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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)
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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.
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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?
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(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
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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.
Small market capitalization and very high book-to-market ratio using data provided in the file PortfolioManagementAssignment2.xlsx.
In my case, the period I was tasked to examine was calculated as follow:
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.
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