Assignment 1 Answers free essay sample

An American call option gives one the right, but not an obligation, to buy a specified number of shares of a stock for a specified price called exercise or strike price before the maturity date or on the maturity date (a future date). In comparison to European options, American options can be exercised before the maturity date. 2. Define Skewness and Kurtosis and also explain why these are useful10 pts Answer Skewness and Kurtosis are measures of dispersion of the data around its mean as they measure shape of probability distribution. Skewness measures the degree of asymmetry. Its value ranges between 0 and 1, where 0 implies symmetry (normal distribution). A positive skewness indicates a relatively long right tail and vice versa. Kurtosis indicates the extent to which probability is concentrated in the center and the tail of the distribution. A value of 3 indicates normal distribution, while a value of K gt; 3 indicates heavy tails. The skewness and kurtosis of a random variable are Sk (n,p) = E {X – E(X)}3 / ? 3 and K = E {X – E(X)}4 / ? 4 3. Read Sewell (2011) paper and . define calendar effects, and b. discuss briefly seven different calendar effects identified in literature (your answer shall not exceed one page) 30 pts Answer a. Calendar effects are viewed as cyclical anomalies in returns, where the cyclical patterns in data can be ascribed to change in volume and activity during certain time periods. For instance intraday effects, the weekend effect, the Monday effect, intra-month effects, the January effect, holiday effects, the Halloween indicator and the daylight saving anomaly. The most important calendar anomalies identified by Sewell are the January effect and the weekend effect. b. There are several different types of calendar effects identified in literature. * Intraday effects are known to exist, * the weekend effect seems to have all but disappeared, * intramonth effects were found in most countries, * the January effect has halved, and * holiday effects exist in some countries. Halloween Indiactor: a trading strategy of tactical asset allocation based on the old saying * ‘sell in May and go away’ generated abnormal returns in comparison with stock market indices in most countries * Daylight Saving Effect: Daylight-saving weekends are typically followed by large negative returns on financial market indices (roughly 200 to 500 per cent in comparison to weekend effect), and researchers argue that the effect could be because of changes in sleep patterns. Part II: R-Code Programming 1. An R programmer ran the following code and he/she got an error message. ) gt; testnorm lt;- rnorm(1000) gt; hist(testnorm, prob = TRUE) gt; mu lt;- mean(testnorm) gt; sigma lt;- sd(mynorm) Error in sd(mynorm) : object mynorm not found b) gt; x lt;- seq(-4, 4, length = 1000) gt; y lt;- dnorm(x, mu, sigma) Error in dnorm(x, mu, sigma) : object sigma not found c) gt; lines(x, y, col = ‘blue’) Error: unexpected input in lines(x, y, col = ‘ Please indicate in each case what caused the error in command if possible write the required correction for the code. 20 Pts a. Answer: The variable mynorm needs to be created prior to using in a command. Here the variable we created is testnorm, which is used in the calculation of mu and same variable can be used (or renamed) in sigma (SD) calculation. Correction required here is gt; sigma lt;- sd(testnorm) Or alternatively gt; mynorm lt;- testnorm b. Answer: Same as above, one needs to calculate sigma and mu prior to executing the second command line. One needs to add the following code lines. x lt;- seq(-4, 4, length = 1000) mu lt;- mean(x) sigma lt;- sd(x) y lt;- dnorm(x, mu, sigma) c. Answer: One needs to specify quotation marks â€Å"† around the option ‘blue’ lines(x, y, col = â€Å"blue†) . Do the following using R and attach a printout of graphs and codes used in analysis30 pts You may submit a black and white printout of the graph if you do not have a color printer, but code is required as it will verify the commands used for coloring the graph. a. Download the manual and data for Time Series Analysis with R, Part I by Walter Zucchini, Oleg Nenadi? for reference as you may need it to complete the assignment. http://www. statoek. wiso. uni-goettingen. de/veranstaltungen/zeitreihen/sommer03/ts_r_intro. pdf b. Download data file tui. ip from the website given in manual http://134. 76. 173. 220/tui. zip and read it in R using appropriate code. c. Write down last three digit of your student ID number __ __ __ In case you are working in a group, just use the group # instead in place of last digit. d. If the last number of the three numbers written above in part ‘c’ (or your group number) is: i. Even: plot a line graph of series in second column using red color [warning: do not do this if the number is odd, rather do (ii)]. Label your graph appropriately ii. If your last digit is not even (is odd instead): Plot a line graph of series in third column in blue color. Label the graph appropriately. For Even Number in (c) tui lt;- read. csv(C:/ratsdata/tui. csv, header=T, dec=,, sep=;) plot(tui[,2], type=l, lwd=2, col=red, xlab=time, ylab=opening values, main=Any Title, ylim=c(0,60) ) For Odd Number in (c) tui lt;- read. csv(C:/ratsdata/tui. csv, header=T, dec=,, sep=;) plot(tui[,3], type=l, lwd=2, col=blue, xlab=time, ylab=high values, main=Any Title, ylim=c(0,60) ) | |