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A) Calculate the discrete rate of return and continuously compounded rate of return for 27 weekly periods..................................................................3
B) Calculate Arithmetic mean return and Geometric mean return............3
A) Weekly rate of return equally weighted portfolio and the Expected Return..................................................................................................................8
B) Variance of equally weighted portfolio (Used of Matrix Algebra).........9
A) Compare and Examine the Portfolio return with each selected stocks and stock index...................................................................................................9
4.0 Report: Part 3.....................................................................................................11
A) Security Characteristic Line (SCL) for each stocks and equally weighted portfolio.............................................................................................12
A) Comment on each stock’s and portfolio performance.........................14
B) Comment on each stock’s and portfolio risk characteristics based on both systematic and unsystematic risk..........................................................15
5.0 Report: Part 4.....................................................................................................16
In addition, from the table 2, we can see that the portfolio performance doesn’t
seems to be volatile because the stock’s movement doesn’t move up and down in a
huge range based on the discrete rate of return in Appendix 12.
Overall, holding a portfolio with different correlated assets is better than
holding a single assets because it able investor to reduce the risk that may
encountered with.
4.0 Report: Part 3 Question 1
A) Yield of the Treasury bill. In this report, the yield of the Treasury bill are taken from the federal reverse of
United States (Selected Interest Rates - Historical Data 2015). The period are slightly
different than our selected stocks period as the weekly time given by federal reverse
is on every Friday while our stock is on Monday. The date taken are from 26 th of
September 2014 to 27th of March 2015 while our selected stocks date taken from 22nd
September 2014 to 30th of March 2015. Full details of the weekly rate are able to be
seen in Appendix 15.
Treasure security basically backed by United States Treasury where it is
important indicator for the economy such as inflation rates movement. Treasury
securities has many category such as 91 days, 182 days, one year, two years and
even up to ten years. Since those securities are backed by U.S treasury, it consider
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as risk-free assets but of course, the longer the time, the riskier it is because things
can be offbeat in the long run (Treasury Bills 2015).
Back to the treasury bills we extracted, it is basically a short-term debt at a
discount which mean discount from the face value (91 Day T Bill Treasury Rate
2015). In our report, the average discount rate is 8.1071% based on the calculation
from Appendix 16.
Since yield that are reported is in 6 months figured, we don’t need to divide it
by 52 weeks but 26 weeks thus those rate will be the proxy of our risk-free rate.
Question 2
A) Security Characteristic Line (SCL) for each stocks and equally weighted portfolio. Security Characteristic Line known as the Security Market Line (SML) is a line
formed by regression analysis based on the result of excess return over the risk-free
rate on the market (Characteristic Line 2015). To calculate the excess return, we take
each stock discrete return minus the risk-free rate according to the same week. As a
result, the full table of the excess return for Johnson & Johnson, JPMorgan Chase,
The AES Corp as well as the Equally Weighted Portfolio can be seen in Appendix 16
& 17. After the complete calculation, then regression analysis are able to be formed.
Security Characteristic Line are to indicate a stock’s abnormal return which is
known as the (Alpha) where the line intercept with vertical line and indicate the
different between systematic (not diversifiable) risk and unsystematic risk
(diversifiable) risk where it can be tell from the slope of the line (Harvey 2015). The
formula to find out regression is,
SecurityCharacteristic Line :
(Ri )=α i+ βi (RM )+e i
While in Excel, we simply use the Data Analysis, X variable for S&P 500 and Y variable for each stock. The result can be seen in Appendix 18, 19 and 20.
Beta is the sensitivity of share’s return to the market return. Market beta is
always equal 1 therefore when a stock’s beta higher than 1 that means the stock is
more aggressive than market while a stock’s beta lower than 1 that means the stock
is more defensive or less volatile (Bodie et al. 2013).
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Based on the calculation of beta using the excel function of [=Slope (Excess Return of stocks, Excess Return of Market), the result is
Which still can see that JPMorgan is more volatile than the market while Johnson & Johnson and AES Corp is more defensive.
Alpha is representing the stock’s abnormal return (Bodie et al. 2013). When conducting the regression analysis in excel, the value of Alpha is automatically calculated. The Alpha of each stock are
From the result, it clearly shows that all the stocks has negative alpha return
which mean underperformed of its benchmark.
Although slope function and regression function calculated slightly different
beta, but when equation of regression of equation formed, it calculated the same
result as slope function in Excel. From the regression graph, we can see that
Johnson & Johnson dots are moving upwards and it stick closely to the regression
line, JPMorgan and Equally Weighted Portfolio dots are moving upwards as well but
dots are not close to regression line as Johnson and Johnson does. AES Crop
regression graph, dots are disperse and all over the place.
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A complete of summary output as well as the regression graph are able to be
seen in Appendix 18 for Johnson & Johnson, Appendix 19 for JPMorgan and
Appendix 20 for The AES Corp.
Question 3
A) Total risk of each stock and the portfolio.A total risk is a risk that are include both systematic and unsystematic risk.
Systematic risk is the risk that non-diversifiable risk because it affecting the whole
economy as well as the market such as natural disasters or events that cannot the
avoided (Bodie et al. 2013). On the other hand, unsystematic risk is diversifiable
because it only comes from internal issue such as a firm management department
therefore by upgrading or improving that department might reduce the unsystematic
risk (Bodie et al. 2013).
Total risk is calculated based on the formula as below,
σ i2=β i2σm2+σ ¿
Where β i2σm2 is the systematic risk and σ ¿ as the unsystematic risk.
Johnson and Johnson has proportion systematic risk of 0.602653546 and
proportion unsystematic risk of 0.397346454, JPMorgan has proportion systematic
risk of 0.000061891 and proportion unsystematic risk of 0.999938109, AES Corp has
proportion systematic risk of 0.207889944 and proportion unsystematic risk last but
not least Equally Weighted Portfolio has proportion systematic risk of 0.623390182
and proportion unsystematic risk of 0.376609818. Among all the stocks, JPMorgan
has the lowest non-diversifiable risk but also scoring a high diversifiable risk. As a
result, based on the calculation in Appendix 22, JPMorgan might need to improve
internal management to overcome high diversifiable risk issue.
Question 4
A) Comment on each stock’s and portfolio performance.
Overall from the research, we can see that a well-diversified portfolio like S&P
500 can have a stable mean return even there are some economic issue during the
period of last quarter of 2014. In general, all the stock are still considerable because
based on the beta of JNJ 0.8235, JPMorgan 0.0123, AES Corp 0.9192 and Equally
Weighted Portfolio 0.9917, all are less volatility than the market.
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Among the three selected stocks and Equally Weighted Portfolio, none of them
has positive abnormal return but small relatively negative alpha for each of the stocks
thus it means that their share price is overvalued and underperformed against its
benchmark, causing low rate of return for its level of risk.
Based on Appendix 19, JPMorgan Chase & Co's shows sensitive to the market
due to its high beta of 1.2425 compare to Johnson & Johnson beta value of 0.8235,
AES beta value of 0.9192 Corporation and Equally Weighted Portfolio beta value of
0.9917. Among all, Johnson & Johnson has lowest beta of 0.8165 although earlier on
calculation it has negative return which indicate that the stock’s volatility is lesser
than the market. However, JP Morgan Chase & Co's shows lowest alpha of -0.0010
that gives least abnormal return.
Based on standard deviation value in Appendix 7, AES Corp is more risky
compare to other stocks as it reaches highest standard deviation of 4.0816% while
JPMorgan ranked at 2nd position with the and 99.99% of unsystematic risk is showed
at JP Morgan Chase & Co. Therefore, JP Morgan Chase & Co has highest
unsystematic risk among stocks and portfolio.
B) Comment on each stock’s and portfolio risk characteristics based on
both systematic and unsystematic risk.
Based on Appendix 22, holding a portfolio is better than holding single based
on the higher value of unsystematic risk. Unsystematic risk as discuss earlier on
are the risk that came from company or internal sources which mean the risk are
able to be reduce which generally decrease the total portfolio risk. In addition,
high unsystematic risk often result the company stock in risk and might affect the
reputation in general.
Appendix 22 indicate that equally weighted portfolio has alpha of -0.0032 thus
showing that portfolio is overpriced. However, standard deviation of portfolio is
2.54% which is the third highest among three stocks and market index. Such
occasion signify that risk of portfolio will not be lowered down by diversified of its
stock. Reason being that the correlation coefficient among three stocks does not
show negative sign. This further clarify that when one share price decrease, the
other two share price will fall as well. In addition, equally weighted portfolio shows
lowest percentage of unsystematic risk of 37.66%.
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As a result, we can see that investing in portfolio, risk can be diversified and
reduce loss on riskier stock when particular stock can turn out to be bad
investment such as AES’s stock. However, it is not an efficient and effective way
for all of the portfolio. An efficient portfolio can signify higher return for the given
level of risk or less risk for a given return. Furthermore, it does show method on
lessen risk through diversification. Reason is due to the behaviour and
preferences of investor as risk seeker is willing to put their money on stock that is
at high risk.
5.0 Report: Part 4In this report, regression analysis shows the relationship between returns of
each stock and equally weighted portfolio to market index. It helps the investors to
anticipate future expected return and decide on investment decision as it helps
providing quantitative support and shows a line of best fit for data point (Bodie et al.
2013).
However, there is downfall for regression analysis this is because market
index may vary over time due to changes of economy, market changes or currency
exchange crisis. Furthermore, extracting data of 28 weeks can be regard as short
time, indicating failure to build stable reasonable relationship. To further elaborate,
regression analysis can be unusable in the financial world as it failed to produce
statistically effective judgement regards to company's value but it can only be apply
to theory base for understanding purpose.
Portfolio analysis can access the performance of each stock in regards to risk
and return. Portfolio analysis represent underperforming or excess risky stock and
helps to assist investor to set aside investment in order to meet their financial
objectives (Ehow 2014). Furthermore, investors can make decision in allocating
investment as they are able to select the risk and return of each stock. However,
portfolio analysis provide downfall as well. For instance, analysing stock that is from
historical closing price is not efficient way as past performance cannot be assure for
future accurate outcome.
The further analyses are focusing at fundamental analysis. Fundamental
analysis contain the sheer determination of company's stock price from its earnings
and dividend, future interest rate and risk assessment. To further elaborate, financial
analyst is trying to learn of future performance of a company by looking into
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economic ways such as company’s position in the industry, assessment of the
company management and overall forecast of the industry. As fundamental analysis
is difficult to analyse and is not available to the public, investor has the privilege to
purchase it from investment firm at a certain price. This can grant them access to buy
low price of shares of a company and can make higher return.
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AppendixAppendix 1
Johnson & Johnson (JNJ) Historical Price on every MondayDate Open Average Volume Adjusted Close