= = Example 3.4 Suppose that S(0) = 100 dollars. 1. Consider a scenario in which S(1) = 110 and S(2) = 100 dollars. In this case K(0, 2) = 0%, while K(1) = 10% and K(2) -9.09%, the sum of the one-step returns K(1) and K(2) being positive and greater than K(0,2). 2. Consider another scenario with lower price S(1) = 90 dollars and with S(2) = 100 dollars as before. Then K(1) -10% and K(2) - 11.11%, their sum being once again greater than K(0,2) = 0%. 3. In a scenario such that S(1) = 110 and S(2) = 121 dollars we have K(0,2) 21%, which is greater than K(1) + K(2) = 10% + 10% = 20%. - = = = = = = = Exercise 3.5 Find K(0,2) and K(0,3) for the data in Exercise 3.3 and compare the results with the sums of one-step returns K(1)+K(2) and K(1)+K(2)+ K(3), respectively. = = Example 3.4 Suppose that S(0) = 100 dollars. 1. Consider a scenario in which S(1) = 110 and S(2) = 100 dollars. In this case K(0, 2) = 0%, while K(1) = 10% and K(2) -9.09%, the sum of the one-step returns K(1) and K(2) being positive and greater than K(0,2). 2. Consider another scenario with lower price S(1) = 90 dollars and with S(2) = 100 dollars as before. Then K(1) -10% and K(2) - 11.11%, their sum being once again greater than K(0,2) = 0%. 3. In a scenario such that S(1) = 110 and S(2) = 121 dollars we have K(0,2) 21%, which is greater than K(1) + K(2) = 10% + 10% = 20%. - = = = = = = = Exercise 3.5 Find K(0,2) and K(0,3) for the data in Exercise 3.3 and compare the results with the sums of one-step returns K(1)+K(2) and K(1)+K(2)+ K(3), respectively