Two companies’ data are here: (i) Apex Footwear Ltd. and (ii) BRAC Bank Ltd. Two companies’ stock prices and dividends,
Posted: Sun Apr 10, 2022 8:44 am
Two companies’ data are here: (i) Apex Footwear Ltd. and (ii)
BRAC Bank Ltd. Two companies’ stock prices and dividends, along
with the Dhaka Stock Exchange (DSE) Index, are given here for the
period 2016-2021. The DSE Index data are adjusted to include
dividends. Data as given in the problem are shown in the following
table (Note that the data here may mismatch with the original data
of the companies.): In BDT Year Apex Footwear Ltd. BRAC Bank Ltd.
Market Index Stock Price Dividend Stock Price Dividend Includes
Divs. 2016 34.625 1.600 53.750 1.600 5,447.00 2017 31.375 2.766
52.500 2.300 4,524.28 2018 32.350 1.750 54.000 3.650 6,244.03 2019
31.400 1.540 51.750 4.550 8,192.98 2020 33.550 2.500 54.300 2.500
7,584.70 2021 31.250 1.600 55.750 2.500 9,650.98
Requirements:
1. Use the data given to calculate annual returns for Apex
Footwear, Brac Bank, and the Market Index, and then calculate
average returns over the five-year period. Hints: (i) Remember,
returns are calculated by subtracting the beginning price from the
ending price to get the capital gain or loss, adding the dividend
to the capital gain or loss, and dividing the result by the
beginning price. Assume that dividends are already included in the
index. Also, you cannot calculate the rate of return for 2016
because you do not have 2015 data.) (ii) How to calculate average
returns over the five-year period? Add the annual returns of every
year and then divide by the number of years. Here you will get
annual returns of five years. You will not get annual return of the
year 2016, because you don’t have the data of 2015.
2. Calculate the standard deviation of the returns for Apex
Footwear, BRAC Bank, and the Market Index. Hints: i. Use the sample
standard deviation formula to get standard deviations for both Apex
Footwear, Brac Bank. The formula is given below: Note: this can
also be solved with the help of STDEV function in MS Excel. Where:
S = Sample Standard Deviation N = Number of the Observations (In
the problem, number of observations is 6: from year 2016 to 2021)
Xi = Observed Values of a Sample Item (Here Observed Values are
Each Year’s Annual Rate of Return) x = Mean Value of the
Observations (Here Mean Value is the Overall Average Annual Return
of Each Company) ii. You will solve in table format, say as given
below: Apex Footwear Ltd. BRAC Bank Ltd. (Xi) Xi – x (Xi – x) 2
(Xi) Xi – x (Xi – x) 2
3. Now calculate the coefficients of variation (CV) Apex
Footwear, Brac Bank, and the Market Index. Hint: CV = S x
4. Construct a scatter diagram graph that shows Apex Footwear’s
and BRAC Bank’s returns on the vertical axis (that is, Y axis) and
the market index’s returns on the horizontal axis (that is X axis).
Because, individual company’s return depend on the market index
return. (Hint: You can take the help of MS Excel)
5. Estimate Apex Footwear’s and BRAC Bank’s betas against the
Market Index’s returns. Are these betas consistent with your graph?
Hints: i. You may calculate betas, with the help of MS Excel, by
two ways: a) Slope Tool, b) Regression Tool (How to calculate will
be shown with hands on practice)
6. Assume that the risk-free rate on long-term treasury bonds
(risk free security) is 6.04% and market risk premium is 7% and
value is 0.3. What is the expected return on the market?
7. Again assume risk-free rate on long-term treasury bonds (risk
free security) is 6.04% and market risk premium is 7%. Take the
beta values for the two companies found under question number 5 and
use SML equation. Determine the required rate of returns for the
two companies. Hints: i. The SML equation is as follows: ii. The
value of risk premium = Rm – Rf = 7%
8. If you formed a portfolio that consisted of 42% Apex Footwear
and 58% BRAC Bank, what would be its beta and its required return?
Hint: Follow the formulae under portfolio rate of return and
portfolio beta.
9. Suppose an investor wants to include Apex Footwear’s stock in
his or her portfolio. Stocks A, B, and C are currently in the
portfolio, and their betas are 0.769, 0.985, and 1.423,
respectively. Calculate the new portfolio’s required return if it
consists of 25 percent of Apex Footwear, 15 percent of Stock A, 40
percent of Stock B, and 20 percent of Stock C.
BRAC Bank Ltd. Two companies’ stock prices and dividends, along
with the Dhaka Stock Exchange (DSE) Index, are given here for the
period 2016-2021. The DSE Index data are adjusted to include
dividends. Data as given in the problem are shown in the following
table (Note that the data here may mismatch with the original data
of the companies.): In BDT Year Apex Footwear Ltd. BRAC Bank Ltd.
Market Index Stock Price Dividend Stock Price Dividend Includes
Divs. 2016 34.625 1.600 53.750 1.600 5,447.00 2017 31.375 2.766
52.500 2.300 4,524.28 2018 32.350 1.750 54.000 3.650 6,244.03 2019
31.400 1.540 51.750 4.550 8,192.98 2020 33.550 2.500 54.300 2.500
7,584.70 2021 31.250 1.600 55.750 2.500 9,650.98
Requirements:
1. Use the data given to calculate annual returns for Apex
Footwear, Brac Bank, and the Market Index, and then calculate
average returns over the five-year period. Hints: (i) Remember,
returns are calculated by subtracting the beginning price from the
ending price to get the capital gain or loss, adding the dividend
to the capital gain or loss, and dividing the result by the
beginning price. Assume that dividends are already included in the
index. Also, you cannot calculate the rate of return for 2016
because you do not have 2015 data.) (ii) How to calculate average
returns over the five-year period? Add the annual returns of every
year and then divide by the number of years. Here you will get
annual returns of five years. You will not get annual return of the
year 2016, because you don’t have the data of 2015.
2. Calculate the standard deviation of the returns for Apex
Footwear, BRAC Bank, and the Market Index. Hints: i. Use the sample
standard deviation formula to get standard deviations for both Apex
Footwear, Brac Bank. The formula is given below: Note: this can
also be solved with the help of STDEV function in MS Excel. Where:
S = Sample Standard Deviation N = Number of the Observations (In
the problem, number of observations is 6: from year 2016 to 2021)
Xi = Observed Values of a Sample Item (Here Observed Values are
Each Year’s Annual Rate of Return) x = Mean Value of the
Observations (Here Mean Value is the Overall Average Annual Return
of Each Company) ii. You will solve in table format, say as given
below: Apex Footwear Ltd. BRAC Bank Ltd. (Xi) Xi – x (Xi – x) 2
(Xi) Xi – x (Xi – x) 2
3. Now calculate the coefficients of variation (CV) Apex
Footwear, Brac Bank, and the Market Index. Hint: CV = S x
4. Construct a scatter diagram graph that shows Apex Footwear’s
and BRAC Bank’s returns on the vertical axis (that is, Y axis) and
the market index’s returns on the horizontal axis (that is X axis).
Because, individual company’s return depend on the market index
return. (Hint: You can take the help of MS Excel)
5. Estimate Apex Footwear’s and BRAC Bank’s betas against the
Market Index’s returns. Are these betas consistent with your graph?
Hints: i. You may calculate betas, with the help of MS Excel, by
two ways: a) Slope Tool, b) Regression Tool (How to calculate will
be shown with hands on practice)
6. Assume that the risk-free rate on long-term treasury bonds
(risk free security) is 6.04% and market risk premium is 7% and
value is 0.3. What is the expected return on the market?
7. Again assume risk-free rate on long-term treasury bonds (risk
free security) is 6.04% and market risk premium is 7%. Take the
beta values for the two companies found under question number 5 and
use SML equation. Determine the required rate of returns for the
two companies. Hints: i. The SML equation is as follows: ii. The
value of risk premium = Rm – Rf = 7%
8. If you formed a portfolio that consisted of 42% Apex Footwear
and 58% BRAC Bank, what would be its beta and its required return?
Hint: Follow the formulae under portfolio rate of return and
portfolio beta.
9. Suppose an investor wants to include Apex Footwear’s stock in
his or her portfolio. Stocks A, B, and C are currently in the
portfolio, and their betas are 0.769, 0.985, and 1.423,
respectively. Calculate the new portfolio’s required return if it
consists of 25 percent of Apex Footwear, 15 percent of Stock A, 40
percent of Stock B, and 20 percent of Stock C.