Suppose that the annual return for a particular stock follows the same distribution every year, and that the return for any given year is independent of the returns for any prior years. Based on an analysis of the stock's annual returns over an 12 year period, it is determined that the 95% confidence interval for the stock's expected annual return is given by (-0.1724, 0.2861). Find the volatility of the stock. Use the approximation formula from Berk and DeMarzo. 38.52% 40.90% 42.09% 37.32% 39.71%
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- A challenge we run into when forecasting future stock returns is that stock returns compound. So, when using historical averages to forecast the future, we need to average together the arithmetic and geometric average returns using Blume's Formula: R(T) = T GeoAvg + NT Arith Avg N-1 In this formula, N is the number of historical annual returns you are using to calculate your averages and T is the number of future annual returns you are forecasting. Suppose you gather the following prices for a stock in order to calculate the last 10 (N = 10) annual returns. The stock does not pay dividends. Time 0 1 Time 0 calculate the last 10 (N=10) annual returns. The stock does not pay dividends. 1 2 3 4 5 10 6 . 7 8 9 10 Price $23.16 $32.81 Price $23.16 $32.81 $33.63 $36.83 $41.95 $41.04 $33.83 $37.45 $30.56 $29.90 $47.93 Using Blume's formula, what is the expected return per year for the next 4 years (T = 4)? Enter your answer as a percentage, rounded to the nearest 0.0001. For example, for…Assume these are the stock market and Treasury bill returns for a 5-year period: Required: a. What was the risk premium on common stock in each year? b. What was the average risk premium? c. What was the standard deviation of the risk premium? (Ignore that the estimation is from a sample of data.)Consider the following average annual returns for Stocks A and B and the Market. Which of the possible answers best describes the historical betas for A and B? Years Market Stock A Stock B 1 0.03 0.16 0.05 2 −0.05 0.20 0.05 3 0.01 0.18 0.05 4 −0.10 0.25 0.05 5 0.06 0.14 0.05 a. bA > +1; bB = 0. b. bA = 0; bB = −1. c. bA < 0; bB = 0. d. bA < −1; bB = 1. e. bA > 0; bB = 1.
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- You have developed data which give (1) the average annual returns of the market for the past five years and (2) similar information on Stocks A and B. If these data are as follows, which of the possible answers best describes the historical beta for A and B? Please circle the correct answer: Years Market Stock A Stock B 1 .03 .16 .05 2 -.05 .20 .05 3 .01 .18 .05 4 -.10 .25 .05 5 .06 .14 .05 a. bA > 0; bB = 1. b. bA > +1; bB = 0. c. bA = 0; bB = -1. d. bA < 0; bB = 0. e. bA < -1; bB = 1.Assume these are the stock market and Treasury bill returns for a 5-year period: Required: a. What was the risk premium on common stock in each year? b. What was the average risk premium? c. What was the standard deviation of the risk premium? (Ignore that the estimation is from a sample of data.) Complete this question by entering your answers in the tabs below. What was the standard deviation of the risk premium? (Ignore that the estimation is from a sample of data.) Note: Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.The table below presents the returns on stocks ABC and XYZ for a five-year period. Year ABC XYZ 1 0.16 0.12 2 0.42 0.62 3 -0.02 -0.23 4 -0.26 -0.62 5 0.48 0.52 Calculate the average return, and standard deviation of stock ABC and XYZ. Also calculate the correlation between the two stocks. What does the correlation tell you about the return movements of the two stocks? Calculate the weight of each stock in the minimum variance portfolio, assume the expected return equals to average return for each stock. Find the mix of stocks ABC and XYZ that gives a portfolio on the efficient frontier AND demonstrate why this portfolio is on the efficient frontier by showing that there exists another portfolio of stocks ABC and XYZ that has the same level of risk (portfolio standard deviation) but inferior return. Hint: manipulate the weights you get from part b. Suppose the risk-free rate is 6%. Also assume the…
- Assume that you are given the following partial covariance and correlation matrices for Securities J, K and the Market. Also assume that the expected risk-free rate for the coming year is 3.0 percent and that the expected risk premium on the market is 7.0 percent. Given this information, determine the required rate of return for Security J for the coming year, using CAPM. J Market Correlation J K Market Covariance J K Market Standard Deviation O 18.48% O 20.20% O 15.48% O 12.71% O 15.04% 0.44 0.86 J 0.014400 J K 0.64 K CAN 0.016900 K 1.00 Market 0.003600 MarketGiven six years of percentage return of Stock A and Stock B, identify the expected return, and risk of each instrument. Assume that each year, has equal chances of reoccurrence. Stock A Stock B 20X1 10 20 20X2 -15 -20 20X3 20 -10 20X4 25 30 20X5 -30 -20 20X6 20 60 a. Which of the two stocks is riskier? Why? b. Which of the stocks is expected to yield a higher return? Why? c. Where will you invest?You are given the following partial covariance and correlation tables from historical data: Securities J K Market Securities J K Market 1.24 1.11 1.17 1.03 Covariance Matrix K 0.90 J 0.0020480 0.0021600 Also, you have estimated that the market's standard deviation is 4.3 percent. For the coming year, the expected return on the market is 14.0 percent and the risk-free rate is expected to be 4.0 percent. Given this information, determine the beta for Security K for the coming year, assuming CAPM is the correct model for required returns. Correlation Matrix K 0.60 1.00 0.90 1.00 0.60 0.80 Market 0.0020480 0.0021600 Market 0.80 0.90 1.00 Ston sharing Hidel lines We