Consider the information below relating to the monthly rates of return for two companies X and Y over a period of 4 months: Y 2 xRate of return yRate of Return Date Month 1 -4.76 -4.75 Month 2 5.34 7.65 Month 3 12.09 6.98 Month 4 -2.98 9.65 Calculate the covariance per month between the two companies. Show all your working.
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Consider the information below relating to the monthly rates of return for two companies X and Y over a period of 4 months:
Y
2
xRate of return yRate of Return Date Month 1 -4.76 -4.75 Month 2 5.34 7.65 Month 3 12.09 6.98 Month 4 -2.98 9.65
Calculate the
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- Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results: RHD =-0.03+2.10RM+eHD R-squared =0.7 RML =0.06+1.60RM+eML R-squared =0.6 σM =0.15 where M is S&P/TSX Comp Index and RX is the excess return of stock X. What is the covariance and the correlation coefficient between HD and ML?Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results: RHD =-0.03+2.10RM+eHD R-squared =0.7 RML =0.06+1.60RM+eML R-squared =0.6 σM =0.15 where M is S&P/TSX Comp Index and RX is the excess return of stock X. What is the covariance and the correlation coefficient between HD and ML? For portfolio P with investment proportion of 0.4 in HD and 0.6 in ML, calculate the systematic risk, non-systematic risk, and total risk of P.Given the monthly returns that follow, find the R2, alpha, and beta of the portfolio. Compute the average return differential with and without sign. Do not round intermediate calculations. Round your answers to two decimal places. Month Portfolio Return S&P 500 Return January 5.8 % 6.1 % February -2.9 -3.7 March -1.9 -1.4 April 2.4 2.0 May 0.6 0.0 June -1.0 -0.7 July 0.1 0.8 August 1.2 1.6 September -0.8 -0.6 October -3.1 -3.5 November 2.6 2.2 December 0.3 0.2 R2: Alpha: % Beta: Average return difference (with signs): % Average return difference (without signs) %
- Calculate Karl Pearson's coeffcient of skewness from the following data:Weekly Sales (Ksh) 10-12 12-14 14-16 16-18 18-20 20-22 22-24 24-26Number of Companies 12 18 35 42 50 30 8 4Assume that as a portfolio manager the beta of your portfolio is 1.15 and that your performance is exactly on target with the SML data under condition 1. If the true SML data is given by condition 2, how much does your performance differ from the true SML? (1) RFR = 0.0625 Rm(proxy) = 0.12 (2) RK = 0.078 Rm(true) = 0.10The accompanying data represent the annual rates of return of two companies' stock for the past 12 years. Complete parts (a) through (k). Year Rate of Return of Company 1 Rate of Return of Company 21996 0.203 0.3981997 0.310 0.5101998 0.267 0.4101999 0.195 0.4362000 -0.101 -0.0602001 -0.130 -0.1512002 -0.234 -0.3572003 0.264 0.3282004 0.090 0.2072005 0.030 -0.0142006 0.128 0.0932007 -0.035 0.027 (j) Plot residuals against the rate of return of Company 1. Does the residual plot confirm that the relation between the rate of return of Company 1 and Company 2 is linear? Yes or No? (k) Are there any years where the rate of return of Company 2 was unusual? Yes or No?
- Ank Consider the following data set Y X 24 4 19 3 21 5 26 7 21 2 28 6 35 8 42 10 17 1 28 9 Compute Spearman's Rank correlation between the absolute value of the residuals and the independent variable X. Which of the following values for ρS suggests heteroskedasticity? Select one: a. ρS = 0.6642 b. ρS = 0.7954 c. ρS = 0.6970 d. ρS = 0.7438Suppose that X and Y are unknown with E(X) = 20, Var (X) = 4 , E(Y) = 12, and Var (Y) = 16. In addition, suppose that E(XY) = 248. Then what is the correlation of X with Y?If there is a very strong correlation between two variables, then the correlation coefficient must beA. any value greater than 1.B. much smaller than 0, if the correlation is negative.C. much larger than 0, regardless of whether the correlation is negative or positive.D. None of these.
- In a typical multiple linear regression model where x1 and x2 are non-random regressors, the expected value of the response variable y given x1 and x2 is denoted by E(y | 2,, X2). Build a multiple linear regression model for E (y | *,, *2) such that the value of E(y | x1, X2) may change as the value of x2 changes but the change in the value of E(y | X1, X2) may differ in the value of x1 . How can such a potential difference be tested and estimated statistically?You have the following data: Gasoline Sales during 2017.1 to 2020.4 (in 000 of barrels) Year and quarter Gasoline Sales Year and quarter Gasoline sales 2017.1 22434 2019.1 22776 2017.2 23766 2019.2 24491 2017.3 23860 2019.3 24751 2017.4 23391 2019.4 24170 2018.1 22662 2020.1 23302 2018.2 24032 2020.2 24045 2018.3 24171 2020.3 25437 2018.4 23803 2020.4 25272 (A)Using data on gasoline sales (in thousands of barrels) from the first quarter of 2017 to the last quarter of 2020, estimate the secular linear trend equation. (B) Accordingly, forecast gasoline sales for the four quarters of 2021. (C)Use the dummy variables methods to adjust the trend forecasts for the four quarters of2021 you made in (B) above to take the seasonal…