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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)

0.010

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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[Accessed 28 February 2024].

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