If two securities are perfectly negatively correlated then the global-minimum variance portfolio has a standard deviation that is always A) greater than zero. B) equal to zero. C) equal to the sum of the securities' standard deviations. D) equal to −1. Choose the correct answer and justify it
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- Security A has an expected return of 7%, a standard deviation of returns of 35%, a correlation coefficient with the market of −0.3, and a beta coefficient of −1.5. Security B has an expected return of 12%, a standard deviation of returns of 10%, a correlation with the market of 0.7, and a beta coefficient of 1.0. Which security is riskier? Why?1) The standard deviation of a portfolio of risky securities is A) the square root of the weighted sum of the securities' variances. B) the square root of the sum of the securities' variances. C) the square root of the weighted sum of the securities' variances and covariances. D) the square root of the sum of the securities' covariances Provide accurate answer and justify it.The covariance between stocks A and B is 0.0014, the standard deviation of stock A is 0.032, and the standard deviation of stock B is 0.044. Which of the following is the most appropriate to depict the risk-return characteristics of a portfolio consisting of only stocks A and B, and explain why?
- Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 12% and a standard deviation of 17%. B has an expected rate of return of 9% and a standard deviation of 14%. What will be the weights of A and B in the global minimum variance portfolio?Assume that security returns are generated by the single-index model, Ri = αi + βiRM + ei where Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 3%. Suppose also that there are three securities A, B, and C, characterized by the following data: Security βi E(Ri) σ(ei) A 1.4 14 % 23 % B 1.6 16 14 C 1.8 18 17 a. If σM = 22%, calculate the variance of returns of securities A, B, and C. b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C? (Enter the variance answers as a percent squared and mean as a percentage. Do not round intermediate calculations. Round your answers to the nearest whole number.)Assume that two securities, A and B, constitute the market portfolio, their proportions and variances are 0.39, 160, and 0.61, 340, respectively. The covariance of the two securities is 190. Estimate the systematic risk (beta) of the two securities. Note that the covariance of security-i with the market portfolio is simply the weighted average of the covariances of security-i with all the securities included in the market portfolio – the lesson you learned in the context of the bordered covariance matrix. Answer step by step.Do all part.Answer must be correct.
- Portfolios that offer the highest expected return for a given variance (or standard deviation) are known as efficient portfolios. O true falseAssume that security returns are generated by the single-index model, Ri = alphai + BetaiRM + ei where Ri is the excess return for security i and RM is the market's excess return. The risk-free rate is 2%. Suppose also that there are three securities A, B, and C, characterized by the following data. Security Betai E(Ri) sigma(ei) A 1.4 15% 28% B 1.6 17% 14% C 1.8 19% 23% a. If simaM = 24%, calculate the variance of returns of securities A, B, and C (round to whole number). Variance Security A Security B Security C b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C (enter the variance answers as a whole number decimal and the mean as a whole number percentage)? Mean Variance Security A ?% Security B ?% Security C ?%When working with the CAPM, which of the following factors can be determined with the most precision? a. The most appropriate risk-free rate, rRF. b. The market risk premium (RPM). c. The beta coefficient, bi, of a relatively safe stock. d. The expected rate of return on the market, rM. e. The beta coefficient of "the market," which is the same as the beta of an average stock.
- 4) Which of the following statement(s) is(are) true regarding the variance of a portfolio of two risky securities? 1.I) The higher the coefficient of correlation between securities, the greater the reduction in the portfolio variance. 2.II) There is a linear relationship between the securities' coefficient of correlation and the portfolio variance. 3.III) The degree to which the portfolio variance is reduced depends on the degree of correlation between securities. A) I only B) II only C) III only D) I and II E) I and III Justify the correct answer.If a stock portfolio is well-diversified, then the portfolio variance Group of answer choices -will be a weighted average of the variances of the individual securities in the portfolio. -will equal the variance of the most volatile stock in the portfolio. -must be equal to or greater than the variance of the least risky stock in the portfolio. -may be less than the variance of the most volatile stock in the portfolio. -will be an arithmetic average of the variances of the individual securities in the portfolio.When working with the CAPM, which of the following factors can be determined with the most precision? a. The beta coefficient of "the market," which is the same as the beta of an average stock. b. The beta coefficient, bi, of a relatively safe stock. c. The market risk premium (RPM). d. The most appropriate risk-free rate, rRF. e. The expected rate of return on the market, rM.
