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2006%20spring

# 2006%20spring - MATH 218 FINAL EXAM MAY 4 2006 of the...

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MATH 218 FINAL EXAM MAY 4, 2006 Problem 1 (25 pts) . A portfolio manager offers two assets to potential investors. Half of the investors select Asset A; the remaining investors select Asset B. Asset A has three possible returns: 8%, with a probability of 1/4; 12%, with a probability of 1/2; 16%, with a probability of 1/4. Asset B also has three possible returns: 8%, with a probability of 1/3; 14%, with a probability of 1/3; 20%, with a probability of 1/3. (a) Draw the appropriate probability tree. Be sure to in- clude the labels of events, probabilities, and condi- tional probabilities. (b) Find the probability that a randomly chosen investor earns a return of at least 10%. (c) Given that a randomly chosen investor earns a return of at least 10%, find the probability that the investor selected Asset A. (d) Given that a randomly chosen investor earns a return of at least 10%, find the probability that the return is greater than 15%. Problem 2 (20 pts) . The annual rate of return (in percent), X , of stock A has the following probability distribution: x - 10 0 10 20 30 P ( X = x ) 0.17 0.20 0.26 0.20 0.17 For example, - 10 represents a loss of 10% of the initial in- vestment, while 10 represents a gain of 10 % of the initial in- vestment. After one year, an investor will hold the amount of the initial investment plus any amount gained and minus any amount lost. (a) Find the expected annual rate of return on stock A (in percent). (b) Find the standard deviation of the annual rate of re- turn on stock A (in percent). (c) Jane starts with \$ 1,000, borrows \$ 200 at a constant annual risk-free rate of 6 % , and then invests the sum of \$ 1, 200 in stock A. After one year, Jane’s invest- ment will be worth \$ 1200 ( 1 + 0.01X ) - \$ 200 ( 1.06 ) = \$ 988 + \$ 12X . Find the expected value of Jane’s investment (in dol- lars and cents) after one year. (d) Find the standard deviation of Jane’s investment (in dollars and cents) after one year. Problem 3 (20 pts) . The two common types of errors made by programmers are syntax errors and logic errors. For a simple language such as BASIC the number of such errors is usually small. Let X denote the number of logic errors and Y

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2006%20spring - MATH 218 FINAL EXAM MAY 4 2006 of the...

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