PROBLEM FIVE (15 MARKS) You work for a large investment management firm. The analysts in your firm have made the following forecasts for the returns of stock One and stock Two: AFF 210 Stock Probability Stock Two One VERY VERY WEAK 4% 55% -54% VERY WEAK 12% 25% -44% WEAK 16% 18% 15% SOFT 18% 16% 17% STRONG 20% 15% 18% 5 PROBLEM SET ONE WINTER 2025 VERY STRONG 15% 10% 20% VERY VERY STRONG 10% -25% 46% ROBUST 5% -75% 66% 100.0% a) Calculate the expected returns, variances and standard deviations for Stock One and Stock Two. b) What is the covariance of returns for Stock One and Stock Two? What is the correlation coefficient between the returns of Stock One and Stock Two? c) What are the expected return and standard deviation of a portfolio where 30% of the portfolio is in Stock One and 70% of the portfolio is in Stock Two? d) Create a table (like the one shown below) showing the portfolio expected return and standard deviation for different weights in each stock. This can be done using an Excel data table. Start with 100% in Stock One and 0% in Stock Two, and complete the table considering increments of 10%. The last row will have 0% in Stock One and 100% in Stock Two. e) Based on your table, create a chart (or graph) with your results. Weight in Stock One 100% 90% 80% 70% 60% 50% 40% 30% 20% Portfolio standard deviation Portfolio expected return 10% 0% Note: All calculations should be rounded to two decimal places if you are using percentages. If you are using decimals, the answer should be rounded to four decimal places. PROBLEM SIX (15 MARKS) You work for a small investment management firm. You have been provided with the following historical information for three stocks and the market index. The information is shown in the table below. The amounts are in dollars ($). ✗ Inc. Y Inc. Z Inc. Market Stock Stock Stock Dividend Dividend Dividend Index Price Price Price 2014 36 28 131 21,720 2015 48 0.75 35 1.75 141 3.65 24,325 2016 35 0.80 32 1.75 101 3.65 19,920 2017 43 0.85 44 1.80 129 3.75 23,100 2018 55 0.90 56 2.10 148 3.80 24,500 2019 72 1.05 65 3.00 165 4.33 28,020 6 AFF 210 PROBLEM SET ONE WINTER 2025 2020 78 1.10 98 3.20 184 4.85 31,572 2021 91 1.25 108 3.80 192 5.45 37,445 2022 80 1.25 115 4.00 181 5.45 33,283 2023 105 1.55 130 4.50 220 6.25 40,975 2024 120 1.75 150 4.75 204 6.25 43,220 Using the data provided, calculate the following for each of the stocks and the market index: a) What is the average annual return for the past ten years? b) What is the geometric average annual return for the past ten years? c) What is the population standard deviation and the sample standard deviation? d) What is the correlation coefficient between stocks X and Y, between stocks X and Z, and between stocks Y and Z, respectively? e) What is the sample covariance between stocks X and Y, between stocks X and Z, and between stocks Y and Z, respectively? f) What is the coefficient of variation for each of the stocks and the market index? You should consider the sample standard deviations in your calculations. g) What is the beta of each stock? You can use Excel's "slope" function to estimate this. h) Assume that the beta of stock X is 1.50, the beta of stock Y is 0.80, and the beta of stock Z is 1.20. What is the beta of a portfolio where the weight in stock X is 25%, the weight in stock Y is 35%, and the weight in stock Z is 40%? 1) Assuming the risk-free rate is 4.25% and the expected return on the market is 8.10%, what is the expected return on the portfolio in part (h) above?

PROBLEM FIVE (15 MARKS) You work for a large investment management firm. The analysts in your firm have made the following forecasts for the returns of stock One and stock Two: AFF 210 Stock Probability Stock Two One VERY VERY WEAK 4% 55% -54% VERY WEAK 12% 25% -44% WEAK 16% 18% 15% SOFT 18% 16% 17% STRONG 20% 15% 18% 5 PROBLEM SET ONE WINTER 2025 VERY STRONG 15% 10% 20% VERY VERY STRONG 10% -25% 46% ROBUST 5% -75% 66% 100.0% a) Calculate the expected returns, variances and standard deviations for Stock One and Stock Two. b) What is the covariance of returns for Stock One and Stock Two? What is the correlation coefficient between the returns of Stock One and Stock Two? c) What are the expected return and standard deviation of a portfolio where 30% of the portfolio is in Stock One and 70% of the portfolio is in Stock Two? d) Create a table (like the one shown below) showing the portfolio expected return and standard deviation for different weights in each stock. This can be done using an Excel data table. Start with 100% in Stock One and 0% in Stock Two, and complete the table considering increments of 10%. The last row will have 0% in Stock One and 100% in Stock Two. e) Based on your table, create a chart (or graph) with your results. Weight in Stock One 100% 90% 80% 70% 60% 50% 40% 30% 20% Portfolio standard deviation Portfolio expected return 10% 0% Note: All calculations should be rounded to two decimal places if you are using percentages. If you are using decimals, the answer should be rounded to four decimal places. PROBLEM SIX (15 MARKS) You work for a small investment management firm. You have been provided with the following historical information for three stocks and the market index. The information is shown in the table below. The amounts are in dollars ($). ✗ Inc. Y Inc. Z Inc. Market Stock Stock Stock Dividend Dividend Dividend Index Price Price Price 2014 36 28 131 21,720 2015 48 0.75 35 1.75 141 3.65 24,325 2016 35 0.80 32 1.75 101 3.65 19,920 2017 43 0.85 44 1.80 129 3.75 23,100 2018 55 0.90 56 2.10 148 3.80 24,500 2019 72 1.05 65 3.00 165 4.33 28,020 6 AFF 210 PROBLEM SET ONE WINTER 2025 2020 78 1.10 98 3.20 184 4.85 31,572 2021 91 1.25 108 3.80 192 5.45 37,445 2022 80 1.25 115 4.00 181 5.45 33,283 2023 105 1.55 130 4.50 220 6.25 40,975 2024 120 1.75 150 4.75 204 6.25 43,220 Using the data provided, calculate the following for each of the stocks and the market index: a) What is the average annual return for the past ten years? b) What is the geometric average annual return for the past ten years? c) What is the population standard deviation and the sample standard deviation? d) What is the correlation coefficient between stocks X and Y, between stocks X and Z, and between stocks Y and Z, respectively? e) What is the sample covariance between stocks X and Y, between stocks X and Z, and between stocks Y and Z, respectively? f) What is the coefficient of variation for each of the stocks and the market index? You should consider the sample standard deviations in your calculations. g) What is the beta of each stock? You can use Excel's "slope" function to estimate this. h) Assume that the beta of stock X is 1.50, the beta of stock Y is 0.80, and the beta of stock Z is 1.20. What is the beta of a portfolio where the weight in stock X is 25%, the weight in stock Y is 35%, and the weight in stock Z is 40%? 1) Assuming the risk-free rate is 4.25% and the expected return on the market is 8.10%, what is the expected return on the portfolio in part (h) above?

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Problem Three (15 marks)

You are an analyst in charge of valuing common stocks. You have been asked to value two stocks. The first stock NEWER Inc. just paid a dividend of $6.00. The dividend is expected to increase by 60%, 45%, 30% and 15% per year, respectively, in the next four years. Thereafter, the dividend will increase by 4% per year in perpetuity.

Calculate NEWER’s expected dividend for t = 1, 2, 3, 4 and 5.

The required rate of return for NEWER stock is 14% compounded annually.

What is NEWER’s stock price?

The second stock is OLDER Inc. OLDER Inc. will pay its first dividend of $10.00 three (3) years from today. The dividend will increase by 30% per year for the following four (4) years after its first dividend payment. Thereafter, the dividend will increase by 3% per year in perpetuity.

Calculate OLDER’s expected dividend for t = 1, 2, 3, 4, 5, 6, 7 and 8.

The required rate of return for OLDER stock is 16% compounded annually.

What is OLDER’s stock price?

Now assume that both stocks have a required rate of return of 40% per year compounded annually for the first six years, 25% per year compounded annually for the following five years, then 12% per year compounded annually thereafter.

What is NEWER’s stock price?
What is OLDER’s stock price?

(Hint: You may need to forecast more dividends than you did in parts a, and c.)

Note 1: You cannot use the NPV function to immediately value the stocks at time 0, as the required rate of return changes during the forecast period.

Note 2: All calculations should be rounded to the nearest cent. That is two decimal places.

Problem Four (15 marks)

On December 31st, 2004, your grandmother decided to buy a 30-year Government of Canada bond. The bond had a face value of $1,000,000. The annual coupon rate on the bond was 4.40%. Coupons were paid semi-annually. On December 31st, 2004, the yield to maturity on Government of Canada bonds was 3.70% per year. (The term structure of interest rates or yield curve was flat.)

After holding the bond for 20 years, your grandmother decided to sell the bond on December 31st, 2024. Prior to selling the bond, your grandmother received the December 31st, 2024 coupon payment. On December 31st, 2024, the yield to maturity on Government of Canada bonds had increased to 4.10% per year. (The term structure of interest rates or yield curve was flat.)

How much did your grandmother pay for the bond on December 31st, 2004?

How much did your grandmother sell the bond for on December 31st, 2024?

What was the rate of return that your grandmother earned on her investment during the 20 years?
Quote it as an effective periodic rate.
Quote it as an effective annual rate.

What would have been your grandmother’s rate of return on her investment if she had held the bond until maturity instead?
Quote it as an effective periodic rate.
Quote it as an annual percentage rate. What do you notice about this rate?

ANSWER ALL QUESTIONS #3-6

PROBLEM FIVE (15 MARKS)
You work for a large investment management firm. The analysts in your firm have made the
following forecasts for the returns of stock One and stock Two:
AFF 210
Stock
Probability
Stock Two
One
VERY VERY WEAK
4%
55%
-54%
VERY WEAK
12%
25%
-44%
WEAK
16%
18%
15%
SOFT
18%
16%
17%
STRONG
20%
15%
18%
5
PROBLEM SET ONE
WINTER 2025
VERY STRONG
15%
10%
20%
VERY VERY STRONG
10%
-25%
46%
ROBUST
5%
-75%
66%
100.0%
a) Calculate the expected returns, variances and standard deviations for Stock One and Stock
Two.
b) What is the covariance of returns for Stock One and Stock Two? What is the correlation
coefficient between the returns of Stock One and Stock Two?
c) What are the expected return and standard deviation of a portfolio where 30% of the
portfolio is in Stock One and 70% of the portfolio is in Stock Two?
d) Create a table (like the one shown below) showing the portfolio expected return and
standard deviation for different weights in each stock. This can be done using an Excel data
table. Start with 100% in Stock One and 0% in Stock Two, and complete the table
considering increments of 10%. The last row will have 0% in Stock One and 100% in Stock
Two.
e) Based on your table, create a chart (or graph) with your results.
Weight in
Stock One
100%
90%
80%
70%
60%
50%
40%
30%
20%
Portfolio standard deviation
Portfolio expected return
10%
0%
Note: All calculations should be rounded to two decimal places if you are using percentages. If you
are using decimals, the answer should be rounded to four decimal places.

PROBLEM SIX (15 MARKS)
You work for a small investment management firm. You have been provided with the following
historical information for three stocks and the market index. The information is shown in the table
below. The amounts are in dollars ($).
✗ Inc.
Y Inc.
Z Inc.
Market
Stock
Stock
Stock
Dividend
Dividend
Dividend
Index
Price
Price
Price
2014
36
28
131
21,720
2015
48
0.75
35
1.75
141
3.65
24,325
2016
35
0.80
32
1.75
101
3.65
19,920
2017
43
0.85
44
1.80
129
3.75
23,100
2018
55
0.90
56
2.10
148
3.80
24,500
2019
72
1.05
65
3.00
165
4.33
28,020
6
AFF 210
PROBLEM SET ONE
WINTER 2025
2020
78
1.10
98
3.20
184
4.85
31,572
2021
91
1.25
108
3.80
192
5.45
37,445
2022
80
1.25
115
4.00
181
5.45
33,283
2023
105
1.55
130
4.50
220
6.25
40,975
2024
120
1.75
150
4.75
204
6.25
43,220
Using the data provided, calculate the following for each of the stocks and the market index:
a) What is the average annual return for the past ten years?
b) What is the geometric average annual return for the past ten years?
c) What is the population standard deviation and the sample standard deviation?
d) What is the correlation coefficient between stocks X and Y, between stocks X and Z, and
between stocks Y and Z, respectively?
e) What is the sample covariance between stocks X and Y, between stocks X and Z, and
between stocks Y and Z, respectively?
f) What is the coefficient of variation for each of the stocks and the market index? You should
consider the sample standard deviations in your calculations.
g) What is the beta of each stock? You can use Excel's "slope" function to estimate this.
h) Assume that the beta of stock X is 1.50, the beta of stock Y is 0.80, and the beta of stock Z
is 1.20. What is the beta of a portfolio where the weight in stock X is 25%, the weight in
stock Y is 35%, and the weight in stock Z is 40%?
1) Assuming the risk-free rate is 4.25% and the expected return on the market is 8.10%, what is
the expected return on the portfolio in part (h) above?

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