The standard deviation of a two-security portfolio is used to measure the volatility of the portfolio from the portfolio mean. It is estimated by finding the square root of the minimum variance of the portfolio ( Serban et al., 2013) . Note that the minimum variance of the portfolio is used to determine the riskiness of a portfolio. This, therefore, means that there is a strong positive correlation between the volatility and riskiness of a 2-security portfolio. So, investors should prefer investing in 2-security portfolios with lower standard deviations to those with high standard deviations. That is because the chances of making losses are lower in the former case than in the letter.
The return of a two-security portfolio is the percentage of the price that investors bear on the monthly, quarterly or annual basis. The return can be positive or negative. It is estimated by dividing the current total portfolio price by the previous one, then subtracting 1 ( Serban et al., 2013) . For example, if the last month total price of a 2-stock portfolio was $50, then increased to $55 this month, the return will be: (55/50)-1 =0.1=10%
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Question Two: The Minimum Variance Combination of Two Securities
The minimum variance of a two stock combination measures the riskiness and volatility of the portfolio. It is calculated by squaring the difference between the return on the portfolio at a given time and the mean return of a portfolio, then adding those squares ( Kao et al., 2015) . For instance, if the mean return of a portfolio is 0.05 and the returns for the last two months were 0.03 and 0.07, the minimum variance will be: (0.03-0.05)2 + (0.07-0.05)2 =0.0008. Note that investors are advised to choose portfolios with the least minimum variance possible because the chances of making losses are very low.
Question Three: Covariance and Correlation Coefficients
Covariance coefficient of a portfolio is used to estimate the degree to which the individual stock returns move in the same direction ( Mensi et al., 2013) . Therefore, a positive covariance coefficient like 3 means that the returns of the two stock move in the same directions (both of them either increase or decrease over time). On the contrary, negative coefficient covariance like -3 means that the returns of the two stocks move in the opposite directions (one increases as the other decrease over time). Investors should choose portfolios with negative covariance coefficients and not the ones with positive ones since the former are less risky than the letter.
The correlation coefficient is also used to estimate the nature of the relationship between the returns of two individual stocks. It is estimated by dividing the covariance coefficient of a portfolio by the product of the standard deviation of the individual stocks ( Mensi et al., 2013) . For example, if the covariance coefficient if a 2-stock portfolio is 12 and the standard deviation of stock A and B are 0.4 and 0.5, respectively, then the correlation coefficient will be: 12/(0.4×0.5) =60.
Question Four: The Importance of Diversification
Diversification in stock refers to the act of the investors investing in more than one financial instrument or companies ( Miyajima et al., 2015) . For example, an investor can buy the shares of Apple and Microsoft, or he can buy stock and bonds of different companies. The main advantage of diversification is that it reduces the risk (chances of making losses). Taking the first example, if the shares of Apple makes a loss, the investor can use the gain from Microsoft’s shares to compensate for, or minimize, the loss.
References
Kao, C., & Steuer, R. E. (2016). Value of information in portfolio selection, with a Taiwan stock market application illustration. European Journal of Operational Research , 253 (2), 418-427.
Mensi, W., Beljid, M., Boubaker, A., & Managi, S. (2013). Correlations and volatility spillovers across commodity and stock markets: Linking energies, food, and gold. Economic Modelling , 32 , 15-22.
Miyajima, K., Mohanty, M. S., & Chan, T. (2015). Emerging market local currency bonds: diversification and stability. Emerging Markets Review , 22 , 126-139.
Serban, F., Stefanescu, V., & Ferrara, M. (2013). Portfolio optimization in the framework mean-variance-VaR. Econ Comput Econ Cybern Stud Res , 1 , 61-79.
