Question

6. Calculating a beta coefficient for a single stock Aa Aa Suppose that the standard deviation of returns for a single stock A is σΑ-30%, and the standard deviation of the market return is 얘-10%. If the correlation between stock A and the market is ρΑΜ-0.3, then the stock's beta is Is it reasonable to expect that the volatility of the market portfolio's future expected returns will be greater than the volatility of stock A's returns? O Yes O No Next, consider a two-asset portfolio consisting of stock A with WA-75% and an expected return ra = 5% and a standard deviation of ƠA-496, and stock B with rB-8% and Og-10%. Assuming that the correlation between stocks A and B is zero, the expected return to the portfolio is , and the portfolio's standard deviation is Suppose that the correlation between stocks A and B is pAB 1, instead of zero. Which of the following statements correctly reflects the new data? The risk associated with the portfolio is higher. The expected return to the portfolio is lower. The risk associated with the portfolio is lower. O The risk associated with the portfolio is the same as when the correlation is zero.

please answer

Answer 1

Stock's Beta = Correlation(r_A,r_M) x σ_A / σ_M = ρ_{AM x} σ_A / σ_M = 0.3 x (0.3/0.1) = 0.9

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Given that σ_A = 0.3 and σ_M = 0.1.

This means that the stock A's future expected returns are more volatile than market portfolio's future expected returns.

This is because Standard Deviation (σ) measures the variability/ volatility of the expected future returns of a security or portfolio.

As σ_A > σ_M , it is not reasonable to expect the volatility of the market portfolio's future expected returns be greater than the volatility of the Stock A's returns.

Answer: No

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Expected Return to the portfolio, r_P = r_AW_A + r_BW_B

_=> r_P = (0.05 x 0.75) + (0.08 x 0.25) = 0.0375 + 0.02 = 0.0575 = 5.75%

Therefore, Expected Return to the portfolio, r_P = 5.75%.

Given that, Correlation between A and B = 0. i.e.Corr_AB = 0

Portfolio's Standard Deviation = σ_AB = (W_A²σ_A² + W_B²σ_B² + 2W_AW_Bσ_Aσ_B. Corr_AB)^1/2

= [(0.75)²(0.04)² +(0.25)²(0.10)² + 2(0.75)(0.25)(0.04)(0.10)(0) ] ^1/2

= (0.0009 + 0.000625 + 0)^1/2 = (0.001525)^1/2 = 0.039051 = 3.91%

Portfolio's standard deviation is 3.91%