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- You have observed the following returns over time: Assume that the risk-free rate is 6% and the market risk premium is 5%. What are the betas of Stocks X and Y? What are the required rates of return on Stocks X and Y? What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y?Consider the rate of return of stocks ABC and XYZ. Year rABC rXYZ 1 20 % 28 % 2 8 11 3 16 19 4 4 1 5 2 −9 (PLEASE SKIP THE FIRST THREE QUESTIONS) a. Calculate the arithmetic average return on these stocks over the sample period. b. Which stock has greater dispersion around the mean return? multiple choice A. ABC B. XYZ c. Calculate the geometric average returns of each stock. What do you conclude? (Do not round intermediate calculations. Round your answers to 2 decimal places.) d. If you were equally likely to earn a return of 20%, 8%, 16%, 4%, or 2%, in each year (these are the five annual returns for stock ABC), what would be your expected rate of return? (Do not round intermediate calculations.) e. What if the five possible outcomes were those of stock XYZ? f. Given your answers to (d) and (e), which measure of average return, arithmetic or geometric, appears more useful for predicting future…Consider the rate of return of stocks ABC and XYZ. Year rABC rXYZ 1 20 % 28 % 2 8 11 3 16 19 4 4 1 5 2 −9 a. Calculate the arithmetic average return on these stocks over the sample period. b. Which stock has greater dispersion around the mean return? A. ABC B. XYZ c. Calculate the geometric average returns of each stock. What do you conclude? (Do not round intermediate calculations. Round your answers to 2 decimal places.) d. If you were equally likely to earn a return of 20%, 8%, 16%, 4%, or 2%, in each year (these are the five annual returns for stock ABC), what would be your expected rate of return? (Do not round intermediate calculations.) e. What if the five possible outcomes were those of stock XYZ? f. Given your answers to (d) and (e), which measure of average return, arithmetic or geometric, appears more useful for predicting future performance? A. Arithmetic B. Geometric
- K (Expected rate of return and risk) Syntex, Inc. is considering an investment in one of two common stocks. Given the information that follows, which investment is better, based on the risk (as measured by the standard deviation) and return? Common Stock A Probability 0.20 0.60 0.20 Common Stock B Return 13% 17% 18% Probability 0.10 0.40 0.40 0.10 (Click on the icon in order to copy its contents into a spreadsheet.) Return -7% 5% 16% 21% www a. Given the information in the table, the expected rate of return for stock A is 16.40 %. (Round to two decimal places.) The standard deviation of stock A is 1.74 %. (Round to two decimal places.) b. The expected rate of return for stock B is 9.8 %. (Round to two decimal places.) The standard deviation for stock B is 6.12 %. (Round to two decimal places.)4. Suppose that we have three stocks with the following parameter values. Expected Standard Correlations of Returns Return Deviation Stock 1 Stock 2 Stock 3 Stock 1 0.20 0.25 1.00 0.30 0.40 Stock 2 0.25 0.35 1.00 0.60 Stock 3 0.15 0.15 1.00 (a) Find the expected return and standard deviation of a portfolio with 25% in stock 1, 50% in stock 2, and 25% in stock 3. Show your steps. (b) For the portfolio in part (a), find the covariance of its return with the return of the equally weighted portfolio of stock 1 and stock 2. (Equal weighting for a two-asset portfolio means that the weights are 50% and 50%.) Show your steps. (c) Someone claims that the portfolio in part (a) is the tangency portfolio of these three stocks. (Note that the concept of the tangency portfolio was explained in Class 5.) Do you believe this claim? Justify your answer. Hint: It may be useful to compare the portfolio in part (a) to a portfolio with somewhat different weights.5. Given the following expectations for the next year, what is the expected return, standard deviation, and beta of Stock A? Use the excel sheet we covered to find the answer. Returns Probability Stock A Market 0.10 0.05 0.02 0.25 0.09 0.08 0.30 0.13 0.12 0.25 0.19 0.15 0.10 0.21 0.16
- QG. The following information is available about the stocks of two companies A and B: Stock A Stock B Expected Return (%) Probability -5 12 15 20 0.05 0.55 0.35 0.05 Expected Return (%) Probability 5 15 18 20 0.05 0.65 0.20 0.10 Stock Standard Deviation of Returns (%) A B 25 35 The coefficient of correlation between the returns on A and B is 0.05. A portfolio is constructed by allocating the funds between A and B in the ratio of 2:3. Calculate the expected return on the portfolio. b. Calculate the portfolio risk.Q.Which of the following statements are true/false: I: The implied volatility of a stock can be calculated by deternining the standard deviation of stock returns over the last one year. II: The implied volatility of a stock can be calculated by deternining the standard deviation of stock returns over the last six months. A. I is true, II is false B. I is false, II is true C. I and II are both false D. I and II are both trueWhat are the components of the risk-free rate and What is financial risk? If the standard deviation of a stock’s return is 5% and its expected return is 8%, what it the C.V.?
- (Expected rate of return and risk) Syntex, Inc. is considering an investment in one of two common stocks. Given the information that follows, which investment is better, based on the risk (as measured by the standard deviation) and return? Common Stock A Common Stock B Probability Return Probability Return0.20 10% 0.15 -4% 0.60 16% 0.35 7%0.20 21% 0.35 13% 0.15 20% a) Syntex, Inc. is considering an investment in one of two common stocks. Given the information that follows, what is the expected rate of return for stock A? What is the standard deviation? b. Syntex, Inc. is considering an investment in one of two common stocks. Given the information that follows, what is the expected rate of return for stock B? What is the standard deviation? c. Based on the risk (as measured by the standard deviation) and return of each stock, which…1. If a stock has a(Alpha)=0.002, b(Beta)=1.4, Using the market model (eq. 7.4), find the expected percent return for the above stock if the market return is expected to be 2% and the risk free rate is 1%. 2. Assume stock prices follow a random walk and a particular stock has had the following recent stock prices: Day 1: 129.5 Day 2: 126.9 Day 3: 127.1 what is the best estimate of day 4 prices?1.2. Refer to the following observations for stock A and the market portfolio in the table: Month Rate of return Stock A Market portfolio 1 0.30 0,12 0.24 0,08 3 -0,04 -0,10 -0,02 0,08 0,07 4 0,10 5 0,06 6 0,10 a) Calculate the main statistic measures to explain the relationship between stock A and the market portfolio: i) The sample covariance between rate of return for the stock A and the market. ii) The sample Beta factor of stock A. iii) The sample correlation coefficient between the rates of return of the stock A and the market. iv) The sample coefficient of determination associated with the stock A and the mar- ket. b) Draw in the characteristic line of the stock A and give the interpretation - what does it show for the investor? c) Calculate the sample residual variance associated with stock's A characteristic line and explain how the investor would interpret the number of this statistic. d) Do you recommend this stock for the investor with the lower tolerance of risk?
