Investment in Public Equity: Final Individual Assignment
Dr. Bige Kahraman Alper
TRINITY TERM 2023
There are FOUR questions in this assignment.
Please start the answer to each question on a separate page.
The necessary data for question 4 is in Excel file: Assignment_data.xlsx
Submit written answers to all questions (preferably in pdf file). Each question is 25 points in total.
Most of the questions indicate a suggested length of an answer. This is only a guidance for students.
For question 4, submit also the underlying calculations in form of an Excel file OR a code in a
programming language of your choice (preferably MATLAB, Python, or R). The Excel spreadsheet OR
the programming code serves as students’ additional opportunity to demonstrate their individual
effort.
Disclaimer: Note that the numbers and data provided are from sources (WRDS, CRSP,
Yahoo.com/finance and Kenneth French website) that are available publicly or through university
library and are further adjusted for the purpose of this assignment. The numbers and data are
provided purely for the purpose of this assignment and no judgment on the performance of the funds,
funds’ current or past managers should be done beyond the scope of this assignment.
1. Academic research over the last few decades has shown that there seems to be a number of so-
called anomalies which have delivered superior returns. [25 points]
a. Describe one such anomaly that has been documented to deliver on average superior returns and
is based purely on selecting stocks on their past performance. (Hint: Describe the selection rule, which
stocks are expected to perform better and which worse. Describe how this anomaly can be
implemented in a trading strategy.) (Suggested length of the answer is ca. five lines.) [5 points]
b. Describe one such anomaly that has been documented to deliver on average superior returns and is
based on valuation metrics. (Hint: Describe the selection rule, which stocks are expected to perform
better and which worse. Describe how this anomaly can be implemented in a trading strategy.)
(Suggested length of the answer is ca. five lines.) [5 points]
c. There are at least two views about the source of the superior performance of such anomalies that
have fundamentally different implications about interpretation of risk-adjusted performance. Explain
these two views and discuss the implications of these two different views for the debate on efficient
markets hypothesis (Suggested length of the answer is ca. five lines.) [5 points]
d. Discuss the ‘Big Data’ applications for aiming to generate alpha based on guest speaker lectures
(Suggested length of the answer is ca. five lines.) [5 points]
e. What are the potential problems associated with such trading strategies an investor should be
aware of? (Hint: State TWO aspects.) (Suggested length of the answer is ca. five lines.) [5 points]
2. ETFs, open-end mutual funds and hedge funds are the most popular pooled investment vehicles.
Compare these investment vehicles in terms: [25 points]
a. value they provide to their clients (Suggested length of the answer is ca. five-ten
lines.) [10 points]
b. impact they have on market efficiency (Suggested length of the answer is ca. five-ten
lines.) [10 points]
c. future growth projections (Suggested length of the answer is ca. five-ten lines.)
[5 points]
3. You are in charge of managing the equity portfolio of an institutional investor and currently you are
reviewing the allocation to individual active mutual funds. The investor invested in these actively
managed mutual funds five years ago and would like to review this allocation and potentially make
some changes to improve net performance. Table A below gives an overview of the active mutual
funds the investor wants to review. It shows the funds’ performance and return characteristics over
the last five years and their expenses/costs. Other parts of the investors’ equity portfolio are invested
in well-diversified broad equity indexes and are not described in more detail here. Table B gives an
overview of exchange traded funds (the performance and return characteristics are also based on the
period of last five years).
Table A. Summary of the investor’s active mutual funds. Total performance is in percentage points and
shows the total performance from 2015 to 2019. Average return, volatility and alpha are annualized
and expressed in percentage points. R squared and expense ratio are also in percentage points.
Cusip 00191K83 92828N59 03332V77 00142F12 00141T27
Name AQR Large
Cap
Defensive
Style Fund
Virtus KAR
Small-Cap
Growth
Fund
Ancora
Special
Opportunity
Fund
Invesco Value
Opportunities
Fund
Invesco
Endeavor
Fund
Total
performance
88.38
164.66
50.69
31.65
23.08
Average return 13.21 20.64 9.15 7.37 5.21
Volatility 9.84 14.35 13.73 19.45 14.64
Alpha and loadings to 3-factor Fama and French 1993 model
Alpha 3.14 10.42 0.06 -5.54 -4
Alpha t-stat 2.17 2.91 0.02 -2.96 -2.6
Market 0.77 0.82 0.88 1.36 0.98
Market t-stat 22.61 9.79 12.35 20.64 16.81
SMB 0.77 0.82 0.88 1.06 0.98
SMB t-stat 22.61 9.79 12.35 20.64 16.81
HML -0.16 0.5 0.31 0.53 0.28
HML t-stat -3.11 3.95 2.86 3.45 3.2
R squared 90.57 73.03 78.35 90.85 87.31
Expense ratio 0.3 1.37 1.73 0.85 2.14
Front-end load 0 0 0 0 0
Back-end load 0 0 0 0 0
Table B. Summary of the potential Exchange Traded Funds. Total performance is in percentage points
and shows the total performance from 2015 to 2019. Average return, volatility and alpha are
annualized and expressed in percentage points. R squared and expense ratio are also in percentage
points.
Ticker VTI IJR SPLV RFV DIG IWC WBIL
Name Vanguard
Total
Stock
Market
Index
Fund ETF
Shares
iShares
Core
S&P
Small-
Cap ETF
Invesco
S&P 500
Low
Volatility
ETF
Invesco
S&P
MidCap
400 Pure
Value
ETF
ProShares
Ultra Oil
& Gas
iShares
Russell
2000 ETF
WBI
BullBear
Quality
3000 ETF
Total
performance
69.94
57.6
71.45
36.19
-48.38
37.19
16.17
Average return 11.39 10.4 11.24 8.27 -4.62 7.77 3.49
Volatility 12.23 16.02 9.19 20.61 41.38 16.99 10
Alpha and loadings to 3-factor Fama and French 1993 model
Alpha -0.14 0.39 3.03 -0.84 -21.24 -0.24 -4.12
Alpha t-stat -0.55 1.07 1.11 -0.9 -1.89 -0.16 -1.39
Market 0.98 0.89 0.59 1.3 2.24 0.97 0.64
Market t-stat 160.78 32.7 9.18 17.77 8.53 27.19 9.24
SMB -0.01 0.87 -0.18 1.01 0.92 0.98 -0.03
SMB t-stat -0.55 17.07 -1.82 6.04 2.33 21.11 -0.3
HML -0.01 0.32 -0.16 0.58 1.52 0.25 0.06
HML t-stat -1.8 7.03 -1.88 6.26 4.39 5.11 0.6
R squared 99.8 97.16 61.52 91.2 68.13 96.83 62.14
Expense ratio 0.03 0.07 0.25 0.35 0.95 0.6 1.21
Front-end load NA NA NA NA NA NA NA
Back-end load NA NA NA NA NA NA NA
Each of the mutual funds have kept the same fund manager over the last five years. Although you
understand that it is difficult to predict exactly how active manager will perform in future, you believe
that the five-year period provides enough data to have solid estimates about managers’ performance,
which also gives decent estimate for future performance.
a. Investment in which of these mutual funds turned out to be a good decision? Why? Do you
recommend to keep the investments in these fund(s)? State the CUSIPS. (Suggested length of
the answer is ca. two lines.) [5 points]
b. Which of the positions in the active mutual funds should be closed? Why? State the CUSIPS.
(Suggested length of the answer is ca. two lines.) [5 points]
c. The investor would like to replace each of the mutual funds you suggested to close in part b.
by an ETF from Table B. In doing so, the investor would like to focus on earning returns solely
from the exposures to the three factors. For this reason, the investor would like to maintain
the exposure of each position to the underlying factors as close as possible. How would you
replace each of these mutual funds investment with an investment in the ETFs in table B so
that each ETF investment has as close exposure to the risk factors as the mutual fund
investment to be replaced? (Hint: For each mutual fund you want to replace, suggest only one
ETF from Table B.) State the CUSIPS and tickers. (Suggested length of the answer is ca. two
lines.) [5 points]
d. Using the estimates in the two tables, what would be the expected improvement by giving up
the actively-managed part of the return for each of the suggested replacements? (For each
replacement state the expected improvement in percentage points.) (Suggested length of the
answer is ca. three lines.) [5 points]
e. What would be the expected change in performance due to different investment costs in each
of the suggested replacements? (For each replacement state the expected improvement in
percentage points.) (Suggested length of the answer is ca. three lines.) [5 points]
4. Fidelity Magellan Fund (Magellan) is a mutual fund that was launched in 1963 and became one of
the best-known and largest active management funds. During its long history, a handful of prominent
fund managers were in charge of managing this fund. Peter Lynch took over the fund in 1977 and is
associated with large increase in fund’s assets under management and stunning fund’s performance.
In this question, you will focus on the performance of the fund and the fund’s managers in later years
after departure of Peter Lynch. You will focus on the period starting from July 1992, when Jeffrey Vinik
took over the management of the fund. The term periods of the Magellan’s managers from July 1992
are:
• Jeffrey Vinik: July 1992 – June 1996
• Robert Bob Stansky: July 1996 – October 2005
• Henry W. Lange: November 2005 – September 2011
• Jeffrey S. Feingold: October 2011 – present
The Magellan funds investment approach is described in its factsheet as: “The fund employs a unique
risk-managed portfolio construction process that attempts to optimize alpha (risk-adjusted excess
return). Rather than adjusting security weights according to conviction, we use an equal-active-weight
approach, which limits the impact of dramatic fluctuations in any single position, while still allowing
for high active share (benchmark differentiation).” The factsheet further states that the fund’s
expense ratio is 0.67%.
The data for this exercise are provided in a separate excel file ‘Assignment_data.xlsx’. The file contains
this data:
- Magellan fund’s:
o Fund return: Magellan’s monthly returns (simple return), net of fees
o Adj Close: Magellan’s Adjusted Close from Yahoo.com/finance
- Data from Kenneth French website for:
o Market excess return: US Aggregate market excess return
o SMB: Size factor (SMB) return
o HML: Value factor (HML) return
o Risk-free rate
a. Calculate the following statistics for the Magellan fund and the aggregate US stock market for
the period from July 1992 to February 2020: Total performance in percentage points, average
monthly return, standard deviation of monthly return, average monthly excess return and
standard deviation of the excess return. Use simple (not log) returns. Express the results in
percentage points, at monthly frequency. Round to two decimal places where necessary.
Organize your results in a table with one column for the fund’s statistics and second column
for the aggregate US stock market statistics. [2 points]
b. Calculate the following statistics for the Magellan fund and the aggregate US stock market for
the period of each fund manager listed above: Total performance in percentage points,
average monthly return, standard deviation of monthly return, average monthly excess return
and standard deviation of the excess return. Use simple (not log) returns. Express the results
in percentage points, at monthly frequency. Round to two decimal places where necessary.
Organize your results in a table with the statistics of each manager in individual columns next
to columns with statistics for aggregate market for the same time period. See a suggested
format below. [2 points]
Vinik Market
during Vinik
… Feingold Market during
Feingold
Total
performance
…
St. dev.
Excess return
c. For a better comparison, transform the summary statistics calculated in previous question
to annual frequency and calculate the Sharpe ratio for every fund and aggregate market
during each manager’s term. Please report only the Sharpe ratios, not the underlying
statistics. Round to three decimal places. Under which managers did the fund perform
worst and best according to Sharpe ratio. Did any of these managers achieve better Sharpe
ratio than aggregate market? [2 points]
d. In this part, you will perform a relative performance evaluation of the Magellan fund under
each of the four fund managers. Consider the following two benchmarks for evaluating the
performance of the Magellan fund:
a. One factor model with respect to aggregate US stock market excess return.
b. Three factor model (Fama and French 1993) with respect to aggregate US stock
market excess return, the size factor and value factor.
Both benchmarks should be estimated using fund’s net excess returns (simple return
minus
risk-free rate) [10 points]
Tasks of this sub-question:
(i) For each of the two benchmarks, estimate the fund’s alpha, its 95% confidence
interval, factor loadings, R-squared for each manager’s term. Then calculate the
information ratio for each manager’s term. When reporting results, please
annualize the estimates of alpha and its confidence interval and express in
percentage points (i.e., multiply by 12 to annualize and then by 100 to express in
percentage points). Round your estimates to three decimal places.
(ii) Using the results, briefly comment on the differences in the estimated alphas
between the two models and across the managers. (Suggested length of the answer
is ca. three lines.)
(iii) Which manager seems to best fit to the description of a closet tracker (i.e., manager
who is supposed to perform active management but rather follows/track an
aggregate benchmark)? Why? (Suggested length of the answer is ca. two lines.)
(iv) Which manager’s management style seems to be most active (i.e., least replicable
with the benchmarks). (Suggested length of the answer is ca. two lines.)
(v) Which manager was having the best judgment in taking ‘idiosyncratic’ risk by
deviating from the benchmarks? Why? (Suggested length of the answer is ca. two
lines.)
e. Now, you are in position to give advice to institutional investor who invested in the Magellan
fund. Would you recommend keeping investment in the Magellan fund? Why? (Suggested
length of the answer is ca. two lines.) [5 points]
f. Discuss why it is still possible that all fund managers have good skills in actively managing
investment funds. (Suggested length of the answer is ca. five lines.) [4 points]