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Write a report on the risk and return of the above stocks with the following parts:
(a) Analysis of asset returns:
The analysis of asset returns includes the discussion on average return, maximum and minimum return and distribution of returns.
(b) Portfolio Return and Risk:
You need a create a three-asset portfolio having the equal weighting for each stock above. After creating the portfolio, you need to analyse portfolio return and risk.
(c) Risk Measure (Sharpe Ratio):
You need to calculate the Sharpe Ratio of each stock return, assuming the risk free return during the analysis period is 3% and choose the best stock on the basis of Sharpe Ratio.
(d) Value at Risk (VaR):
You need to calculate the Value at Risk using a normal distribution at 95% confidence level for each stock listed above and choose the best stock on the basis of VaR.

The following table demonstrates the average, maximum, and minimum returns of the three companies of Australia:

 Average return and maximum & minimum CBA Return RIO Return WOW Return Mean .0007 .0003 .0002 Median .001 .000 .000 Mode .000 .000 .000 Std. Deviation .010 .016 .012 Minimum -.058 -.075 -.097 Maximum .037 .089 .082

From the above analysis, it can be observed that the average return of CBA, RIO, and WOW are 0.0008, 0.0003 and 0.00028 respectively, signifying that CBA has the highest return and WOE has the lowest return among the three companies. The mid value of the return of the three companies is 0.001, 0.00 and 0.00 respectively. However, a mode value of return of all the three companies is observed as 0.00, i.e. most often no return has been obtained from the stock of the three companies.

The maximum value of stock return in CBA, RIO, and WOW is observed as 0.037, 0.089 and 0.0824 respectively, which signify that RIO has the highest maximum return and CBA has the lowest maximum return among the three companies. The minimum value of return in the companies are -0.58, -0.75 and -0.98 respectively. It signifies that RIO has the lowest and CBA has the highest minimum return among the companies.

The standard deviation of return for CBA, RIO, and WOW are 0.01, 0.16 and 0.12 respectively, it signifies that there is a high level of similarity with respect to the return of share. There is not much difference with respect to the distribution of return among the three companies.

Distribution of Returns

The following table demonstrates the distribution of return for the three companies

 Descriptives Statistic Std. Error CBA Return Mean .0007 .0002 95% Confidence Interval for Mean Lower Bound .0001 Upper Bound .001 5% Trimmed Mean .0008 Median .001 Variance .000 Std. Deviation .010 Minimum -.058 Maximum .037 Range .095 Interquartile Range .012 Skewness -.258 .069 Kurtosis 1.915 .137 RIO Return Mean .0003 .0004 95% Confidence Interval for Mean Lower Bound -.0006 Upper Bound .001 5% Trimmed Mean .000 Median .000 Variance .000 Std. Deviation .016 Minimum -.075 Maximum .089 Range .164 Interquartile Range .020 Skewness .151 .069 Kurtosis 1.522 .137 WOW Return Mean .0002 .0003 95% Confidence Interval for Mean Lower Bound -.0004 Upper Bound .0009 5% Trimmed Mean .0002 Median .000 Variance .000 Std. Deviation .012 Minimum -.097 Maximum .082 Range .179 Interquartile Range .012 Skewness -.483 .069 Kurtosis 8.757 .137

From the above analysis, it can be observed that the value of Skewness for CBA, RIO, and WOW are -0.258, 0.151 and -0.483 respectively. Since the value of Skewness is near zero, it can be stated that the data of share return is symmetric (Medhi, 2002). Besides, it can also be stated that the share data of CBA and WOW is skewed left and share return data of RIO is skewed right.

 Distribution Kolmogorov Smirnov Shapiro Wilk Statistic df Sig. Statistic df Sig. CBA Return .044 1266 .000 .981 1266 .000 RIO Return .028 1266 .018 .989 1266 .000 WOW Return .063 1266 .000 .926 1266 .000

The above analysis represents outcome of two evaluation of distribution which is Kolmogorov Smirnov test and Shapiro Wilk test. Since the sample size is more than 50, the Kolmogorov Smirnov test will be appropriate (Ruppert, 2014). From the above table, it can be observed that for CBA, RIO, and WOW, the P values are 0.00, 0.018 and 0.00 respectively which is less than the significance level of 0.05. Therefore, it can be stated that for these three companies the stock market return is normally distributed.

Portfolio Return and Risk

In order to understand the risk of the portfolio, covariance analysis is undertaken for the stock return of the three companies:

 Descriptive Statistics N Range Variance CBA_Return 1266 .095 .000 RIO_Return 1266 .164 .000 WOW_Retrun 1266 .179 .000 Valid N (listwise) 1266

From the above analysis, it can be observed that variance is 0.00 for the three companies studied. Low level of variance signifies that there is a low level of volatility in the stock return of the three companies (Vliet, 2017). Therefore, there is low risk in investing in the stock of the three companies.

In order to analyze the portfolio return bivariate correlation analysis is undertaken, as described in the following table):

## Distribution of Returns

 Correlations CBA_Return RIO_Return WOW_Retrun CBA_Return Pearson Correlation 1 .415 .451 Sig. (2-tailed) .000 .000 RIO_Return Pearson Correlation .415 1 .295 Sig. (2-tailed) .000 .000 WOW_Retrun Pearson Correlation .451 .295 1 Sig. (2-tailed) .000 .000

From the correlation analysis, it can be observed that the value of correlation coefficient between CBA and RIO is 0.415, which signify that positive relationship exists between the variables, i.e. increase in CBA share return is related with an increase in RIO share return. The value of correlation coefficient between CBA and WOW is observed as 0.451 which also signify positive. Thus, it can be stated that positive relationship exists between the variables and that increase in the return of CBA share is associated with an increase in the return of Wow share price (Marty, 2014). However, the value of correlation coefficient between RIO and Wow is observed as 0.295 which is much lesser than 1. Therefore, it can be stated that positive but very weak relationship exists between the variables.

The regular return of the portfolio can be measured as the following formula

On the basis of the formula, the regular return of the portfolio is as follows:

 CBA Return RIO Return WOW Return Annual return -0.997 -0.997 -0.997 Weekly return -0.980 -0.980 -0.980

From the above table, it can be observed that the annual return of stock for CBA, RIO, and WOW are -0.99724, -0.99718 and -0.99721 respectively. The weekly return of stock of the companies is -0.9809, -0.9808 and -0.98095 respectively.

Risk Measure (Sharpe Ratio)

In order to measure the risk of the portfolio investment, Sharpe ratio is computed. It is an important tool to evaluate the performance of an investment by adjusting the risk. This ratio evaluates the additional return per unit of deviance in an investment asset or trading approach, typically termed as risk (Vishwanath, 2009). The Sharpe ratio characterized how effectively the return of stock compensate the shareholder for the risk taken. The following table demonstrates the Sharpe ratio of the three companies with risk-free return of 3%:

 Average (CBA) -2.999 Average (RIO) -2.999 Average (WOW) -2.999 Standard deviation (CBA) 0.01 Standard deviation (RIO) 0.016 Standard deviation (WOW) 0.012 Sharpe ratio (CBA) -282.913 Sharpe ratio (RIO) -177.072 Sharpe ratio (WOW) 0.016

From the above figure, it can be observed that the Sharpe ratio of CBA, RIO, and WOW are -4.64, -2.93 and 0.017 respectively. This signifies that WOW has the highest Sharpe ratio and CBA has the lowest Sharpe ratio of among the three companies. Therefore, it can be stated that with similar risk category, WOW will give a better return on share in comparison with others and CBA will give the lowest return on the share. Thus, on the basis of Sharpe ratio, WOW is the best stock.

Value at Risk (VaR)

VaR is regarded as a measurement of risk of investment. It assesses how much a set of investment might lose in specific market situations is a certain time period (Alexander, 2009). This method is characteristically utilized by organizations and regulators in the share market in order to measure the level of assets required in order to cover possible losses.

The following table demonstrates the VaR rate of CBA at 95% confidence level:

 CBA Portfolio value 100 Average return 0.0007 Standard deviation 0.01 Confidence level 0.95 Mean return with 95% probability -0.015 Value of portfolio 98.432 VaR 1.567

From the above table, it can be observed that the value of VaR is 1.57. This indicates that there is 0.016% probability that the portfolio will fall in value by 100. The following table demonstrates VaR of RIO at 95% confidence level:

 RIO Portfolio value 100 Average return 0.0003 Standard deviation 0.17 Confidence level 0.95 Mean return with 95% probability -0.279 Value of portfolio 72.070 VaR 27.929

From the analysis, it can be observed that the value of VaR is 27.92 in RIO, this indicates that there is 0.28 probability that the portfolio will fall under 100. The following table demonstrates VaR of WOW at 95% confidence level:

 WOW Portfolio value 100 Average return 0.0002 Standard deviation 0.012 Confidence level 0.95 Mean return with 95% probability -0.019 Value of portfolio 98.054 VaR 1.945

From the above table, it can be observed that the value of VaR is 1.945 which signifies that there is 0.019 probability that the portfolio will fall under 100.

References

Alexander, C., 2009. Market Risk Analysis, Value at Risk Models. John Wiley & Sons.

Marty, W., 2014. Portfolio Analytics: An Introduction to Return and Risk Measurement. Springer Science & Business Media.

Medhi, J., 2002. Statistical Methods: An Introductory Text. New Age International.

Ruppert, D., 2014. Statistics and Finance: An Introduction. Springer.

Vliet, P. V., 2017. High Returns from Low Risk: A Remarkable Stock Market Paradox. John Wiley & Sons.

Vishwanath, R., 2009. Investment Management: A Modern Guide to Security Analysis and Stock Selection. Springer Science and Business Media.

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