UTSA- ALVAREZ COLLEGE OF BUSINESS
FIN 3013 002- PRINCIPLES OF BUSINES FINANCE- SPRING 2022
PROBLEM SET 11- CAPITAL MARKETS, RISK AND RETURN (CHAPTERS 12 AND 13)
PROBLEMS (INDIVIDUAL WORK, PAPER OR EXCEL-BASED)
STOCK DIVERSIFICATION (PORTFOLIOS)
Download 5 years of historical daily stock prices, from 01-01-2017 to 12-31-2021 (approximately), for the 6
companies below, from Yahoo Finance:
1- Chevron- CVX (call stock A)
2- American Express- AXP (call stock B)
3- DaVita- DVA (call stock C)
4- Caterpillar- CAT (call stock D)
5- Accenture- CAN (call stock E)
6- Sherwin-Williams SHW (call stock F)
*To make your data cleaner, you can delete all columns other than date column and adjusted close price column.
(a) Project the expected stock returns for each company for three states of the USA Economy, as the simple average
stock returns during recession, normal or expansion times. For the sake of this exercise, we will consider as a normal
state of the Economy the period from Jan/2017 to Dec/2019. For an estimate of the returns during recession times
we will assume as a period of recession from Jan/2020 to Dec/2020. For last, the period used for economic expansion
times will be from Jan/2021 to Dec/2021. The probabilities of each state of the Economy to happen are given:
(b) Calculate expected returns for all the 6 individual stocks, considering the probabilities of the states of the
Economy above.
1- State of Economy 2- Probability of
State of Economy
3- Chevron ReturnsR(A)
4- Amex ReturnsR(B)
5- DaVita ReturnsR(C)
6- Caterpillar
Returns- R(D)
7- Accenture
Returns- R(E)
8- Sherwin-Williams
Returns- R(F)
Recession 10%
Normal 65%
Boom 25%
Chevron (A) Amex (B) DaVita (C) Caterpillar (D) Accenture (E) Sherwin-Williams (F)
Expected Return- E (RA)
Expected Return- E (RB)
Expected Return- E (RC)
Expected Return- E (RD)
Expected Return- E (RE)
Expected Return- E (RF)
Decimals Percentage
Expected Return on Stock A- E (RC)
Expected Return on Stock Z- E (RD)
Variance of Stock A Returns- Var (RC)
Variance of Stock Z Returns- Var (RD)
Standard Deviation of Stock A Returns- St Dev (RC)
Standard Deviation of Stock Z Returns- St Dev (RD)
Covariance between Returns of A and Z- Cov (RC,RD)
Correlation between Returns of A and Z- Corr (RC,RD)
Portfolio 2 (Stocks C and D)
1- Relevant Information 2- Values
(c) Estimate the Variance and Standard Deviations of the returns of all of the 6 individual stocks.
(d) Because you already know about the principle of the diversification, you want to build portfolios of stocks to try
to mitigate unsystematic risk. For now, you will combine stocks in portfolios of 2 different stocks per portfolio. From
the 6 stocks we are using here, pick 4 stocks to build two portfolios of 2 stocks each (no repeated stock). For example:
Portfolio 1 will have Stock A and Stock B, and Portfolio 2 will have Stock C and Stock D. Describe here the composition
of these two portfolios (just company names, not the weights in the portfolio).
(e) For the stocks in each of the Portfolios (call Portfolio 1 and Portfolio 2), calculate the Covariance and the
Correlation between their daily returns. Don’t forget to weight the products of the return deviations of the 2 stocks
of each portfolio, by the probabilities of states of the Economy.
(f) Consolidate the relevant data in a table to evolve to the portfolios analysis:
(g) Set an initial weight of 50% per stock in their respective portfolios. Example: Portfolio has 50% of A and 50% of
B, and Portfolio 2 has 50% of C and 50% of D.
(h) Determine the variance and standard deviation of both of the Portfolios 1 and 2. Example for Portfolio 1 (do for
both):
Chevron (A) Amex (B) DaVita (C) Caterpillar (D) Accenture (E) Sherwin-Williams (F)
Expected Return- E(R)
Variance- Var(R)
Standard Deviation- St Dev(R)
Decimals Percentage
Expected Return on Stock A- E (RA)
Expected Return on Stock Z- E (RB)
Variance of Stock A Returns- Var (RA)
Variance of Stock Z Returns- Var (RB)
Standard Deviation of Stock A Returns- St Dev (RA)
Standard Deviation of Stock Z Returns- St Dev (RB)
Covariance between Returns of A and Z- Cov (RA,RB)
Correlation between Returns of A and Z- Corr (RA,RB)
Portfolio 1 (Stocks A and B)
1- Relevant Information 2- Values 1- Relevant Information 2- Values
Weight of Stock A on the Portfolio- XA
Weight of Stock B on the Portfolio- XB
Variance of Stock A Returns- Var (RA)
Variance of Stock B Returns- Var (RB)
Covariance between RA and RB- Cov (RA,RB)
Variance of the Portfolio Returns- Var (RP1)
Standard Deviation of the Portfolio Returns- St Dev (RP1)
Portfolio 1
(i) Calculate the weighted average standard deviations of the returns for each portfolio. For that multiply the stock
weights by the individual stocks’ standard deviations and sum them.
(j) For both portfolios, calculate the variance of the portfolio return and the standard deviation of the portfolio
return. Assess the gains in terms of riskiness that you had by proceeding with diversification, making portfolios of 2
stocks.
(k) As you can find on Blackboard > Module 3 > Week 14 > Diversification Analysis- 2-Stock Portfolio Example
with Different Stock Weights > fin_3013_002_spring_2022_2_stock_port_study_different_stock_compositions.slsx,
for each of the portfolios (Portfolio 1 and 2), re-weight the stocks in these different compositions:
(l) As in letter (k), assess the gains with the diversification. Describe the data you’re seeing, how it evolves as the
concentration of the assets changes. Describe what happens with the expected returns of portfolios that have 100%
of the weight on a single asset.
CHALLENGE PROBLEM (50 EXTRA POINTS TO BE ADDED TO THE COURSE FINAL GRADE)
Using the same resources we used above, restricted to the Excel files and course materials, build a single portfolio
(call it Portfolio P) with all the 6 stocks listed in the first page. Perform the whole analysis in the same style as we
did from (a) to (l).
If you have doubts on some steps of the problem, I am here to clarify and guide you. I will not guide you from the
beginning to the end of the assignment. Needing, contact me.
Good luck!
David Tavares
100% of A
and 0% of B
90% of A and
10% of B
80% of A and
20% of B
70% of A and
30% of B
60% of A and
40% of B
50% of A and
50% of B
40% of A and
60% of B
30% of A and
70% of B
20% of A and
80% of B
10% of A and
90% of B
0% of A and
100% of B
100% of C
and 0% of D
90% of C and
10% of D
80% of C and
20% of D
70% of C and
30% of D
60% of C and
40% of D
50% of C and
50% of D
40% of C and
60% of D
30% of C and
70% of D
20% of C and
80% of D
10% of C and
90% of D
0% of C and
100% of D
Portfolio 2
Portfolio 1

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