Download Assignment 3 - Introduction to Computational Finance | CSCI 6961 and more Assignments Computer Science in PDF only on Docsity! CSCI 6961 RPI Introduction to Computational Finance Fall 2008 ASSIGNMENT 3, due Thursday, October 2 Homeworks are due at the begining of class or in my mail box by 2pm on the due date. The point value for the 6000 level is indicated in small font. 1 (100 (50) points) Trading Systems Let ri, i = 0 to N be a series for which we are interested in computing statistics. (a) [40 (20)] Give a linear time algorithm to compute the mean return, the Sharpe ratio and the Sterling ratio that makes one pass through the data to compute all three. (b) From the website, you can download ibm.dat, dell.dat and bond.dat. The first column is the time (in minutes), and the second is the quote ((bid + ask)/2). (i) [10 (5)] Consider the buy and hold strategy. Compute the the three statistics for the three intruments. You will encounter a problem with the Bond? For this reason, one usually subtracts the risk-free return from each ri at each time step, before computing the statistics. These are refered to as the statistics adjusted for the risk- free rate. Repeat the computations adjusting for the risk-free rate (assume that 0 0 = 0). When you adjust for the risk free rate, which of the following will change: µ, σ,MDD? These are buy and hold benchmarks. One could compare any trading strategy with these to determine if they are significantly better than these trivial strategies. (ii) [10 (5)] Compute the statistics adjusted for the risk-free rate using a randomly gener- ated strategy on bond and IBM. Assume that the bid-ask spread is constant, equal to a fraction of the mean instrument value (instrument specific), and vary this spread using the fractions [0, 0.0001, 0.0002, 0.0005]. Repeat this experiment 1000 times and give a table of the average values of the statistics for each fractional spread. This is another bench-mark for performance. If you have a trading system, you can see how much better it is than a random trading system and whether this difference is significant. What conclusion can you draw about the buy and hold strategies. (c) [40 (20)] Implement the algorithm we discussed in class to determine the optimal trading strategy. Use this algorithm to determine the optimal trading strategy for (BOND, IBM), (BOND,DELL) and (DELL,IBM), using the spread fraction 0.02 NOTE: Make sure that your algorithm is a linear time algorithm. This is not a completely trivial problem. 1
