of $118.
b.
Calculate how much the current stock price would need to change for the purchaser of the call option to break even in 15 months.
c.
Calculate the fair price for a 15 month European put option with an exercise price of $118.
d.
Calculate how much the current stock price would need to change for the purchaser of the put option to break even in 15 months.
e.
Calculate the level of volatility that would make the $118 call option sell for $30.
f.
Calculate the level of volatility that would make the $118 put option sell for $25.
5.
On July 1, 2021 you purchased an option which will allow you to sell a commercial building on June 25, 2025 for $30 million. Your current estimate of the value of the building is $28 million. The annual volatility for the change in the building’s value is 25% and the annual T-bill rate is 8%.
a.
Calculate the value of the option to sell the building.
6.
The Excel file Monthly Return Data
contains return data for several stocks and the S&P 500. Use this data to determine the probability that INTC’s
monthly return is likely to exceed MSFT’s
monthly return. Run 75 simulations to determine this probability.
7.
Demand for Coca Cola at a local restaurant is 125 bottles per day with a standard deviation of 10
bottles per day.
a.
Compute the probability that demand will exceed 5100 bottles during the next 40 days.
b.
Compute the number of bottles the restaurant should stock to have at most a 8% chance of running out over the next 40 days.
8.
A stock sells today for $65. The price of the stock in a year is expected to be $70. The annual volatility of the stock is 30%. Assume stock prices follow a lognormal probability distribution.
a.
Calculate the probability that in four years the stock will sell for more than $80.
b.
Calculate the probability that in four years the stock will sell for less than $60.
c.
Calculate the probability that in four years the stock will sell for a price between $54 and
$68.
d.
You are 80% confident the stock price in four years will be between what two values?
9.
Explain the principle of immunization when used with a bond portfolio.
a.
What is bond portfolio immunization attempting to achieve?
b.
How is bond portfolio immunization achieved?
c.
Which bond risk components interact to make immunization successful?
i.
Explain how these bond risk components interact to immunize a bond portfolio.
10.
A company forecasts it will sell 54 units of a product next year. Use the Excel file Sales Data
to determine the probability that it will sell between 45 and 60 units of the product next year.
11.
A stock is selling today for $30. The stock has an annual volatility of 50 percent, and the annual T-bill rate is 8 percent.
a.
Use Excel’s data table feature to construct a One-Way Data Table to demonstrate the impact of the stock price on both the price and intrinsic value for an 18-month European
call option with an exercise price of $28. Use stock prices ranging from $10 to $80 in increments of $5.
i.
Based on your data table, construct a graph that demonstrates the impact of the stock price on both the price and intrinsic value of this call option.
ii.
How is the intrinsic value of the call option impacted as the stock price changes?
iii.
How is the time value of the call option impacted as the stock price changes?
12.
The Excel file Moving Averages Data
contains quarterly sales data. Use the Ratio to Moving Average approach (based on a 4 quarter moving average) to:
a.
Using all the data, forecast the sales for each quarter in 2009.
b.
Using data from 2006 & 2007, forecast the sales for each quarter in 2009 using a trend estimate.
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Related Questions
A 252.
arrow_forward
Here are the returns on two stocks.
January
February
March
April
May
June
July
August
Digital
Cheese
+14
-4
+6
+8
-5
+4
-3
-9
Executive
Fruit
+8
+2
+5
+12
+3
+6
w At t
-4
-3
Required:
a-1. Calculate the variance and standard deviation of each stock.
a-2. Which stock is riskier if held on its own?
4
b. Now calculate the returns in each month of a portfolio that invests an equal amount each month in the two stocks.
c. Is the variance more or less than halfway between the variance of the two individual stocks?
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Stock A has the following returns over the past periods. Calculate the downside risk measured by semi-variance? (answer with 4 decimal spaces)
0.0057
-0.0255
0.0621
-0.0879
-0.0983
0.0813
0.0356
-0.0015
-0.0307
0.0427
0.0297
0.0192
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Please solve using Excel and show formulas.
Here are the percentage returns on two stocks.
Month
Digital Cheese
Executive Fruit
January
15
%
7
%
February
–4
2
March
5
5
April
7
13
May
–5
1
June
3
5
July
–3
–3
August
–9
–1
a-1. Calculate the monthly variance and standard deviation of each stock. (Do not round intermediate calculations. Round your answers to 1 decimal places.)
b. Now calculate the variance and standard deviation of the returns on a portfolio that invests an equal amount each month in the two stocks. (Do not round intermediate calculations. Round your answers to 1 decimal places.)
c. Is the variance more or less than half way between the variance of the two individual stocks?
multiple choice
more than the 50%-50%Not attempted
less than the 50%-50%Not attempted
arrow_forward
The last four years of returns for a stock are as shown here: E
a. What is the average annual return?
b. What is the variance of the stock's returns?
c. What is the standard deviation of the stock's returns?
Note: Notice that the average return and standard deviation must be entered in percentage format. The variance must be entered in decimal format.
.....
Data table
(Click on the icon located on the top-right corner of the data table below in order to
copy its contents into a spreadsheet.)
Year
1
2
3
4
Return
- 4.3%
+ 27.9%
+ 12.3%
+ 3.6%
arrow_forward
Here are the percentage returns on two stocks.
Digital
Executive
Month
Cheese
Fruit
January
February
14%
68
-3
1
March
6
4
April
May
8
14
-4
2
June
6
July
August
-2
-4
-8
-2
a-1. Calculate the monthly variance and standard deviation of each stock. (Do not round intermediate calculations. Round your
answers to 1 decimal places.)
Executive Fruit
Digital Cheese
Variance
Standard deviation %
a-2. Which stock is the riskier if held on its own?
Digital Cheese
arrow_forward
Here are the returns on two stocks.
Digital
Executive
Cheese
Fruit
January
+15
+8
February
-2
+1
March
+4
+6
April
+6
+16
May
-3
+2
June
+2
+6
July
-1
-2
August
-7
-1
Required:
a-1. Calculate the variance and standard deviation of each stock.
a-2. Which stock is riskier if held on its own?
b. Now calculate the returns in each month of a portfolio that invests an equal amount each month in the two stocks.
c. Is the variance more or less than halfway between the variance of the two individual stocks?
Complete this question by entering your answers in the tabs below.
Req A1
Req A2
Req B
Req C
Calculate the variance and standard deviation of each stock.
Note: Do not round intermediate calculations. Round your answers to 2 decimal places.
Variance
Standard deviation
Digital Cheese
Retum
Executive Fruit
Return
%
%
arrow_forward
Here are the returns on two stocks.
Digital
Cheese
+14
-3
+5
+7
-4
+3
-2
-8
Executive
Fruit
+7
+1
January
February
March
April
May
+4
+12
+2
+7
-3
-2
June
August
Required:
a-1. Calculate the variance and standard deviation of each stock.
a-2. Which stock is riskier if held on its own?
b. Now calculate the returns in each month of a portfolio that invests an equal amount each month in the two stocks.
c. Is the variance more or less than halfway between the variance of the two individual stocks?
arrow_forward
hi there, i need requirement C. Thankss
arrow_forward
The last four years of returns for a stock are as shown here:
LOADING...
.
a. What is the average annual return?
b. What is the variance of the stock's returns?
c. What is the standard deviation of the stock's returns?
Note:
Notice that the average return and standard deviation must be entered in percentage format. The variance must be entered in decimal format.
Question content area bottom
Part 1
a. What is the average annual return?
The average return is
enter your response here%.
(Round to two decimal places.)
Part 2
b. What is the variance of the stock's returns?
The variance of the returns is
enter your response here.
(Round to five decimal places.)
Part 3
c. What is the standard deviation of the stock's returns?
The standard deviation is
enter your response here%.
(Round to two decimal places.)
figure
Year: 1, 2, 3, 4
Return: -4.2%, +27.9%, +11.8%, +3.8%
arrow_forward
Here are the returns on two stocks.
Digital
Executive
Cheese
Fruit
January
+16
+9
February
-4
+1
March
+6
+7
April
+8
+16
May
-5
+2
June
+4
+7
July
-4
August
-9
-3
Required:
a-1. Calculate the variance and standard deviation of each stock.
a-2. Which stock is riskier if held on its own?
b. Now calculate the returns in each month of a portfolio that invests an equal amount each month in the two stocks.
c. Is the variance more or less than halfway between the variance of the two individual stocks?
Complete this question by entering your answers in the tabs below.
Req A1
Req A2
Req B
Req C
Calculate the variance and standard deviation of each stock.
Note: Do not round intermediate calculations. Round your answers to 2 decimal places.
Variance
Standard deviation
Digital Cheese
Retum
Executive Fruit
Return
%
%
arrow_forward
he last four years of returns for a stock are as shown here:
LOADING...
.
a. What is the average annual return?
b. What is the variance of the stock's returns?
c. What is the standard deviation of the stock's returns?
Note:
Notice that the average return and standard deviation must be entered in percentage format. The variance must be entered in decimal format.
Question content area bottom
Part 1
a. What is the average annual return?
The average return is
enter your response here%.
(Round to two decimal places.)
Part 2
b. What is the variance of the stock's returns?
The variance of the returns is
enter your response here.
(Round to five decimal places.)
Part 3
c. What is the standard deviation of the stock's returns?
The standard deviation is
enter your response here%.
(Round to two decimal places.)
Time Remaining: 00:26:16
pop-up content starts
Data table
(Click on the following icon
in order…
arrow_forward
Using the data in the following table,, estimate the:
a. Average return and volatility for each stock.
b. Covariance between the stocks.
c. Correlation between these two stocks.
a. Estimate the average return and volatility for each stock.
The average return of stock A is %. (Round to two decimal places.)
Data table
(Click on the following icon in order to copy its contents into a spreadsheet.)
Year
2010
2011
20%
2013
- 1%
- 13%
Stock A
Stock B
20%
12%
- 9%
Print
2012
8%
9%
C
Done
2014
4%
- 9%
2015
11%
27%
- X
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The table summarizes the annual mean returns, variances and standard deviations using the monthly return data for four major
stock market indexes. Which market is considered most risky using CV (coefficient of variation) as a measure of risk?
Market
A
B
C
D
Market A
Market B
Market C
Market D
Mean Return (%)
5
9.4
12
9.3
Variance of
Return
184.96
501.76
462.25
368.64
STDEV (%)
13.6
22.4
21.5
19.2
arrow_forward
3. Consider three stocks A, B and C and a market index M with the following prices:
Year
TO
T1
T2
T3
A
85
108
110
125
B
12
14
13
15
C
50
60
70
75
M
1128
1435
1578
1786
The risk-free rate equals 4%.
a. Compute the expected return and risk on each stock and the market index.
b. Construct the matrix of variances and covariances between these assets.
c. Construct the matrix of the correlation coefficients.
d. Compute the beta coefficients of these companies and the expected return at equilibrium.
e. Construct the minimum risk portfolio P1 composed of A and C. Compute the expected return
and risk on this portfolio.
f. Construct a portfolio P2 composed of A, B and C in proportions of 20%, 30% and 50%.
Compute the expected return and risk on this portfolio. What is the contribution of each security
to the return and risk pf this portfolio?
g. Construct an equally weighted portfolio P3 composed of A, B, C and the risk-free rate.
Compute the beta coefficient and position this portfolio with…
arrow_forward
Here are the returns on two stocks.
Digital
Executive
Cheese
Fruit
January
+19
+8
February
-3
+1
March
+5
+4
April
+7
+17
May
4
+2
June
+3
+4
July
August
2
8
aces
Required:
a-1. Calculate the variance and standard deviation of each stock.
a-2. Which stock is riskier if held on its own?
b. Now calculate the returns in each month of a portfolio that invests an equal amount each month in the two stocks.
c. Is the variance more or less than halfway between the variance of the two individual stocks?
arrow_forward
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