rt Consider the daily stock prices of Company A. Let x, = log(P), where P, is the opening price of the stock at time 1. Let r, be the log return series of the stock prices, where r; = x; x4. The summary statistics of the daily log returns are given in R Output 1.1. Answer the following questions using R Output 1.1. basicstats (rt) nobs 500.000000 Minimum -0.073041 Maximum 0.051974 Mean 0.000916 Median 0.002127 Sum 0.458006 SE Mean ???????? variance 0.000269 skewness -0.393878 Kurtosis 2.185739 R Output 1.1 (Edited to shorten the output.) (a) Find the SE Mean. Leave your answer in 6 decimal places. (3 marks) (b) Construct a 95% confidence interval for the daily log returns. Leave your answer in 6 decimal places. (4 marks) (c) Let S denotes the skewness of the daily log returns. Test H:S=0 versus H:S#0 using the critical value approach at a 5% significance level. Comment on your result. (4 marks) (d) Let K denotes the kurtosis of the daily log returns. Test H, K = 3 versus H:K #3 using the critical value approach at a 5% significance level. Comment on your result. (4 marks) (e) Sketch the empirical and normal density plots for the daily log return series of Company A. Use a solid line to denote the empirical density function. Use a dashed line to denote the normal density function that has the same mean and standard deviation as those of the daily log return series. (6 marks) (1) Suppose one invested on Company A stock at the very beginning and held the investment for 500 days. Find the 500-day simple return. Leave your answer in 4 decimal places. (4 marks) rt Consider the daily stock prices of Company A. Let x, = log(P), where P, is the opening price of the stock at time 1. Let r, be the log return series of the stock prices, where r; = x; x4. The summary statistics of the daily log returns are given in R Output 1.1. Answer the following questions using R Output 1.1. basicstats (rt) nobs 500.000000 Minimum -0.073041 Maximum 0.051974 Mean 0.000916 Median 0.002127 Sum 0.458006 SE Mean ???????? variance 0.000269 skewness -0.393878 Kurtosis 2.185739 R Output 1.1 (Edited to shorten the output.) (a) Find the SE Mean. Leave your answer in 6 decimal places. (3 marks) (b) Construct a 95% confidence interval for the daily log returns. Leave your answer in 6 decimal places. (4 marks) (c) Let S denotes the skewness of the daily log returns. Test H:S=0 versus H:S#0 using the critical value approach at a 5% significance level. Comment on your result. (4 marks) (d) Let K denotes the kurtosis of the daily log returns. Test H, K = 3 versus H:K #3 using the critical value approach at a 5% significance level. Comment on your result. (4 marks) (e) Sketch the empirical and normal density plots for the daily log return series of Company A. Use a solid line to denote the empirical density function. Use a dashed line to denote the normal density function that has the same mean and standard deviation as those of the daily log return series. (6 marks) (1) Suppose one invested on Company A stock at the very beginning and held the investment for 500 days. Find the 500-day simple return. Leave your answer in 4 decimal places. (4 marks)
