Portfolio Returns, Risk, And Portfolio Optimization

Calculating portfolio historical average rate of return and standard deviation

a.1) Historical monthly rates of return for the market index:

Date	All Ords Accumulated	Return
Sep,2017	55,459.75
Oct,2017	57,712.86	4.063%
Nov,2017	58,813.50	1.907%
Dec,2017	60,007.77	2.031%
Jan,2018	59,809.19	-0.331%
Feb,2018	59,916.01	0.179%

a.2.i) Historical average rate of return and standard deviation of returns for JB HiFi (JBH):

Date	JB HiFi (JBH)
Sep,2017
Oct,2017	-0.087%
Nov,2017	3.100%
Dec,2017	5.633%
Jan,2018	17.201%
Feb,2018	-8.279%
Average returns	3.514%
Standard deviation	9.27%

a.2.ii) Historical average rate of return and standard deviation of returns for reference company:

Date	Reference Company
Sep,2017
Oct,2017	-8.000%
Nov,2017	-2.000%
Dec,2017	7.000%
Jan,2018	-2.000%
Feb,2018	6.000%
Average returns	0.200%
Standard deviation	6.26%

a.2.iii) Historical average rate of return and standard deviation of returns for the market index:

Date	All Ords Accumulated
Sep,2017
Oct,2017	4.063%
Nov,2017	1.907%
Dec,2017	2.031%
Jan,2018	-0.331%
Feb,2018	0.179%
Average returns	1.570%
Standard deviation	1.74%

b) Calculating portfolio historical average rate of return and standard deviation:

Date	JB HiFi (JBH)	Reference Company	Portfolio	Portfolio
Sep,2017
Oct,2017	-0.087%	-8.000%	(50% * -0.087%) + (50% * -8%)	-4.044%
Nov,2017	3.100%	-2.000%	(50% * 3.1%) + (50% * -2%)	0.550%
Dec,2017	5.633%	7.000%	(50% * 5.633%) + (50% * 7%)	6.317%
Jan,2018	17.201%	-2.000%	(50% * 17.201%) + (50% * -2%)	7.601%
Feb,2018	-8.279%	6.000%	(50% * -8.279%) + (50% * 6%)	-1.140%
Average returns				1.857%
Standard deviation				4.96%

The above table relatively calculate the portfolio value by combining returns provided by JB hi fi and reference company. The overall average returns of the company for the period of October 2017 to February 2018 is at the levels of 1.857%. moreover, the standard deviation of the created portfolio is mainly at the levels of 4.96%. Therefore, from the table the relevant returns and risk of the portfolio is detected, which could provide investors with in-depth knowledge to conduct relevant investment decisions. In this context, McLean and Pontiff (2016) stated that investors with the help of risk evaluation can create a Portfolio with low risk and high return.

c) Calculating CAPM for JB HiFi (JBH) and reference company:

Particulars	Value
Risk Free rate	2.81%
Market Premium	6.60%
Beta	0.84
CAPM JB HiFi (JBH)	Rf + Beta * (Rm – Rf)
CAPM JB HiFi (JBH)	2.81% + 0.84 * (6.6% - 2.81%)
CAPM JB HiFi (JBH)	5.99%

The above table indicates the overall beta and CAPM return of JB HiFi, which is relatively high due to beta of the company. This relatively indicates that returns from the company is expected to increase over time.

Particulars	Value
Risk Free rate	2.70%
Market Premium	6.60%
Beta	-0.20
CAPM Reference Company	Rf + Beta * (Rm – Rf)
CAPM Reference Company	2.70% + -0.20 * (6.6% - 2.7%)
CAPM Reference Company	1.92%

The above table indicates the overall beta and CAPM return of JB HiFi, which is relatively negative due to inverse beta of the company. This relatively indicates that returns from the company is expected to deteriorate.

d) Calculating Expected portfolio return and Beta:

Particulars	Value
Weight	50%
Weight	50%
Reference Company	1.92%
Reference Company Beta	-0.20
JB HiFi (JBH)	5.99%
JB HiFi (JBH) Beta	0.84
Portfolio beta	(50% * -0.20) + (50% * 0.84)
Portfolio beta	0.32
Portfolio return	(50% * 1.92%) + (50% * 5.99%)
Portfolio return	4.02%

The above table depicts the portfolio beta and return, which comprises 50% weight of Reference Company and 50% weight of JB HiFi. Furthermore, the portfolio beta is calculated to be at the levels of 0.32, while the portfolio return is at 4.02%. However, from the evaluation it could be indicated that the portfolio is highly correlated with market, which is driving the overall portfolio returns to positive. Therefore, relevant adjustments to the portfolio needs to be conducted by the investor for increasing the return and reducing the risk from investment (Agarwal, Ruenzi and Weigert 2017). 

e) Discussing the risk and return measure of JB HiFi (JBH):

From the evaluation of JB HiFi return from October 2017 to February 2018 relevant risk and expected return of the company can be identified. This relatively indicates that expected return of the company is a relatively high due to the overall rising beta. Furthermore, the derivation of calculation indicates that returns provided by JB Hi-Fi is relatively correlated, as beta is less than 1 for the company. Therefore, the risk measure of the company is relatively high, as beta of the company is at the levels of 0.84, which depicts the high risk from investment, as it is close to 1. The beta is relatively calculated from the returns provided by the company and market, which helps in identifying the risk involved in investment. The overall returns of JB HiFi is detected from the calculation of CAPM, which evaluates risk free rate, market return, and beta of the company. This evaluation mainly stated a total return of 5.99%, which is provided by JB HiFi. This positive relationship between JB HiFi returns and market returns can be used by investors to increase their portfolio returns against adverse market volatility. In this context, Zhang, Liu and Xu (2014) mentioned that use of expected return and risk allows investors to formulate portfolios, which are risk averse and could provide higher returns from investment.

The overall risk attributes of JB HiFi is detected from the valuation of six months, which is relatively short duration for identifying the actual attribute of the stock. The increment in months need to be conducted for the calculation of beta and returns. The calculations indicate that during short period beat of the company is relatively high, which is indicating a high return, as depicted by CAPM. The high correlation between the market return and JB HiFi return indicates that any increment in capital market would raise share price of the company. Furthermore, JB HiFi can be used in portfolio to reduce its risk and improve return generation capacity of the investors. On the other hand, Bollerslev, Todorov and Xu (2015) argued that risk identification loses its friction if economic crisis is in motion, where all the stocks lose their value due to highly volatile capital market. 

References

Agarwal, V., Ruenzi, S. and Weigert, F., 2017. Tail risk in hedge funds: A unique view from portfolio holdings. Journal of Financial Economics, 125(3), pp.610-636.

Aliu, F., Pavelková, D. and Dehning, B., 2017. Portfolio risk-return analysis: The case of the automotive industry in the Czech Republic.

Beshears, J., Choi, J.J., Laibson, D. and Madrian, B.C., 2016. Does Aggregated Returns Disclosure Increase Portfolio Risk Taking?. The review of financial studies, 30(6), pp.1971-2005.

Bollerslev, T., Todorov, V. and Xu, L., 2015. Tail risk premia and return predictability. Journal of Financial Economics, 118(1), pp.113-134.

Bruni, R., Cesarone, F., Scozzari, A. and Tardella, F., 2015. A linear risk-return model for enhanced indexation in portfolio optimization. OR spectrum, 37(3), pp.735-759.

Hoffmann, A.O. and Post, T., 2015. How return and risk experiences shape investor beliefs and preferences. Accounting & Finance.

Hung, K., Yang, C.W., Zhao, Y. and Lee, K.H., 2018. Risk Return Relationship in the Portfolio Selection Models. Theoretical Economics Letters, 8(03), p.358.

Pfaff, B., 2016. Financial risk modelling and portfolio optimization with R. John Wiley & Sons.

Shinde, P.U. and Deshmukh, S.R., 2014, December. Risk management in electricity market by portfolio optimization. In India Conference (INDICON), 2014 Annual IEEE (pp. 1-6). IEEE.

Zhang, W.G., Liu, Y.J. and Xu, W.J., 2014. A new fuzzy programming approach for multi-period portfolio optimization with return demand and risk control. Fuzzy Sets and Systems, 246, pp.107-126.