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3330%20PS1

# 3330%20PS1 - Cornell University Fall 2009 Economics 3330...

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Cornell University Fall 2009 Economics 3330: Problem Set 1 Due 9/14/09 1. Derivatives Solve for the first and second derivatives with respect to x for both a) (1+x) -t+2 and b) e rx. 2. Expected Value and Variance There are two securities: X and Y. Security X takes the values -2, 4, and 10 in states L, M and H with probabilities 0.25, 0.5, and 0.25, respectively. Security Y takes the values -6, 4, and 14 with the same probabilities a. What is the expected value of each security? b. What is the variance of each security’s value? c. Which security would you expect to be more expensive? Explain your answer. d. Now suppose that there is a trader who can purchase either one or the other of the securities. The trader will receive 20% of the value of the security above zero as compensation; i.e., the trader receives a portion of the gains but none of the losses. What is the expected value received by the trader for each security? Explain why it is possible that the trader would be willing to pay more for security Y than X. Now suppose that Security A takes the values -12, 3, and 4 in states L, M, and H with

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3330%20PS1 - Cornell University Fall 2009 Economics 3330...

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