We have 50 years of annual data on (detrended) ex post prices P∗ t and on (detrended) actual stock prices Pt . We find that the sample variances (svar) are as follows: svar(P∗ t ) = 120 and svar(Pt) = 80. What does this tell us and why?
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We have 50 years of annual data on (detrended) ex post prices P∗
t and on
(detrended) actual stock prices Pt . We find that the sample variances (svar) are
as follows:
svar(P∗
t ) = 120 and svar(Pt) = 80.
What does this tell us and why?
Step by step
Solved in 4 steps
- The variance ratio (VR) can be used to determine whether returns satisfy the efficient market hypothesis (EMH). Let n = 5 and r5,t be the five period log return at time t, where t = 1, 2,..., T. 1. Express (r5,t — Ã5) in terms of deviations of the relevant one period log returns from their respective means. Denote 75 to be the mean of the five period log return.3. Suppose the index model for stocks A and B is estimated with the following results:rA = 2% + 0.8RM + eA, rB = 2% + 1.2RM + eB , σM = 20%, and RM = rM − rf . The regressionR2 of stocks A and B is 0.40 and 0.30, respectively. Answer the following questions. (a) What is the variance of each stock? (b) What is the firm-specific risk of each stock? (c) What is the covariance between the two stocks?Consider the following variance-covariance matrix for Security A, Security B, and the Market: Variance-Covariance Matrix A B Market A 0.562500 0.091875 0.028125 0.091875 0.122500 0.021000 B Market 0.028125 0.021000 0.022500 For the coming year, the Market Risk Premium is 5.5 percent and the risk-free rate is 2.0 percent. Determine the required return for Security A using both the Capital Market Line and the Security Market Line (CAPM). What is the (absolute) difference between these two required returns? 12.375% O 16.875% 20.625% Ⓒ 7.700% 6.300%
- Stock A has the following returns over the past periods. Calculate the downside risk measured by semi-variance? (answer with 4 decimal spaces) 0.0057 -0.0255 0.0621 -0.0879 -0.0983 0.0813 0.0356 -0.0015 -0.0307 0.0427 0.0297 0.0192Suppose the index model for stocks A and B is estimated with the following results:rA = 2% + 0.8RM + eA, rB = 2% + 1.2RM + eB , σM = 20%, and RM = rM − rf . The regressionR2 of stocks A and B is 0.40 and 0.30, respectively.(a) What is the variance of each stock? (b) What is the firm-specific risk of each stock? (c) What is the covariance between the two stocks?In a regression of the single-index model, the R-square is 68%, residual variance is 0.08, beta estimate is 0.7. What is the variance of the market excess return?
- Consider the following time series: a. Construct a time series plot. What type of pattern exists in the data? Is there an indication of a seasonal pattern? b. Use a multiple linear regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data: Qtr1 = 1 if quarter 1, 0 otherwise; Qtr2 = 1 if quarter 2, 0 otherwise; Qtr3 = 1 if quarter 3, 0 otherwise. c. Compute the quarterly forecasts for next year.In a regression of the single-index model, the R-square is 66%, residual variance is 0.02, beta estimate is 1.3. What is the variance of the market excess return? Answer: (in decimal format, keep 4 decimal places).he last four years of returns for a stock are as shown here: LOADING... . a. What is the average annual return? b. What is the variance of the stock's returns? c. What is the standard deviation of the stock's returns? Note: Notice that the average return and standard deviation must be entered in percentage format. The variance must be entered in decimal format. Question content area bottom Part 1 a. What is the average annual return? The average return is enter your response here%. (Round to two decimal places.) Part 2 b. What is the variance of the stock's returns? The variance of the returns is enter your response here. (Round to five decimal places.) Part 3 c. What is the standard deviation of the stock's returns? The standard deviation is enter your response here%. (Round to two decimal places.) Time Remaining: 00:26:16 pop-up content starts Data table (Click on the following icon in order…
- Over the past 3 years an investment returned 0.16, -0.11, and 0.08. What is the variance of returns?Which of the following statements are correct? I.The standard deviation is a measure of risk.II.The variance of yearly returns is roughly the variance of monthly returns multiplied with 12.III.To decide whether asset A is more risky than asset B we can either use their standard deviations or their variances. Group of answer choices II and III only I, II and III I and II only I and III onlyHere are the returns on two stocks. A. Calculate the variance and standard deviation of each stock. Which stock is riskier if he'll on its own? B. Now calculate the returns in each month of a portfolio that invests an equal amount each month in the two stocks C. Is the variance more or less than halfway between the variance of the two Individual stocks?