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part 4 5 6
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- Consider the following securities: state Probability A B A B H M L 0.2 0.5 0.3 с 6 10 6 3 7 12 2 5 14 1. The expected payoff of A is: 2. The standard deviation of A is: 3. If the price of A is 3, its expected return is: 4. The covariance between A and B is: 5. The correlation coefficient between A and B is: 6. Is it possible to build a portfolio that has zero variance using A and C? YES/ NOSupposing the return from an investment has the following probability distribution Return Probability R (%) 8 0.2 10 0.2 12 0.5 14 0.1 Required: What is the expected return of the investment? What is the risk as measured by the standard deviation of expected returns?Mf1. Question: 1 (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-/ with the market portfolio is simply the weighted average of the covariances of security-i with all the securities included in the market portfolio.
- Consider the probability distribution p(s) of the returns rA and rB of two securities A and B: state p(s) rA rB роог 0.2 0.1 0.16 medium 0.5 0.2 0.1 доod 0.3 0.3 0.05 Calculate the covariance oAB between rA and rB. The correct answer (up to four decimals is) Select one: GAB = 0.0013 GAB = -0.0027 GAB = -0.0102 None of the aboveAssume that security returns are generated by the single-index model,Ri = αi + βiRM + eiwhere 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 βi E(Ri) σ(ei) A 0.7 7 % 20 % B 0.9 9 6 C 1.1 11 15 a. If σM = 16%, 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.)E(FAssume that using the Security Market Line (SML) the required rate of return (RA) on stock A is found to be half of the required return (Rs) on stock B. The risk-free rate (R;) is one-fourth of the required return on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (BA) to beta of B (BB). a o
- An investor wishes to contruct a portfolio consisting of security 1 and security 2. the expected return on the two securities are E(R1) = 0.08 And E(R2) = 0.12 and the standard deviation 1 = 0.04 and Standard deviation 2 = 0.06. the correlation coefficient between thier returns is P1,2 = -0.5. Investor is free to choose the investment proportions W1 And W2 only to requirment that w1+w2=1 and both w1 and w2 are positive.There is no limit to the number of portfolios that meet thses requirements, since there is no limit to the number of proportions that sum to 1. Therefore a representative selection of values is considered w1: 0, 0.2, 0.4, 0.6, 0.8, and 1Consider the following data for two risk factors (1 and 2) and two securities (J and L):λ0 = 0.07 λ1 = 0.04 λ2 = 0.06bJ1 = 0.10 bJ2 = 1.60 bL1 = 1.80 bL2 = 2.45a. Compute the expected returns for both securities. b. Suppose that Security J is currently priced at $50 while the price of Security L is $15.00.Further, it is expected that both securities will pay a dividend of $0.95 during the coming year.What is the expected price of each security one year from now? c. Compute the correlation between stock A and stock B considering the following data.Standard deviation of stock A = 10 percentStandard deviation of stock B = 17 percentCovariance between the two stocks = 90.4. Valuation of a Derivative Consider a derivative on a stock with the time to expiration T and the following payoff: 0 K₁ 0 if ST K₁. What is the present value of the derivative? Provide an analytic expression of the price using N(), the cumulative probability distribution function of a standard normal random variable.
- 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.)5. You are considering investing in two securities, X and Y. The following data are available for the two securities: Security X Security Y Expected return 0.10 0.07 Standard deviation of returns 0.08 0.04 Beta 1.10 0.753) i) Calculate the average returns, variance and standard deviation for three securities X, Y and Z that have performed as follows. Returns % Year X Y Z 1 11 36 -3 2 6 -7 0 3 -8 21 5 4 28 -12 9 5 13 43 5 ii) Is there any basis for preferring one of these securities over the others? iii) Calculate the covariances between X, Y and Z.