8
Major Project
Part A
The file PortfolioManagementAssignment1.xlsx placed on the Learning Management System
subject page provides daily share price data and dividend data from 31 December 2014 to 31
December 2019 for 30 of the largest, by market capitalization, companies listed on the ASX.
Daily values of the All-Ordinaries Accumulation Index are also provided in that file. Note that for
this exercise the yield on Australian Government 10-year bonds is set at approximately 5 per
cent per annum (which may be used as a proxy for the risk-free rate of interest) and the equity
risk premium is 4 per cent per annum.
Each student will be allocated a portfolio comprising seven of these companies. Students whose
student number ends in 1 or 2 will be allocated companies 1, 3, 5, 7, 9, 11 and 14. Students
whose student number ends in 3 or 4 will be allocated companies 2, 4, 6, 8, 10, 12 and 15.
Students whose student number ends in 5 or 6 will be allocated companies 15, 17, 19, 21, 23, 1
and 4. Students whose student number ends in 7 or 8 will be allocated companies 16, 18, 20, 22,
2, 4 and 7. Students whose student number ends in 9 or 0 will be allocated companies 1, 3, 5,
10, 12, 17, and 19.
For your portfolio of companies and using the file PortfolioManagement3_8.xlsx as a template,
show the efficient frontier of all efficient portfolios (with and without short selling), and the capital
allocation line. For this analysis, expected returns are calculated using the Capital Asset Pricing
Model. Also, document the security market line for your portfolio of companies.
(5 marks)
9
Part B
This question uses monthly returns observed on US shares from 1926 to 2020 and specifically
uses data from Professor Ken French’s website -
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
You have been asked to assess the performance of a fund that invests in companies with very
small market capitalizations and very high book-to-market ratios. The file
PortfolioManagementAssignment2.xlsx placed on the Learning Management System subject
page provides the monthly returns to this portfolio for the period July 1926 to December 2020
inclusive. It also provides monthly excess returns (return on a market portfolio less the return on
a risk-free asset), monthly returns on a portfolio of small market capitalization companies less
returns on a portfolio of big market capitalization companies (the so-called SMB portfolio),
monthly returns on a portfolio of companies with high book-to-market ratios less returns on a
portfolio of companies with low book-to-market ratios (the so-called HML portfolio), and monthly
returns on a risk-free asset.
The period for you to examine is the sixty-year period beginning in 1937 plus the truncated value
of the number provided by the last two digits of your student number divided by four. So, if the
last two digits of your student number are 00, then TRUNC (0/4) = 0 and your sixty-year period is
from 1937 to 1996 inclusive. If the last two digits of your student number are 15, then TRUNC
(15/4) = 3 and your sixty-year period is from 1940 to 1999 inclusive. If the last two digits of your
student number are 99, then TRUNC (99/4) = 24 and your sixty-year period is from 1961 to 2020
inclusive. [This method is just a way of dividing the class into 25 groups].
For your period of sixty years, use regression analysis to determine and examine whether or not
the portfolio of companies with very small market capitalizations and very high book-to-market
ratios has outperformed when benchmarked against the Capital Asset Pricing Model, and also
whether it has outperformed when benchmarked against the Fama-French three factors.
(5 marks)
Part C
PortfolioManagementAssignment3.xlsx placed on the Learning Management System subject
page provides end-of-month prices (adjusted for dividends) for eighty-one Australian listed
companies from December 2001 to December 2015 and monthly returns from January 2002 to
December 2015. It also provides the market capitalisation, the book-to-market ratio, and the 52-
week high share price of each of these companies at the end of each year from 2002 to 2015.
10
Form three equally weighted portfolios. The first portfolio (HML) to be formed is long the N
companies with the highest book-to-market ratios and short the N companies with the lowest
book-to-market ratios. The second portfolio (SMB) to be formed is long the N companies with the
smallest market capitalisation and short the N companies with the largest market capitalisation.
The third portfolio (WML) to be formed is long the N companies that have share prices that are
closest to their 52-week high share price and short the N companies that have share prices that
are farthest away from their 52-week high share price. Each portfolio is rebalanced at the end of
each year.
N is equal to 5 plus the truncated value of the number provided by the last two digits of your
student number divided by five. So, if the last two digits of your student number are 00, then
TRUNC (0/5) = 0 and the portfolios have 5 long positions and 5 short positions. If the last two
digits of your student number are 19, then TRUNC (19/5) = 3 and the portfolios have 8 long
positions and 8 short positions. If the last two digits of your student number are 99, then TRUNC
(99/5) = 24 and the portfolios have 24 long positions and 24 short positions.
What is the return performance of the each of these portfolios over the period January 2003 to
December 2015? If your brief was to establish a long-only value fund of N shares (within the
investible universe of the 81 companies), what shares would be held in January 2016? If your
brief was to establish a long-only fund of smaller companies (within the investible universe of the
81 companies), what shares would be held in January 2016? If your brief was to establish a
long-only fund of companies based on a 52-week high strategy (within the investible universe of
the 81 companies), what shares would be held in January 2016?
11
(5 marks)
Part D
The daily closing prices of GameStop (NYSE: GME) shares from 11 June 2020 to 10 June 2021
are provided below.
One definition of an efficient market is one where prices are an unbiased estimate of value and
where information is incorporated into prices instantaneously and without bias. Using this
definition it is difficult to argue that estimated values could have changed to such an extent, as to
be able to argue that at each point in time over this period that prices were unbiased estimates of
values at that time. Indeed, the person synonymous with research providing evidence supportive
of markets being highly efficient, Eugene Fama, when interviewed in March 2021, stated that
“GameStop (was) a clear case where, for a couple of days, the market was inefficient” (Gold
(2021)). In this interview it is the definition of market efficiency referred to above that is being
discussed.
However, in order for abnormal returns to be able to be earned, prices must be biased estimates
of value and there must be not limits to arbitrage. In the case of Gamestop, what limits to
arbitrage may have existed to prevent abnormal returns from being earned?
Your answer should compare the case of Gamestop shares in 2021 with the case of the relative
pricing of Royal Dutch shares and Shell shares from 1990 to 2002, and the case of the relative
pricing of Palm shares and 3Com shares in 1999. These cases are discussed in Bodie, Kane
and Marcus (2021, pp. 378 – 379), Froot and Dabora (1999), Lamont and Thaler (2003), and in
12
the Lecture Recording for this subject titled “Behavioural Finance and Market Efficiency - Limits
to Arbitrage”.
References
Froot, K. A. and E. M. Dabora, (1999), ‘How Are Stock Prices Affected by the Location of the
Trade?’, Journal of Financial Economics, Vol. 53, pp. 189 – 216.
Gold, H, (2021), ‘Nobel Winner Eugene Fama on GameStop, Market Bubbles and
Why Indexing is King’, MarketWatch, March 3, 2021. Retrieved 11 June 2021.
https://www.marketwatch.com/story/nobel-winner-eugene-fama-on-bubbles-why-indexing-is-stillking-
and-gamestop-11614776294
Lamont, O. A. and R. H. Thaler, (2003), ‘Can the Market Add and Subtract? Mispricing in Tech
Carve-outs’, Journal of Political Economy, Vol. 111, pp. 227 – 268.
(15 marks)
The word limit for the major project is 3000 words. It is recommended that the majority of the
words be allocated to Part D.
Solution
Major
Project
Part
A
In
this part of the project I was required to find the efficient
frontier of all the efficient portfolios, the capital allocation line
while calculating the expected returns using the Capital Asset
Pricing Model
(CAPM), and to document the security market line of all these
companies assigned to me for part A.
I,
therefore,
used the PortfolioManagementAssignment1.xlsx to find the seven
companies (together with their data) allocated to me. I then used
that financial data to answer part A. My workings are found in the
attached file PortfolioManagement3_8.xlsx.
The
seven companies assigned to me are:
Alumina
AWC
ANZ
Bank Limited ANZ
Caltex CTX
Incitec
Pivot IPL
Mirvac
Group MGR
Sonic
Healthcare SHL
Telstra
Corp TLS
I
then took price data of the above companies, calculated daily
returns which is equal to price today-price yesterday – 1. Then, I
got the averages daily returns for each company. After that, I
calculated the variance Covariance matrix/ bordered Covariance
matrix. I found the portfolio weights for the seven companies
(companies = 1/7) so each got weights of 0.142857142857143 which when
added together equals
1 or (100%) meaning that all the capital has been allocated equally.
|Once
I had the portfolio weights, I then calculated the first portfolio
mean and variance.
Portfolio
Return = wTµ
= SUMPRODUCT (w,µ)
Portfolio
Variance = wTΕw
= MMULT(TRANSPOSE
(w), MMULT (E,w))
Then,
used the excel solver function was to calculate the portfolio
weights. After that, the portfolio variances are calculated before
calculating the series of portfolio standard deviation and portfolio
mean.
The
series of portfolio standard deviation and portfolio mean are used to
create the chart
which
is the portfolio frontier.
The
portfolio frontier is then formatted to include the title,
the x-axis
is the
portfolio
standard deviation (which is a measure of risk), while the
y-axis
is
labeled the portfolio
means
(which is a measure of return).
Generally,
the
stocks above the minimum variance are the efficient portfolio
frontier and those below the minimum variance are the inefficient
portfolio frontier.
It
is taken
that any point
at the lower part of the curve gives a lower return for the risk you
take (inefficient) as compared to any
of the
points at the upper point
of the curve. this
means those at the top are more
efficient.
This
is important for rational investors because when
they look at the chat, they would not choose any point at the lower
part of the curve, this is because they can get a higher return for
the same level of risk if they
choose
the points at the upper parts of the curve. ,
the
upper part of the curve is known as the efficient frontier,
and the lower inefficient frontier
Part
B
In
part B of the project, I was required to access the performance of
funds invested in the following companies.
60
year period from 1937 + TRUNC no.
which
is equal to 10/4 =2
1937+2
= 1939+59 = 1998
therefore,
the period to be examined is between 1939
to 1998. This
period was highlighted with
the color yellow
in
the file PortfolioManagementAssignment2.xlsx to
identify
easily.
Using
the data provided in PortfolioManagementAssignment2.xlsx and the
period to be examined of 1939 to 1998, I used together with
regression analysis to determine and examine whether the portfolio of
companies with small market capitalization and the very
high-to-market ratio has outperformed when bench-marked against the
Capital Asset Pricing Model, and small market capitalization and the
very high-to-market ratio has outperformed when bench-marked against
the Fama-French three factors.
The
results were as follow:
The
performance of small/ value portfolio bench-marked against the market
return (or the capital asset pricing model (CAPM) were as follow:
I
used the file PortfolioManagementAssignment2.xlsx (the results
attached) and applied the regression analysis using excel on the
highlighted period of 1939 to 1998 and the output should be the value
(or alpha) under intercept
of
0.50431.
(see
attached file).
It
shows results over the American company history, the positive alpha
is shown under the intercept of that regression.
That
positive alpha is the monthly abnormal return of 0.50431 % on the
portfolio which is also taken as the annual abnormal return and
annual alpha of the order of 5 %.
The
downside of this result from regression analysis is that the return
is unexplained. In addition, this means that when the performance of
small/ value portfolios are benchmarked
against the market return (or the capital asset pricing model (CAPM)
the earned excess return of more than
5 % per year cannot be explained by the figures provided.
The
figures also show that the stock is
riskier than average because of the beta of 1.26779 which
means any person invested in these small value stocks would have made
great returns. But the bottom line is a more realistic model should
be used that takes into account market return, size, and value
factors. And, this will involve benchmarking
the performance of the same small/ value portfolio against 3 factors
that pick up sensitivity to size, sensitivity to the market, and
sensitivity to value.
Assessing
the performance of the small/ value portfolio benchmarked
against the Fama French 3 factor model
I
did another regression of the same period 1939 to 1998 but this time
taking into account the
market
return, size, and value factors and the results were as follows:
A positive alpha of 0.0591 (see attached file) was given as at the
intercept. this figure is the 0.0591% of monthly abnormal return
which translates into over 1% of abnormal year returns.
In
addition, the figures below are the 3 factors x1, x2, and x3 of
market return, size, and value, which measure the sensitivity of the
portfolio and explain returns of a portfolio far more fully than just
the value given when using
the Capital Asset Pricing Model (CAPM)
Thus,
the most appropriate model is the Fama-French 3 factor model, not the
simplistic Capital Assets Pricing model
In
conclusion, the best results for the performance of small market
capitalization and very high book-to-market ratio are obtained when
the Fama-french
model is used because it takes into account 3 factors of
market
return, size and value.
Part
C
For
this part of the project, N is equal to 5 plus the truncated value of
the number provided by the last two digits of the student number
divided by five.
Therefore
for this case N = 5 + 10/5
N
= 5+2
N
= 7
In
addition, what is required is to formulate 3 equally weighted
portfolios and this was done using the provided
PortfolioManagementAssignment3xlxx. The ranking is as follow:
First
portfolio (HML) = 7 companies with the highest book-to-market ratio
and the shot 7 companies with the lowest book-to-market ratios. These
portfolios will be made up of companies that
have less value because they have a
high book-to-value ranking,
meaning that if an investor was to buy from this portfolio they would
pay more funds. They are also referred
to as growth stock companies. Each year the portfolio will be
evaluated and new rankings of companies will determine if the
companies with high book to market ratios are remaining in the
portfolios.
For
instance, in PortfolioManagementAssignment3xlxx the 7 companies that
are in this portfolio
for the year ending December 31 2002 are Sirtex Medical (Ranking Of
81), Cochlear (80), REA Group (79), IREE
(78), Woolworths (77), ASX (74). The portfolio is then rebuilt at the
end of the year according to the performances of those companies.
Therefore, at end of the year December 31, 2003, the 7 companies that
are in the portfolio are Sirtex Medical (81), Cochlear (79)
Woolworths (76), Rea Group (73),
IREE (78),
Rio Tinto (77) Oz Minerals (75). In the new year, a new portfolio is
rebuilt, and the process continues.
The
second portfolio (SMB) = 7 companies with the smallest market
capitalization and short the 7 companies with the largest market
capitalization. What can be noted here is companies with the smallest
market capitalization are good to invest in, because they are ranked
according to their value (the one with a ranking of 1 being with the
most value to invest in) and those with the largest market
capitalization are growth companies ( with higher ranking and are
short sold off by investors)
The
portfolios of these companies are made using the excel worksheet - of
the file PortfolioManagementAssignment3xlxx - labeled market
cap
and I used the rankings to form the portfolios. For instance, on
the year 31 December 2002, the 7 companies with the smallest market
capitalization were
Cash Converters INTL. (1) WEBJET (2), Tox Free Solutions (3),
Western Areas (4), Reckon (5) Rea Group (6) Hansen Technologies (7)
Hansen
Technologies. A
new portfolio is then rebuilt each year according to the performances
of companies in the previous year.
The
third portfolio (WML) = 7 companies that have share prices that are
closest to their 52-week high share price and short the 7 companies
that have share prices that are farthest away from their 52-week high
share price.
Using
the 52-week
excel worksheet of the file PortfolioManagementAssignment3xlxx on 31
Dec 2002, companies that
fall in a portfolio where they can be bought and held or close to
their 52 weeks
high are found using the low ranking of (starting from 1) and they
are Adelaide Brighton, Sky Network TV.(ASX), Skycity ENTM.Group
(ASX), Sims Metal Management, REA GROUP, OZ Minerals, Fletcher
Building (ASX). And again, the portfolio is rebuilt each year and the
companies that remain in the portfolio depending
on the new rankings. Likewise,
those companies furthest from their 52 week high are considered to be
growth companies and are ranked higher. The portfolio of these
companies also changes each year with new ranked firms.
One
might conclude that when using size and value strategy, the portfolio
of small companies outperformed the portfolio of big companies as
shown by the returns (the return worksheet of file
PortfolioManagementAssignment3xlxx). The average return of small
companies in small stock is 1.73% compared to that of portfolios of
big companies which is 0.57%
Using
the book strategy (where companies are ranked from smallest to
largest based on
a market-to-book ratio. These
companies to be invested in are the small ones because they have
better pricing and can be sold in the future. Therefore, they will
outperform larger ones.
When
it comes to how much shares are to be held in January 2016 = (M/B
performance) the average monthly return from a portfolio of value
stocks was 1.35%, the average monthly return of growth stock was
1.17% and the average monthly return of the HML portfolio was 0.18 %
per year.
long-only
fund of companies based on a 52-week high strategy shares to be held
in January 2016 can be found using the momentum strategy and the
52-week
high worksheet showing share prices of stock at their 52 weeks
high in PortfolioManagementAssignment3. companies bought are those
which are close or at their 52 weeks
high and those that are far
away
from their 52 week
high are short sold. All this is done using the ranking found on the
same 52 weeks
high excel
worksheet.
Therefore,
in the return excel worksheet the 52 week high winners were 1.06% and
loser stocks earned returns per month of 0.96 % and winner stocks
outperformed loser stocks by 0.10 % per year which shows the use of
the momentum strategy.
Part
D
The
GameStop saga of January 2021 has taught important lessons about
efficiency, diversification, investing, and trading. These lessons
were stressed more clearly by Statman (2021) in his article
titled:
Trading Isn’t the Same Thing as Investing.
GameStop,
a brick and Mortar
based gaming business has been struggling for some years now –
since most gaming retailers
moved their businesses online. Therefore, most investment
professionals and finance practitioner community expected it to
continue struggling
and the saga started when amateur investors bought shares in Gamestop
to
cause a short squeeze in the market. They did this using a
no-commission mobile app known as Robinhood. Indeed they
caused a viral short trading frenzy in January 2021 from less than
$20 % per share to a high $483. Moreover, in early
February the share price quickly went back to around $50.
Within
that period, those who bought shares
quickly and sold within that short period benefited, but the majority
of irrational investors lost money because they bought shares and
kept them until they were too
low to sell.
Statman
(2021) explained how the rational investors described in standard
finance know that markets are hard to beat, but many of the normal
investors described in behavioral finance, such as GameStop’s
amateur investors who believe that markets are easy to beat.
In
reality, they found out that the market beats most investors who
attempt to beat it and most of the time cognitive and emotional
errors mislead many investors into thinking that they can easily beat
the market. Many people believed
that the market price of GameStop would fall any time through shot
selling (or short Squeeze strategy)
Limits
to Arbitrage
There
are two sources of Limits to Arbitrage and one of them is Fundamental
risk where errors may not be corrected for an (unknown) long time,
the other is implementation costs which are cases where
implementation costs can be high- especially if shares are
overvalued.
To
see in if reality the two forms of limits to arbitrage takes place,
the relative pricing of the Siamese twin companies has been used. For
instance, in the
Royal Dutch Petroleum and Shell Transportation case, the limit to
arbitrage prevented any mispricing from being corrected.
As
Siamese twin companies, Royal Dutch and Shell had a structure where
the two companies agreed to merge their interests on a 60: 40 basis
while remaining separate and distinct entities {Froot & Dabora,
1999). but interestingly they were two separate companies at some
point, where each company had its shares. the shares in one company
were
independent of
the shares of another. Royal Dutch company was from the Netherlands,
while Shell Transportation was listed in the United States. What is
amazing about these two companies is, that they both hard the same
dividends (mainly because the dividends were always paid in US
dollars), taking advantage
of having no foreign exchange difference and they would pay out the
same payouts if the companies were to be liquidated. In addition,
shareholders in the two
companies
also had identical voting rights on management decisions and they
were
a common board for the two companies (Froot & Dabora 1999).
So
what took place?
-
from 1998 to 2002 their prices deviated from one another (Deviation
of parity)
-
And for 10 years when an investor tried to use the Arbitrage strategy
to earn arbitrage profits by short-selling
shares in Royal Dutch and at the same time buy shares in a relatively
undervalued shell company. They took this decision because Royal
Dutch looked overpriced
compared to shell most of the time during that period. but the
problem is with the Arbitrage strategy the investor would be making a
bigger loss
on shares sold of Royal Dutch compared to the gain from buying the
shares in Shell.
Therefore,
Froot & Dabora (1999) explained how arbitrage disciplines the
price gap. It an unrealistic world benefits or gains from the
arbitrage strategy would be realized but not in reality.
The
reason why most investors who used the arbitrage strategy on Royal
Dutch and Sell during that period is because they were fundamental
risks, where the mispricing
may not be corrected for an (unknown)
long time.-And in terms of implementation cost the management cannot
maintain a short-selling
position on a company forever.
Another
realistic cause
of limits to arbitrage and the law of one price is the case of 3com
and Palm.
In
that case, the limits to arbitrage were preventing mispricing from
disappearing, even though the market was not fully efficient, and on
top of that individuals in these companies were
not processing information correctly. in their paper, Can the Market
Add and Subtract? Mispricing in Tech Stock Carve‐outs, Lamont &
Thaler (2003) wrote a paper to investigate the violations of the law
of one price. They used
cases
with detailed evidence of prices that
were wrong or fictitious.
The
conclusion was that the main driver of the law of one price in
financial markets is arbitrage,
In this case, the buying and selling of the same security for two
different prices with the hope of gaining incentives
to
eliminate any violations of the law of one price.
And
indeed one of the investigations done by Lamont & Thaler (2003)
was on 3Com and palm. Palm, which makes hand-held computers, was
owned by 3Com, a profitable company selling computer network systems
and services. So
when
3com spun off Palm, it sold 5% of its subsidiary Palm through an
official public offering and its shareholders retained 95 %.
Interestingly,
3com was expected to perform better than Palm, and the price of 3 com
shares was also expected to be greater than one and a half Palm
shares mainly because each Shareholder
of 3com was to receive a free one and half shares because they had
retained 95% shares of Palm
But
to everyone's surprise, 3Com shares traded at a lower price than that
of its subsidiary Palm. This strange situation happened because, for
the year from 2nd March
2000 to the 18th of September 2000, a graph of dollars per share is
usually used to explain:
-
On
the day of listing Palm the price difference was $82-1.5 x $95
meaning 1 3Com share could be purchased for $82 but on the first day
of listing investors were buying Palm shares and paying $95 per
share. So 1.5 Palm shares would cost 1.5 lots of $95 and you could
buy 1 3com share that entitles you to 1.5 Palm shares for only $82.
-
The mispricing
appeared to
be at least $82 less 1.5 lots of $95 or $62.50.
-when
most investors observed that, they used the arbitrage strategy of
buying 3Com shares and short sell Palm shares, the problem with the
arbitrage strategy,
in reality,
is it was not possible to sell overpriced assets and buy the
under-priced shares, simply because all the Palm shares that were
being held were already shot sold so, in reality, it was not possible
to sell the Palm shares which they did not even own.
Thus
this mispricing occurred because of overconfidence, irrational
behavior by
investors
who were buying too much of Palm shares at the height of the .dotcom
bubble and they didn't benefit from the mispricing at all.
The
lesson learned
here was that when you don't own shares in a company, sometimes it is
not possible to arrange a short sale.
to
do this properly, you might have to find an institutional investor
who will allow you to borrow the shares off them and sell them
temporarily.
Lamont
& Thaler (2003) also documented how shorting costs are the
precise market friction that allows prices to be wrong, and
irrational
investors,
woefully uninformed, endowed with strange preferences, or willing to
hold overpriced assets, usually get it wrong and lose out.
References
Lecture
Recording for this subject titled “Behavioural Finance and Market
Efficiency - Limits to Arbitrage”.
STATMAN,
M. (2021), 'Trading Isn’t the Same Thing as Investing: The Lessons
of GameStop', Journal of Avantis Investors Retrieved
24 July 2021.
https://www.avantisinvestors.com/content/dam/ac/pdfs/ipro/viewpoint/avantis-lessons-of-gamestop.pdf
Froot,
K. A. and E. M. Dabora, (1999), ‘How Are Stock Prices Affected by
the Location of the Trade?’, Journal of Financial Economics, Vol.
53, pp. 189 – 216.
Lamont,
O. A., and R. H. Thaler, (2003), ‘Can the Market Add and Subtract?
Mispricing in Tech Carve-outs’, Journal of Political Economy, Vol.
111, pp. 227 – 268.