Plotting Investment Opportunity Set For Mazda Motor Corporation And Nissan Motor Co., Ltd.

Calculating the annualised mean return, standard deviation, and correlation of Mazda Motor Corporation (MZDAY) and Nissan Motor Co., Ltd. (NSANY):

Table 1: Annualised return, covariance and annualised standard deviation

(Source: As created by the author)

The above table mainly depicts the annualised retunes, which is provided by Mazda Motor Corporation and Nissan Motor Co Ltd. The annualised return is mainly depicted after multiplying the number of months with the average monthly return of the stock. Moreover, the annualised standard deviation is mainly depicted in the table, which is derived by using the STEDV function in excel. Furthermore, the table also depicts the relevant correlation and covariance of the two stocks with the help of CORREL and COVAR function in excel. The derivation of annualised return, correlation annualised risk and covariance is mainly essential for identifying the optimal portfolio, which could help the investor in maximising its return, while reducing the overall risk. Goswami and Mukherjee (2015) mentioned that derivation of risk from an investment is essential as it helps the investor to diversify its portfolio to match it risk profile. Moreover, investors to maximise the expected return of a predetermined leave of risk mainly conduct the mean variance. With the help of covariance of both the stock investors, identify optimal portfolio, which could increase return and reduce risk.

Table 2: Plotting risk and return from 0% to 150% in portfolio

(Source: As created by the author)

The above table mainly depicts the relevant risk and returns, which is been provided from different weights of investment conducted in Mazda Motor Corporation and Nissan Motor Co Ltd. There weights mainly depict the opportunity to invest and acquire a portfolio with least risk and maximum return. Moreover, the derivation of adequate portfolio weights mainly allows investor to identify the relevant opportunity and make adequate investment decision. Fich, Harford and Tran (2015) mentioned that investors have used the portfolio weights to determine the return and risk from the investment. On the other hand, A?t-Sahalia and Matthys (2015) criticises that portfolio segregation mainly loses its friction during an economic crises, where all the relevant stock will provide negative returns and hamper profitability of the investor. 

The above table mainly depicts the optimal portfolio weights, which needs to be invested by the investors to increase its chances for attaining higher profits. The derivation of the optimal portfolio is mainly conducted by using return of stock returns, risk free rate and covariance of both the stocks. These valuations mainly help in identifying the optimal portfolio, which could be used by the investors to maximise its profitability. Johannes, Korteweg and Polson (2014) mentioned that investors to identify the relevant stock investment mainly use optimal portfolio formula, which needs to be conducted to maximise return from the investment. However, Bennett and Zitikis (2014) argued that if the risk free rate is relevantly higher than the stock return overall optimal portfolio valuation will be nullified. This mainly indicates that investor wills directly invest in risk free assets, which does not needed any optimal portfolio risk evaluation 

The above table states the optimal portfolio return and risk associated with investment. Moreover, the optimal return is 0.073 from investment, whereas it has a risk of 0.19. This is mainly optimal as it could help the investor effectively to improve the current condition of their investment. The derivation of the overall return and risk could effectual help the investor to use the adequate strategy for improvement and develop their portfolio. The determination of return and risk from the portfolio mainly helps in ensuring the minimum amount of shares, which is to be purchased by the investor. Bhuyan et al. (2014) stated that investors by using the portfolio valuation are mainly able to attain higher return by indulging in lower risk. 

The above table mainly depicts the minimum variance portfolio weights, which needs to be maintained by the investor. Moreover, the minimum weights are 0.22 for by Mazda Motor Corporation and 0.78 for Nissan Motor Co Ltd. In addition, this could mainly help the investor in attain minimum variance portfolio, which could reduce the risk from volatility market. Maillet, Tokpavi and Vaucher (2015) mentioned that determination of minimum variance portfolio mainly allows the investor to effective understand investment structure for risk averse strategy. On the other hand, Bodnar and Gupta (2015) argued that accommodation of risk less assets could mainly nullify the significance of minimum portfolio variance. 

The minimum variance portfolio (MVP) and optimal risk portfolio (ORP) is effectively depicts the following graph, which could help in generating the maximum return with the least risk associated with the portfolio. MVP is the minimum variance, which is needed by the Thus, with the help of both MVP an ORP investors are mainly able to identify the risk associated with their investment. Xing, Hu and Yang (2014) mentioned that investors only choose the portfolio, which have the minimum risk associated with investment. On the other hand, Yang, Couillet and McKay (2015) criticises that efficient frontier mainly helps in depicting the relevant line, which address both risk and return from the investment. The graphitic representation mainly depicts the upward sloping graph, which includes both risk and return from investment. Moreover, the minimum portfolio variance return is 0.073, which overall risk of the portfolio is 0.76. These values are effectively depicted in the efficient frontiers, which enable the investor to identify the return it could generate by accommodating more risks. Both Minimum variance portfolio (MVP) and optimal portfolio (ORV) is effectively depicted in the efficient frontiers.

It mainly helps in depicting the efficient frontier, which could be used by investees in identify the least investment weights, which reduce risk from investment. Aparicio et al. (2016) mentioned that investors are mainly keen on identifying the minimum risk portfolio, which could be used by companies. The efficient frontier figure mainly depicts both MVP and ORP, where 10.86% return is mainly provided from ORP and 11.17% return is provided from MVP. This indicates the minimum risk portfolio is also increasing the overall return capacity of the investor. Aparicio and Pastor (2014) mentioned the investor to identify the relevant investment opportunity mainly conducts the optimal risky portfolio, which has the least risk.

Discussing in details on diversification with reference to the efficient frontier and comparing the expected return and standard deviation of the optimal risky portfolio to the minimum-variance portfolio:

Efficient frontier is an effective method, which enables the investor to identify the relevant weights of stock, which could be included in their portfolio. The efficient frontier mainly starts from the least risk and rises towards the maximum risk. This rising could mainly help investor to diversify their investment and reduce risk of their portfolio. Yilmaz and Pearson (2016) mentioned that efficient frontier is a region in the graph, which represented by an upward sloping curve. In addition, if the covariance is smaller than the standard deviation then standard deviation of the stock will also be lower.

The expected return and standard deviation of optimal risky portfolio to the minimum-variance portfolio are more or less same. The risk of optimal 
risky portfolio to the minimum-variance portfolio has a difference of 0.01%, whereas the return has a difference of 0.31%. The difference in number if relatively lower and could be ignored. Thus, optimal risky portfolio to the minimum-variance portfolio depicts the same standard deviation and risk (Cui, Li and Li 2015). 

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