RSM332 - Fall 2022 Assignment III
- Your are allowed to work alone or in groups (maximum five persons). Groups can be
formed across sections of different instructors.
- You will submit your electronic copy as a single Excel file. Use the sheet hw3.xlsx to
input your answer, making sure that you use a different sheet for each subquestion,
e.g., Q1.a, Q1.b, etc. The submitted solutions need to be clear enough that the TA
understands how the solution was obtained.
- Assignments are to be submitted on Quercus via file upload in the Assignments section
by 11:59p.m. on Tuesday December 8th. Only one member of the group needs
to submit the assignment, which MUST include a cover page listing all of the members
of the group (first sheet in the file hw3.xlsx). It is your responsibility to ensure that
the person who submits the assignment does not drop the course or the copy will be
lost! We will post the solutions soon after the deadline, so late assignments will
not be accepted.
- Every group should independently work on the calculations and the write-up. It is
expected that all members of the group will be equally involved in working with all
questions.
1. Use the data contained in the sheet “data Q1” from the Excel file hw3.xlsx, that
is available on Quercus. The file contains the monthly stock return data (in decimal
form) for 11 industries: Nondurables, Durables, Manufacturing, Energy, Chemicals,
Equipments, Telecom, Retails, Health, Utilities and Finance. The data sample period
is 2000/01-2022/09. For questions (a) and (b) assume you cannot invest in the risk-free
asset and that there are no short-sale constraints.
(a) Compute the mean and standard deviation for each of the 11 industry portfolios
and plot them in a graph where the x-axis is the standard deviation and the y-axis is
the average return.
(b) Perform a mean-variance optimization using the 11 industry portfolios. In par-
ticular, find the portfolios that minimize the variance for the following levels of mean
(monthly) return: E[Rp] = 0.00%, 0.40%, 0.80%, 1.20%, and 1.60%. Compute the
standard deviation of each of the optimal portfolios. Plot the efficient frontier in a
second graph along with the industry portfolios. Why is the frontier to the left of the
individual industry portfolios?
For the following questions, assume that you have access to the risk-free asset.
(c) Assume the monthly risk-free rate is 0.1 %. Find the mean, standard deviation,
and Sharpe ratio of the portfolio that has the maximum Sharpe ratio. In a third
graph, plot (1) this portfolio, (2) the Capital Market Line (CML), and (3) the optimal
1
frontier obtained in part (b). Why is this portfolio called the tangency portfolio?
What is the Sharpe ratio of this portfolio?
(d) After acknowledging the importance of Environmental, Social, and Governance
(ESG) issues in your investment, you decide not to invest in polluting industries and
those with low governance index. Your research leads you to believe that the following
industries have a low ESG score: Energy, Chemicals, and Nondurables. Thus, you only
have access to the remaining 8 industry portfolios. Re-do the analysis in part (b) and
(c). What happens to the efficient frontier as compared to that from part (b)? What
about the highest achievable Sharpe Ratio as compared to that from part (c)? Explain.
2. Use the data contained in the sheet “data Q2” from the Excel file hw3.xlsx, that is
available on Quercus. The file contains the monthly return data (in decimal form)
for Fama-French 3 factors, risk-free rate and 4 funds that invest in firms with specific
characteristics:
1. Low Beta fund invests in firms with low CAPM betas.
2. High BM fund invests in value firms, i.e., firms with a high book-to-market ratio.
3. Low Net Issuance (NI) fund invests in firms that have not been issuing much
equity lately (net issuance = total proceeds from new share issuance minus shares
redemption).
4. High Dividend yield (DP) fund invests in firms paying a high dividend as a
proportion of equity value.
The data sample period is 1963/07-2022/09.
(a) Run a regression of excess returns on a constant and the excess returns on the
market for each of the 4 funds (you are allowed to use the functions SLOPE and
INTERCEPT ), that is,
Ri,t ?Rf,t = αi + βi(Rm,t ?Rf,t) + ?i,t,where i is the funds
Report your average excess return and estimates of αi and βi for each fund. According
to the CAPM, which fund is the most risky, which is the safest? Briefly comment your
findings.
(b) In a graph where the x-axis is the funds’ β, and the y-axis is the expected return,
report for each fund the expected return (estimated using the sample average) along
with the estimated βi. In the same graph, draw the Security Market Line. Based on
the information in this graph, which one of the funds is the most attractive? Explain.
(c) Your friend advise you to use the Fama French 3-factor model rather than the
CAPM model to evaluate the performance of the fund. That is, run the following
regression model:
Ri,t ?Rf,t = αi + βi(Rm,t ?Rf,t) + βHMLi HMLt + βSMBi SMBt + ?i,t.
Report your estimate of αi for each fund. How does your conclusion from part (b)
change after controlling for the three factors?