RMM assgt1

8/12/2019 RMM assgt1

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Contents

Section I. Distribution of Returns and Risk Measurement ........................................................................................................................................................................ 2

1.a. return of each shares overtime and comment on the volatility and volatility clustering of the return. ........................................................................................... 2

A. return of shares overtime ............................................................................................................................................................................................................... 2

B. Comment on the volatility and volatility clustering of the returns ................................................................................................................................................ 8

1.B. The summary descriptive statistics on the returns ........................................................................................................................................................................ 10

1.C. Comparison of Risk and Return ................................................................................................................................................................................................... 12

1.D. Histogram of the return ................................................................................................................................................................................................................ 13

1.E. Normality Test .............................................................................................................................................................................................................................. 14

Section II. Variance and Covariance Matrix and Portfolio Construction ................................................................................................................................................ 18

2.A. correlation coefficients matrix ..................................................................................................................................................................................................... 18

2.B. variance and covariance matrix .................................................................................................................................................................................................... 18

Section II (D) returns and standard deviations of portfolio ..................................................................................................................................................................... 19


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Section I. Distribution of Returns and Risk Measurement

US$: Exchange rates: United States DollarSP500: Share price indices: United States: S&P 500ASX: Share market: Share price indices: S&P/ASX 200: Industrials

TOPIX: Share price indices: Japan: TOPIXFTSE: Share price indices: United Kingdom: FTSE 100ST: Share price indices: Singapore: Straits Times:

1.a. return of each shares overtime and comment on the volatility and volatility clustering of the return.

A. return of shares overtime US$ SP500 ASX TOPIX FTSE ST-0.12 0.01 0.01 0.05 -0.02 0.00-0.01 0.00 0.02 0.02 0.01 -0.03

-0.07 0.00 0.02 -0.03 0.01 -0.040.01 0.05 0.02 0.03 0.02 0.030.01 0.01 0.00 0.03 -0.06 -0.050.09 -0.01 0.10 -0.04 0.02 -0.05-0.03 -0.01 0.01 0.03 0.06 -0.050.01 -0.04 0.06 0.01 -0.04 0.06-0.01 0.04 0.04 0.00 0.07 0.01-0.02 0.06 -0.04 -0.02 0.04 -0.06-0.01 0.05 0.02 0.04 -0.02 -0.100.05 0.00 0.08 -0.01 0.02 -0.02-0.02 0.07 0.03 0.05 0.08 0.060.02 0.05 0.10 0.13 0.08 -0.080.04 -0.01 0.10 0.02 -0.01 -0.02-0.03 0.05 0.00 0.04 -0.03 0.14-0.05 0.01 -0.05 0.05 0.03 0.15-0.12 -0.06 -0.05 0.05 -0.06 0.020.02 0.07 0.06 0.07 0.07 0.120.03 -0.08 0.03 -0.01 -0.06 -0.030.02 0.05 0.10 -0.07 0.05 0.230.01 0.02 0.02 0.06 0.00 -0.080.02 -0.03 0.07 0.05 0.02 0.02-0.01 0.13 0.00 0.12 0.08 0.060.02 0.04 0.09 0.01 0.09 0.11

0.05 0.03 -0.01 0.05 0.01 -0.010.00 -0.01 -0.02 0.11 0.03 0.050.01 0.01 0.02 0.03 0.07 0.110.01 0.05 0.02 -0.04 0.04 0.03-0.03 0.05 0.11 -0.01 0.03 0.110.02 0.04 0.09 0.07 -0.05 0.030.01 -0.02 0.05 -0.01 0.05 -0.03-0.06 -0.22 -0.40 -0.13 -0.26 -0.410.04 -0.09 0.00 -0.01 -0.10 -0.040.02 0.07 -0.01 -0.07 0.08 0.00-0.01 0.04 0.01 0.11 0.05 0.090.01 0.04 0.02 0.08 -0.01 -0.01

0.03 -0.03 0.11 0.03 -0.01 0.03


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0.00 0.01 -0.04 -0.05 0.10 -0.02-0.03 0.00 -0.03 -0.02 0.04 0.02-0.02 0.03 0.03 0.03 0.05 0.070.01 0.01 0.06 -0.01 0.02 0.03-0.01 0.01 -0.01 -0.01 -0.01 0.030.03 0.01 0.05 -0.01 0.02 0.010.01 0.02 0.03 0.11 0.00 0.000.01 -0.03 0.01 0.13 -0.02 0.06-0.05 0.02 0.02 0.01 0.01 0.04-0.01 0.00 0.00 -0.03 0.02 -0.030.02 -0.01 0.05 0.05 0.01 0.01-0.02 0.03 0.08 0.02 0.06 0.14-0.04 -0.01 0.02 -0.04 -0.02 0.020.03 0.02 0.07 0.00 0.04 0.09-0.01 -0.01 -0.05 -0.16 0.00 -0.020.02 0.01 0.06 0.05 0.08 0.200.06 0.03 0.06 0.13 0.02 -0.05

0.01 -0.03 -0.05 0.00 -0.05 -0.03-0.02 -0.05 -0.07 -0.04 -0.07 -0.120.02 0.01 0.01 0.03 0.01 0.110.03 0.01 -0.02 0.05 -0.05 -0.01-0.01 -0.03 -0.05 -0.01 -0.02 -0.040.01 0.03 0.03 -0.02 0.06 0.020.00 0.04 0.01 0.00 0.05 0.030.00 -0.03 -0.06 -0.04 -0.07 0.010.00 0.02 0.00 0.01 0.02 0.03/0.03 -0.04 -0.05 -0.04 0.00 -0.060.01 0.01 0.01 0.03 -0.01 -0.01-0.02 0.02 -0.02 -0.06 -0.02 -0.08-0.02 0.04 0.07 -0.08 0.01 0.04-0.02 0.03 0.00 -0.03 0.04 -0.010.00 0.03 0.06 0.02 0.03 -0.01-0.02 0.04 0.00 -0.06 0.03 0.07-0.01 0.02 0.00 -0.05 0.00 -0.050.04 0.03 0.03 0.12 0.05 0.020.02 0.00 0.01 0.07 0.00 -0.020.00 0.04 0.02 0.01 0.01 0.000.00 -0.01 -0.03 -0.02 0.01 0.00-0.01 0.04 0.04 0.05 0.04 0.010.00 0.02 0.02 0.06 0.01 0.080.00 0.03 0.05 0.02 0.02 0.100.03 0.01 -0.01 -0.03 -0.01 0.000.02 0.01 -0.03 0.05 -0.01 -0.020.01 0.01 0.03 0.05 0.03 0.000.02 0.02 -0.02 -0.02 -0.02 -0.03-0.01 0.00 0.01 0.02 -0.01 -0.01-0.02 -0.05 -0.02 -0.07 0.00 -0.090.02 0.02 0.04 -0.03 0.04 0.040.00 0.05 0.03 0.06 0.02 0.010.00 0.03 0.03 -0.05 0.01 -0.040.02 0.07 0.01 0.01 0.02 0.07-0.02 -0.02 0.02 -0.06 0.01 0.02

-0.04 0.06 0.00 -0.07 0.04 0.03


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-0.01 -0.01 -0.04 -0.08 -0.02 -0.040.06 -0.06 -0.01 -0.07 -0.03 -0.03-0.08 -0.08 -0.07 -0.07 -0.08 -0.180.03 0.02 0.07 0.04 0.03 0.040.03 0.08 0.02 -0.01 0.03 0.08-0.02 0.01 0.02 -0.02 0.00 0.10-0.01 -0.02 0.01 -0.06 -0.01 0.100.02 -0.02 -0.02 0.04 -0.01 -0.040.03 0.04 0.00 0.04 0.03 0.050.02 -0.06 -0.01 0.02 -0.02 -0.040.05 -0.01 0.00 0.04 -0.02 -0.030.00 -0.07 -0.05 -0.09 -0.08 -0.07-0.03 -0.08 -0.04 -0.06 -0.09 -0.030.01 0.00 0.02 -0.03 0.00 -0.01-0.02 -0.11 -0.05 -0.02 -0.12 -0.090.02 0.09 0.02 -0.06 0.09 0.080.01 0.06 0.00 0.04 0.03 -0.05

0.01 -0.06 -0.02 -0.06 -0.06 -0.040.04 -0.03 -0.01 -0.02 -0.09 -0.040.03 -0.02 -0.06 0.00 0.03 -0.010.00 0.01 0.04 -0.04 -0.01 0.000.03 0.08 0.05 0.01 0.09 0.010.05 0.05 0.01 0.05 0.03 0.050.02 0.01 0.01 0.08 0.00 0.07-0.02 0.02 0.02 0.04 0.03 0.08-0.02 0.02 0.02 0.07 0.00 0.030.06 -0.01 -0.01 0.02 -0.02 0.020.04 0.06 0.02 0.02 0.05 0.060.02 0.01 -0.03 -0.04 0.01 -0.01

0.04 0.05 0.03 0.04 0.03 0.030.02 0.02 0.00 0.00 -0.02 0.050.01 0.01 0.02 0.03 0.02 0.02-0.02 -0.02 0.02 0.09 -0.02 -0.02-0.05 -0.02 0.00 0.01 0.02 -0.01-0.01 0.01 0.01 -0.04 -0.01 -0.03-0.04 0.02 0.02 0.04 0.01 0.030.01 -0.03 -0.01 -0.04 -0.01 0.030.00 0.00 0.01 -0.01 0.01 0.010.02 0.01 0.02 -0.02 0.02 0.030.04 0.01 0.04 -0.02 0.01 0.000.04 0.04 0.03 0.01 0.02 0.020.00 0.03 0.04 0.05 0.02 0.02-0.01 -0.03 0.01 0.00 0.01 0.010.02 0.02 0.00 0.03 0.02 0.01-0.02 -0.02 -0.01 0.00 -0.02 0.010.01 -0.02 -0.02 -0.04 -0.02 -0.01-0.03 0.03 0.03 0.01 0.03 0.020.01 0.00 0.03 0.03 0.03 0.02-0.01 0.04 0.02 0.02 0.03 0.06-0.02 -0.01 0.00 0.05 0.00 -0.030.02 0.01 0.03 0.11 0.03 0.01-0.02 -0.02 -0.03 0.02 -0.03 -0.04

-0.01 0.04 0.03 0.06 0.02 0.04


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-0.01 0.00 0.02 0.07 0.04 0.020.02 0.03 0.02 0.04 0.03 0.03-0.02 0.00 0.02 -0.03 0.01 0.03-0.03 0.01 0.02 0.04 0.03 0.020.05 0.01 0.02 -0.01 0.01 0.030.01 -0.03 -0.05 -0.08 -0.05 -0.09-0.03 0.00 0.01 0.00 0.02 0.020.03 0.00 -0.01 -0.01 0.02 0.000.00 0.02 0.04 0.04 0.00 -0.03-0.02 0.02 0.02 -0.01 0.01 0.030.03 0.03 0.04 0.00 0.03 0.050.02 0.02 0.03 -0.01 -0.01 0.050.01 0.01 0.04 0.05 0.03 0.05-0.02 0.01 0.02 0.02 0.00 0.040.02 -0.02 0.00 0.02 -0.01 0.000.02 0.01 0.02 -0.02 0.02 0.040.02 0.04 0.03 -0.01 0.02 0.04

0.00 0.03 0.01 0.03 0.03 0.050.03 -0.02 -0.02 0.01 0.00 0.010.01 -0.03 -0.03 -0.04 -0.04 0.00-0.04 0.01 0.02 -0.06 -0.01 -0.040.07 0.04 0.02 0.00 0.03 0.100.04 0.01 0.03 0.00 0.04 0.03-0.04 -0.04 -0.04 -0.05 -0.04 -0.07-0.01 -0.01 -0.03 -0.04 0.00 -0.010.01 -0.06 -0.12 -0.09 -0.09 -0.140.07 -0.03 -0.06 -0.02 0.00 0.01-0.03 -0.01 -0.02 -0.08 -0.03 -0.010.02 0.05 0.02 0.12 0.07 0.05

0.02 0.01 -0.02 0.04 -0.01 0.010.01 -0.09 -0.11 -0.06 -0.07 -0.08-0.02 -0.01 -0.01 -0.01 -0.04 -0.01-0.08 0.01 0.04 -0.04 0.04 -0.06-0.07 -0.09 -0.05 -0.13 -0.13 -0.14-0.16 -0.17 -0.10 -0.20 -0.11 -0.24-0.02 -0.07 -0.09 -0.04 -0.02 -0.030.05 0.01 -0.01 0.03 0.03 0.02-0.07 -0.09 -0.06 -0.08 -0.06 -0.010.00 -0.11 -0.07 -0.05 -0.08 -0.090.06 0.09 0.06 0.02 0.03 0.070.06 0.09 0.06 0.08 0.08 0.130.09 0.05 -0.01 0.07 0.04 0.210.03 0.00 0.05 0.03 -0.04 0.000.02 0.07 0.07 0.02 0.08 0.140.01 0.03 0.08 0.02 0.07 -0.030.05 0.04 0.07 -0.06 0.05 0.030.04 -0.02 -0.02 -0.02 -0.02 -0.010.00 0.06 -0.01 -0.06 0.03 0.03-0.02 0.02 0.04 0.08 0.04 0.06-0.01 -0.04 -0.05 -0.01 -0.04 -0.050.00 0.03 0.01 -0.01 0.03 0.000.03 0.06 0.04 0.09 0.06 0.05

0.02 0.01 0.00 0.01 -0.02 0.03


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-0.09 -0.08 -0.09 -0.11 -0.07 -0.070.00 -0.05 -0.04 -0.05 -0.05 0.030.05 0.07 0.04 0.01 0.07 0.05-0.01 -0.05 -0.02 -0.05 -0.01 -0.010.08 0.09 0.03 0.03 0.06 0.050.01 0.04 0.00 -0.02 0.02 0.01-0.01 0.00 -0.03 0.06 -0.03 0.000.06 0.07 0.02 0.04 0.07 0.01-0.02 0.02 0.02 0.01 -0.01 0.000.02 0.03 0.01 0.05 0.02 -0.050.02 0.00 0.00 -0.09 -0.01 0.030.05 0.03 0.01 -0.02 0.03 0.02-0.02 -0.01 -0.03 -0.01 -0.01 -0.010.00 -0.02 -0.01 0.01 -0.01 -0.01

B. Comment on the volatility and volatility clustering of the returns

Overall return

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

D a t e

A u g - 8

5

A p r - 8 6

D e c - 8

6

A u g - 8

7

A p r - 8 8

D e c - 8

8

A u g - 8

9

A p r - 9 0

D e c - 9

0

A u g - 9

1

A p r - 9 2

D e c - 9

2

A u g - 9

3

A p r - 9 4

D e c - 9

4

A u g - 9

5

A p r - 9 6

D e c - 9

6

A u g - 9

7

A p r - 9 8

D e c - 9

8

A u g - 9

9

A p r - 0 0

D e c - 0

0

A u g - 0

1

A p r - 0 2

D e c - 0

2

A u g - 0

3

A p r - 0 4

D e c - 0

4

A u g - 0

5

A p r - 0 6

D e c - 0

6

A u g - 0

7

A p r - 0 8

D e c - 0

8

A u g - 0

9

A p r - 1 0

D e c - 1

0

R e t u r n

Date

Plot of Return Overtime

rUS$rSP500

rASX

rTOPIX

rFTSE

rST


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The plot of return above shows us the fluctuation of return of the shares and exchange overtime. Return is the reward given for undertaking some

investments activities. It is important to record the fluctuation of return over time as it is the indicator of how well the performance of the shares and

exchange rate so that it helps the user data to predict the future performance and return of the shares and the exchange rate.

From the plot of return over time, the market shares return is fluctuated in around 10% increase and 10% decrease. The marke t, during august 2006

until august 2007 shows that the return of the share and exchange rate is low volatile which means that the return is quiet stable thus it is easier to

predict the fluctuation of the income. The market is unstable or high volatile especially from year 1985 until 1990, so it is more difficult for investor to

predict the performance of the market in the future.

The abnormal fluctuation happened in August 1987 where there is a stock market crash for ASX and ST share. The return of the two share has

dropped beyond -0.4% for a short period. This abnormality is usually ignored as it can distort the truth.

1.B. The summary descriptive statistics on the returns

US$ SP500 ASX TOPIX FTSE ST

Mean 0.001437895 0.007340793 0.006395157 0.001320033 0.005932531 0.007472869Standard Error 0.001878526 0.002521744 0.002601265 0.003175514 0.002581881 0.004077115Median 0.002801382 0.01108819 0.011104127 0.002417405 0.009437387 0.011301989ModeStandard Deviation 0.033446211 0.044898373 0.046314205 0.05653842 0.045969088 0.072590964Sample Variance 0.001118649 0.002015864 0.002145006 0.003196593 0.002113157 0.005269448Kurtosis 2.664082691 2.51299664 18.58556136 0.930463084 3.304941796 4.644233028Skewness -0.71524322 -0.851782286 -2.273695551 -0.146963351 -0.815723879 -0.452539101Range 0.257144275 0.350794417 0.515965102 0.386684614 0.404238741 0.687843407Minimum -0.164582291 -0.218461538 -0.402998501 -0.204565408 -0.260869565 -0.406593407


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Maximum 0.092561983 0.132332879 0.112966601 0.182119205 0.143369176 0.28125Sum 0.455812845 2.327031378 2.027264875 0.41845032 1.880612438 2.368899365Count 317 317 317 317 317 317Geometric Mean 1.000870612 1.006312745 1.005225203 0.999711106 1.004852286 1.004751034Coefficient of Variatiom 23.26053145 6.116283713 7.242074296 42.83107999 7.748646371 9.713935538

Probability of obtainingnegative return 0.463722397 0.369085174 0.375394322 0.476340694 0.416403785 0.429022082CWI 1.317668712 7.351102941 5.217804667 0.912476723 4.638795987 4.492957746

Arithmetic mean is the measure of the average performance of the given data. It is simply the sum of all the data given divided by the number of data

given. From the descriptive table above, the return of the shares and exchange rate are making profit. It is indicated by the positive value of the

average performance or mean. It is the best estimate of the rate of return for a single period.

Geometric mean is the average of a set of products, the calculation of which is commonly used to determine the performance results of an investment or portfolio.

The advantages in using the geometric mean is that the actual amounts invested do not need to be known; the calculation focuses entirely on the return figures. It

does indicate the growth of the market and money overtime. The value of geometric mean is always equal or smaller than arithmetic means.

The cumulative wealth index captures cumulative effect of total returns by measuring the cumulative effect of returns over time, given some stated

initial amount. For some purposes it is more useful to measure the level of wealth (or price) rather than the change in the level of wealth.

The risk of the return overtime is shown by the standard deviation. The bigger the value means that it is more risky to make investment in the share or

in the exchange rate and the lower the value is, the less risky the share will be. From the data, it can be seen that the ST share is the most risky share to

be invested into, while exchange rate has the lowest risk among all.

Skewness defines the asymmetry of the probability of normal distribution in a set of statistical data. Skewness can either be positive or negative

skewness. A positive skew is a situation where the mean is larger than median return and both of them are larger than the mode while in the other hand

negative skewness is when the mean of the return is smaller than median and both of them are smaller than the mode. In a graph, positive skew is

represented by a graph that have a right tails, while a negative skew represented by a graph with a left tails.

Kurtosis is a statistical measure that used to explain the distribution of the data around the mean. There are a high kurtosis and a low kurtosis. A high

kurtosis with fat tails and a low even distribution, but a low kurtosis chart has skinny tails and a distribution concentrated towards the mean.

Coefficient of Variation is is a normalized measure of probability that spread in a distribution. Coefficient of variation is the result of standard

deviation divided by the mean. Distributions with less than 1 coefficient of variance are considered as low-variance and the distribution with more

than 1 coefficient of variance are considered high-varianceProbability obtaining negative return is measure the ratio of loss by the profit. By seeing the probability of obtaining negative return, the investor can

directly see the performance of the company. By the statistic table, it can be seen that the NYSE share perform well, because it obtain the smallest

probability of obtaining the negative return compare than the other shares and exchange rate.
http://en.wikipedia.org/wiki/Normalization_(statistics)http://en.wikipedia.org/wiki/Normalization_(statistics)


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1.C. Comparison of Risk and Return

The plot of risk and return above is basically measure the relationship between risk and return of the data. It is important to indicate how much the

return someone will get after taking a given risk in investing activities. Most people believe in the term of high risk high return which means that if

someone invests in a riskier share, then he will gain a better return. The plot above apparently shows the same pattern. For example, exchange rate

with 0.0334 risks will only give back around 0.0015 in returns, while shares like SP500 and ST will give a higher return for the higher risk it given.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

R i s k

Return

Risk and Return

US$

SP500

ASX200

TOPIX

FTSE

ST


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1.D. Histogram of the return

Histogram shows the distribution of the data represent by a graph. It estimates the probability distribution of a continuous variable.


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From all the histogram above, it is concluded that all the histogram are leptokurtosis or are more peaked than the normal distribution histogram. There

are two characteristic of leptokurtosis, first is the fatness in the tails, which is shows if there is a large movements in the financial series excessive

relative to the normal distribution. Second is the sharp peak, where it is shows if there a very little movement in the financial series.

For example, from the return plot for TOPIX share, it is shown that the return of the share is fluctuated more or there is a large movement in the

market for TOPIX. The histograms represent the large movement in the market for TOPIX by showing there is fatness in the tails of the graph. Thereis also a very little movement in the return plot but sometime the jump in return is happening in TOPIX share, indicated in the histogram where it has

a sharp peak on the graph.

1.E. Normality Test

Normality test is done in order to see whether the data set is already well-modeled by a normal distribution or not and also to indentify how the

underlying random variable is to be normally distributed.

The method use is just by comparing the significance value (sig.) with 5% as the research reject normal distribution at that point. All of the

significance value in the table below is lesser than 0.05 (5%) so that it is concluded that the data has a non normal distribution. Non-normal

distribution means that some of the variable in the data is not well- distributed.


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Tests of Normality

Kolmogorov-Smirnov a Shapiro-Wilk

Statistic Df Sig. Statistic df Sig.

SP500 .069 317 .001 .963 317 .000

ASX .076 317 .000 .875 317 .000

TOPIX .054 317 .026 .989 317 .016

FTSE .060 317 .008 .965 317 .000

ST .093 317 .000 .938 317 .000

a. Lilliefors Significance Correction


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Section II. Variance and Covariance Matrix and Portfolio Construction

2.A. correlation coefficients matrix

The correlation coefficient is a mathematical measure which is used in the calculation of portfolio risk. It shows how the changes in one data can

influenced the changes in another data. If the value of the correlation coefficient between two data is +1, it indicates that the changes in one data will

have the same effect of changes to the other data; increase of 10% in A, B data will also increase by 10%. While if the correlation coefficient is -1, it

indicates that the changes in one data will affect the other data inversely; increase of 10% in A, B will decrease by 10%.

If the value of the coefficient correlation is equal to zero, it means that the two data do not have any relation. A non-zero correlation coefficient

(values between 1 and -1) indicates that the two data are related but there are other factors that influence the relationship of the data. In other words the

changes in one data will have a different effect on other data; changes of 5% in A, will caused a 7%changes in B. The closer the correlation coefficient

is to 0, the weaker the relationship of the two data is.

From the table above, some of the values are having weak relationship, for example US$ have weak correlation with SP500 (0.01484), ASX (0.1596).

However, SP500 and FTSE have the strongest positive relationship which is 0.9798 followed by SP500 and ASX which has 0.9312 in value.

2.B. variance and covariance matrix

CorrelationUS$ SP500 ASX TOPIX FTSE ST

US$ 1SP500 0.01484 1ASX 0.159557 0.931229 1TOPIX 0.120238 -0.41537 -0.33574 1FTSE 0.005611 0.979864 0.891656 -0.37759 1ST 0.459225 0.79349 0.850488 -0.26068 0.801164 1


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US$ SP500 ASX TOPIX FTSE ST

US$ 0.011952SP500 0.209833 16727.38ASX 35.72301 246647.6 4193853TOPIX 0.336139 -1373.73 -17581.6 653.8907FTSE 0.046771 9663.295 139235.3 -736.248 5814.216ST 3.762731 7691.422 130534.7 -499.588 4578.448 5616.973

Variance is a measure of how far a set of numbers spread out from each other. Covariance is a raw measure of the degree of association between two

variables moves in the same direction.

In the above table the diagonal value is the return variance of the share market, for example in this case the return variance of ASX is 4193852.598.

While the off-diagonal value represents the covariance, for example the covariance between TOPIX and ASX is 17581.60286. The coefficient of

variation has no upper or lower limits as it differ from the coefficient of correlation, which has upper or lower limit.

All the data above is positive covariance, which means it implies the same direction of movement between the data. Whereby, all the data above is

related to one another, if there is an increasing in the return of US assets then the other tends to increase on their return on assets as well in relation to

the increasing return of US assets. If there is a case of negative covariance it implies the movement in different direction. Whereby, if there is an

increase in return of US assets it will associated with a decrease in return of Japan assets. If the covariance is zero, it means no predictable relationship between the movements of the data.

Section II (D) returns and standard deviations of portfolio

Portfolio 1: 50% Australian share (ASX200) and 50% US share (S&P500).

Portfolio 1

Expected return 0.686

Risk 4.47


20/20

20

Portfolio 2: 45% Singapore share, 35% Australian Share and 20% United Kingdom share.

Portfolio 2


Risk 5.523

Portfolio 3: 20% Australian share, 20% US share , 20% Singapore share, 20% United Kingdom share and 20% Japan share.

Portfolio 3


Risk 3.723

Based on the three portfolios above it shows the calculation of the portfolio where in the first portfolio of 50% Australian share and 50% US share, theexpected return is 0.686 with the risk of 4.47. While in the second portfolio of 45% Singapore share, 35% Australian share and 20% United Kingdom

share, the expected return is 0.678 with the risk of 5.523. As in the third portfolio of 20% Australian share, 20% US share, 20% Singapore share, 20%

United Kingdom share and 20% Japan share, the expected return is 0.570 with the risk of 3.723.

In these three portfolios it shows that the third portfolio has the lowest expected return with the lowest risk than others. The best portfolio is the first

one because the expected return is higher which is 0.686 compared to portfolio 2, it is only 0.678 and portfolio 3 for 0.570 and the risk is higher in

portfolio 2 which is 5.523 while in portfolio 1 it is only for 4.47. So, portfolio 1 has the higher expected return with the lower risk than portfolio 2.

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