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J&G Investment Advisors
250 N. 32nd Street
Philadelphia, PA 19104
215-430-2997
Dear Mr. Black:
Below is our proposal for your new investment opportunities. Thank you for your continued
loyalty to J&G Investment Advisors.
Introduction
As your investment advisors we recommend investment in a portfolio made up of ACE Limited,
IBM and an M&T money market account. After a thorough analysis of the stocks relationship to
each other and the market, along with an evaluation of current state of the economy we believe
the following portfolio will provide the greatest opportunities of return with an acceptable level
of risk for you.
As was discussed during our initial consolation, you are a young entrepreneur with a relatively
large net worth. Due to your extra cash flow, and few financial responsibilities, we determined
that you would be willing to take a reasonable amount of risks with the $100,000 you have set
aside for this portfolio. The following proposal addresses ACE Limited and IBM as individual
stocks and evaluates their expected performance.
ACE Limited (ACE):
The first stock we chose for investment in is ACE limited. They provide a range of insurance and
reinsurance products to commercial and individual customers. The company distributes its
products through brokers, agents, underwriters, direct marketing, and Internet distribution
channels. ACE Limited was founded in 1985 and is headquartered in Hamilton, Bermuda. The
organization began as a fairly small insurance company, and in a relatively short time has
become one of the leaders in its industry. Through successful acquisitions they have been able to
expand their global presence and offer unique products, such as political risk coverage. ACE is a
large cap value stock. These stocks tend to have less price volatility than growth stocks. This
stock's forward earnings yield is 12.66%, this is much higher than the earnings yields of other
stocks in its industry. For this company to generate decent returns for investors, it will probably
only have to realize moderate growth in earnings or a higher valuation by the market. However
the company's net profit margins have only been average (about 15.55) compared with other
companies in its industry. Given that ACE only needs to realize moderate earnings growth, the
uncertainty in the market, and the ever increasing fear of recession, we believe ACE would be an
excellent investment. Insurance companies often perform differently than the market, which will
be a beneficial asset in the future. .
International Business Machine Corp (IBM):
The second stock we chose for investment is IBM. The company was founded in 1910 as
Computing-Tabulating-Recording Co. and changed its name to International Business Machines
Corporation in 1924. It designs computer systems and software, and provides other related
services. The company's hardware products include servers, storage systems, and electronic
subsystems. IBM also offers an array of services including outsourcing, maintenance, and
systems integration. This stock is in the computer equipment industry, which has proven to be
an excellent industry over the 10-year period. This stock has also seen steady revenue growth
over the past three years. Like the industry, this stock's earnings per share have grown at a very
high rate over the past three years. Over the long haul, this company has posted results that are
some of its industry's best. Also the company has had very strong profit margins. Tech
companies tend to outperform the market during the middle of a recovery, or on the way up from
the bottom of the business cycle. While there is still much uncertainty regarding a possible
recession, and how long such a slow down would exist, we still believe that investing in IBM
today would be a smart move. Given IBM’s strong market share and performance in the past few
years, it is likely that even if the industry is not a top performer IBM will still realize moderate
returns.
Initial Analysis
Our conclusions to invest in ACE and IBM came following thorough analysis. We determined
the expected returns and risk associated with each stock. We also determined the relationship
between the two securities in order to ensure that investment in both would create a well
diversified portfolio that would give reasonable protection against market risks. Next, we
evaluated each securities relative sensitivity to the market, and compared expected returns of the
securities to those of the market, based on historical S&P 500 returns. Finally, in creating your
optimal portfolio, we created several portfolios in order to choose one that would give you the
greatest amount of return for a reasonable level of risk. All calculations are in annual terms, but
were calculated using monthly historical data.
Expected Return and Risk of ACE Limited:
The annual expected returns on ACE for the past 10-, 5- and 3-year periods were 12.70%,
15.5%, and 14.92% respectively. The results of this analysis can be seen in Appendix A1, A2
and A3. Based on actual returns and these expected returns, we found the standard deviation of
ACE to be 29.83%, 19.02%, and 15.32% respectively. Again, data and calculations can be found
in the appendix under A4, A5 and A6. As this trend indicates, over the past 10 years the standard
deviation, which is the risk of the security has decreased substantially, while returns have
generally increased. We believe this is a positive trend for the investor because over the past 10
years investors have been able to generate relatively better returns for a lower risk.
Expected Return and Risk of International Business Machines:
The annual expected returns on IBM for the past 10-, 5- and 3-year periods were 12.88%, 6.98%,
and 7.55% respectively. The results of this analysis can be seen in Appendix A7, A8 and A9.
Based on actual returns and these expected returns, we found the standard deviation of IBM to be
31.51%, 18.00%, and 19.64% respectively. Again, data and calculations can be found in the
appendix under A10, A11 and A12. As this trend indicates, over the past 10 years the standard
deviation, which is the risk of the security, has decreased substantially. While expected returns
have also generally increased, we do not look at this as a negative trend. The risk reward tradeoff
indicates that as the risk of an investment goes down, so does the return. Even based on data
from the last five years, IBM is generating moderate returns, and therefore not giving up too
much return for a decrease in risk. In addition, our opportunity to pair this security with ACE,
which is realizing greater returns but with a little more risk, creates an optimal situation.
Relationship between ACE and IBM:
In order to determine the relationship between ACE Limited and International Business
Machines, we determined the correlation between the two stocks. We used this number to
indicate the degree to which the two stocks move together in order to determine what kind of
diversification exists in the portfolio. We decided on ACE and IBM based on their low
correlation figures. A low correlation indicates there is very little relationship between the
movement of one stock and the other. We believe that since both stocks are strong performers
this is an optimal situation. The correlation between the two stock over the last 10-, 5-, and 3year period were .1742, .4179, and .2729 respectively.
Since correlations measure the movement of two stocks together a difference in the calculated
correlation using different amounts of data is not surprising. The more data points used in a
calculation, the more smooth the calculation will be. In places where there are anomalies for
whatever reasons, additional data will help smooth out results. Since stock prices are dependent
upon the activities of each individual organization, forces such as market performance, new
management, competitors or other external factors could cause the stock price to more in
abnormal ways. This abnormal movement of one stock, as compared with normal movement of
another, may not be truly indicative of the relationship between two securities in the future.
As seen by the calculated correlations, that calculated using 5 years of data seems abnormal to
the two calculated using 3 years of data. As expressed above, the main reason for differences in
correlation has to do with the data being used. One explanation for the abnormal correlation
using 5 years of data could have to do with the effects of the September 11, 2001 terrorist
attacks. Given the state of the economy during this time period following these attacks, both
stocks preformed relatively well. This is because the negative effects of September 11 took time
to impact ACE’s stock price. Additionally, such events could trigger some consumers to
purchase additional insurance, which would have a positive impact on the stock price. Also, IBM
are suppliers of hardware, software and information technology related services. Following the
terrorist attacks many organizations needed to replace their information technology infrastructure
that was destroyed during the attack, or may even have needed to outsource some of their IT
activities. Even though the effects of these activates are expressed in the 10 year data, there is a
much more extensive amount of data. This additional data is able to smooth out the anomalies
that are created based on individual stock performance. The three year data does not contain the
impact of these attacks on the market or economy.
Going forward we recommend using the three year correlation. The economy over the past ten
years has seen drastic changes and has been impacted by extraordinary events. Using all of this
data may skew results since the economic and market environment of the late 1990s is much
different than the current state of the economy and markets. Again, using the correlation based
on five years of data may not be truly indicative of the relationship between ACE and IBM
because of the significant weight that is given to data following the September 11 terrorist
attacks. For these reasons we believe using a correlation of .2729 is the best choice when
describing the relationship between ACE and IBM. It captures the most recent economic data,
including the huge drop that occurred after the subprime mortgage incident that occurred during
the summer of 2007.
Beta Determinations:
In order to better understand the relationship between each individual security and the market as
a whole we ran a regression analysis to determine beta. Appendix A38 contains a summary of
the results of this analysis. A regression analysis was run for each security based on a 10-, 5-,
and 3-year basis. Additionally a regression analysis was run for each security based on the state
of the economy; if the economy were growing at a week, normal, good or booming rate.
Both securities showed differences in beta in both the historical calculations and the state of the
economy calculations. This is not an uncommon occurrence. For example, when a company is
focused heavily on development (product expansion, technological improvement/growth) it will
tend to have a high beta. If the market grows during this period the company will grow at a
higher rate, and if the market declines the company will decline more. A company can also go
through periods of low beta, usually when there is stagnant growth within the company. This
can be a period of months or years. However, when you calculate 10 year betas you find an
average among these periods, which makes a straight line, and often mitigates the extreme
points.
(d) published betas sometimes differ from calculated betas because the data collection periods
can be different or the calculations can carry different economic weights. Calculations of the
bull and bear periods are often disagreed upon among economists.
Beta of ACE Limited:
In order to better understand the relationship between ACE Limited and the market as a whole
we ran a regression analysis to determine ACE’s beta. Analysis was done using data from the
last 10-, 5-, and 3-year periods. In addition we examined beta based on the differing economic
periods.
The beta of ACE based on time periods of 3-, 5-, and 10-years are 1.41, 1.32, and .87
respectively. All calculations can be found in appendices A32, A34, A36. It is not unreasonable
to see variations in beta over time. Beta measure the sensitivity of a security’s return relative to
the changes in the overall market. The fluctuations in beta are dependent upon activities within a
particular organization and the industry that the organization belongs to. In comparing the
movement of beta to the movement in the correlations between ACE and IBM there is a good
indication that the data based on 5 years also impacted beta. Again, since this is heavily weighted
by the data from the September 11, 2001 terrorist attacks, it is not unreasonable to see a
deviation from the other calculations of beat. The betas calculated using 10 years of data, which
smooth outs these anomalies, and 3 years of data, which does not contain this anomaly look very
similar. Other reasons that beta could fluctuate include different periods of growth. Since ACE
has an active appetite for acquisitions, their stock price will be affected by every new acquisition,
which could create movement opposite of the market.
The beta of ACE based booming, good, normal and weak economic growth was 1.41, .474, 1.29,
and .52. It is not uncommon that these numbers fluctuate. All calculations can be found in
appendices A23, A25, A27, and A29. The idea that these betas do not fluctuate in a normal
pattern is also not surprising. Insurance companies generally do not follow the normal market
trends. An insurance company makes most of its profits based on its investment portfolio.
During a booming economy this investment portfolio will do extremely well, which will push its
performance relative to the market up. While the economy is growing at a good rate individuals
may be more likely to use investments or other financial instruments to hedge risk instead of
buying insurance, and therefore and insurance company may not do as well as the market. In a
normal period organizations and people are likely to be seeking out insurance to protect them
and mitigate risk; this is why we see a beta pretty close to the market. Finally, in a weak
economy organizations may be trying to cut costs, and excess insurance may be one of these
areas. Additionally since a large portion of an insurance company’s profits come from
investments a week economy would support a low beta. The average of these betas, which is
.925, and can be seen in appendix A38, is relatively close to that of the 10 year beta calculated.
This makes sense since we are merely looking at the relationship of beta during different
economic periods, but are using the same data.
The published beta for ACE is .91. Published betas sometimes differ from calculated betas
because the data collection periods can be different or the calculations can carry different
economic weights. Calculations of the bull and bear periods are often disagreed upon among
economists. However, judging from the calculated beta based on 3 years of data, which is .868
this calculated beta seems reasonable.
Beta of International Business Machines:
The beta of ACE based on time periods of 3-, 5-, and 10-years are 1.386, 1.19, and 1.59
respectively. All calculations can be found in appendices A3, A34, A36. It is not unreasonable to
see variations in beta over time. Beta measure the sensitivity of a security’s return relative to the
changes in the overall market. Betas differ over different time periods because companies, much
like the market, go through different periods of high growth. Since IBM is an information
technology industry there is heavy development and growth that must be continually occurring.
This can be observed in the betas that were calculated. They are above one, and the beta using
the most recent data is the highest. Given the competitiveness in the information technology
market over the past few years, with the emergence of the iPod and other digital sources
becoming everyday necessities this number seems reasonable.
The beta of IBM based booming, good, normal and weak economic growth was .8512, 1.41,
1.12, and 1.89. All calculations can be found in appendices A24, A26, A28, and A30. It is not
uncommon that these numbers fluctuate. The normal idea that beta is high during a weak
economy makes sense. Organizations are not buying information technology, however IBM is
most likely still developing products. These actions together would generate a beta that is overly
sensitive to market changes. The upward movement of beta in a normal and good economy is
expected because as the economy grows people and organizations are going to have the need and
want for more information technology, which would cause the stock price to move with more
sensitivity to the market. Finally, the lower beta that is seeing during a booming economy may
be due to other opportunities for investment with greater returns. The average of these betas,
which is 1.233 and can be seen in appendix A38, is relatively close to that of the 10 year beta
calculated. This makes sense since we are merely looking at the relationship of beta during
different economic periods, but are using the same data.
The published beta for ACE is 1.29. Published betas sometimes differ from calculated betas
because the data collection periods can be different or the calculations can carry different
economic weights. Calculations of the bull and bear periods are often disagreed upon among
economists. However, looking that the three betas calculated this number seems within an
acceptable range.
Return on risk of the S&P 500
The annual expected returns on the S&P 500 for the past 10-, 5- and 3-year periods were 5.38%,
10.47%, and 7.83% respectively. The results of this analysis can be seen in Appendices A20,
A21 and A22. Based on actual returns and these expected returns, we found the standard
deviation of the S&P 500 to be 14.64%, 9.14%, and 7.83% respectively. Again, data and
calculations can be found in the appendix under A20, A21 and A22. Any way you arrange a
portfolio consisting of ACE and IBM the returns fair at least as well, if not better than the S&P
500. Based on data from 5 years the lowest return we generated was just under 10% and the
highest return calculated was over 13%. While there is additional risk, there is the opportunity
for much greater returns. Additionally if you look at the individual expected returns calculated
with 3 years of data, these numbers exceed the return by the S&P 500 by great amounts.
Portfolio Analysis
In order to determine the optimal portfolio for you to invest in Mr. Black we evaluated various
portfolios. We created one using a formula to find the lowest variance portfolio, one that
invested heavily in ACE, which is the stock with the highest expected return, and one that
invested heavily in IBM, which is the stock with the lowest risk. We evaluated the portfolio
based on 5 years of data. We chose this set of data because of the fact that it includes may
different pictures of the economy. It includes an extraordinary event, an economic recession, and
periods where the economy was growing at a good rate. Even though the correlation seems a
little abnormal we believe the data is the most inclusive without having too much, which would
distort results.
Minimum Variance Portfolio:
The first portfolio we created was one with a minimum variance. We used a mathematical
calculation to determine the weights of each stock, and created the portfolio based on that. The
results of these calculations can be seen in Appendix A16. The expected return on this portfolio
is 11.18% with a standard deviation of 15.56%. This is a reasonable return with a reasonable
level of risk.
70% ACE, 30% IBM Portfolio:
The second portfolio we looked at was one that combined the stocks in a way that gave the
security with the greatest expected return a weight of 70% and the other a weight of 30%. The
results of this analysis can be viewed in Appendix A17. The portfolio had and expected return of
13.15% and a standard deviation of 16.32%. This is a pretty desirable return with a moderate
level of risk.
70% IBM, 30% ACE Portfolio:
The final portfolio we evaluated was one that combined the stocks in a way that gave the security
with the smallest expected return a weight of 70% and the other a weight of 30%. The results of
this portfolio can be seen in appendix A18. The expected return on the portfolio is 9.95% and the
standard deviation is 15.86%. The expected return generated by this portfolio as compared with
the level of risk is not optimal.
Recommended Portfolio:
Mr. Black, given your desired return of at least 10% and the fact that you are willing to take on
some risk we recommend the second portfolio created. By adding a risk free asset we believe
that we can mitigate some of the risk associated with the portfolio while still having the
opportunity to achieve greater returns. We calculated the sharp ratios for all three portfolios.
They came out to .54, .64, and .457 respectively. The results can be seen in Appendices A16,
A17, and A18. While the chosen portfolio does have a higher sharp ratio, indicating that for each
extra unit of return we are taking on more risk, we still believe this portfolio is the best choice.
The sharp ratio is not that much smaller than the other two portfolios, but the return is much
greater. Again, the addition of a risk free asset will help to mitigate this problem.
Our final recommendation is a portfolio in which you invest 75% in the 2 risk securities above,
and the remaining 25% in an M&T money market fund that is returning 3.7%. The expected
return of this portfolio is 10.79% with a standard deviation of 12.21%. This portfolio will returns
above your 10% threshold, and with a risk well below the other two portfolios we created. You
will be guaranteed at least a 3.7% return on the funds invested in the money market account and
will have the opportunity to realize superior returns on the funds invested in the two riskier
securities. In calculating the Roy’s safety first ratio we determine that risk that you will not
generate at least a 9% return I only 14.61%. We believe this is a reasonable level of risk given
the state level of return.