**Portfolio Standard Deviation Calculation - Educational Exercise**---**Question:**A portfolio has 30% of its value in IBM shares and the rest in Microsoft (MSFT). The volatility of IBM and MSFT are 35% and 30%, respectively, and the correlation between IBM and MSFT is 0.4. What is the standard deviation of the portfolio?---**Options:**- **A.** 31.02%- **B.** 22.93%- **C.** 26.97%- **D.** 29.67%---**Explanation:**In this problem, you are calculating the standard deviation of a portfolio composed of two stocks, IBM and Microsoft (MSFT), which involves understanding how the volatility of each stock, their respective weights in the portfolio, and the correlation between them contribute to the overall portfolio risk.To solve this, you would use the formula for the standard deviation of a two-asset portfolio:\[ \sigma_p = \sqrt{(w_A \cdot \sigma_A)^2 + (w_B \cdot \sigma_B)^2 + 2 \cdot w_A \cdot w_B \cdot \sigma_A \cdot \sigma_B \cdot \rho_{A,B} } \]where:- $ \sigma_p $ is the standard deviation of the portfolio.- $ w_A $ and $ w_B $ are the weights of IBM and MSFT in the portfolio, respectively.- $ \sigma_A $ and $ \sigma_B $ are the volatilities (standard deviations) of IBM and MSFT, respectively.- $ \rho_{A,B} $ is the correlation coefficient between the returns of IBM and MSFT.Given:- $ w_{IBM} = 0.30 $- $ w_{MSFT} = 0.70 $- $ \sigma_{IBM} = 35\% = 0.35 $- $ \sigma_{MSFT} = 30\% = 0.30 $- $ \rho_{IBM,MSFT} = 0.40 $---By substituting these values into the formula, you can determine the standard deviation of the portfolio.

A portfolio has 30% of its value in IBM shares.And of its value in MSFT.Volatility of IBM is…

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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A portfolio has 30% of its value in IBM shares and the rest in Microsoft (MSFT). The volatility of IBM and MSFT are 35% and 30%, respectively, and the correlation between IBM and MSFT is 0.4. What is the standard deviation of the portfolio? A. 31.02% B. 22.93% C. 26.97% D. 29.67%