HW6 answers - Economics 101-300 Winter 2006 Homework...

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Economics 101-300 Winter, 2006 Homework Problem Set # 6 Problems: 1) You decide that calculating your potential winnings from playing the lottery is entirely too complicated and opt for a simpler way to make cash fast. Like always, a student group on campus, “students for (insert your favorite cause here)” is having a raffle. Tickets are $10 and the prize is $100 in cash. The following five percentages represent probabilities of winning the raffle. What is the lowest probability at which you are willing to buy a raffle ticket? a) 10.1% b) 9.1% c) 91.1% d) 100% e) 10% Answer: e. If the expected value of playing the raffle is more than 0, you are willing to buy a ticket. To determine the minimum probability of winning for which your EV will be $0, solve the following equation (let x equal the probability of winning): 0= (x)(expected winnings) + (1-x)(expected losses) 0 = x(100-10) + (1-x)(0-10) 0 = 90x + 10x - 10 x = 0.1or 10% Thus, for any percentage probability greater than 10%, it is worth it to you to buy a raffle ticket. 2) You are a financial consultant for Yahoo—and you have quite a bit of saving. You know that you need to diversify your portfolio, so you invest in three financial instruments with the expected returns listed in the following table. What is the expected rate of return on your diversified portfolio? Bonds Stocks Gold Amount Invested $1,000 $5,000 $10,000 Expected Rate of Return 10% 50% 25% Answer: The expected rate of return on the diversified portfolio is the weighted average of the returns of each asset by its dollar amount: Expected Rate of Return = [(1,000*.10) + (5,000*.50) + (10,000*.25)]/16,000 = (100 + 2,500 + 2,500)/16,000 = 5100/16,000 = .319(or 31.9%)
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Notice that this is the expected RATE of return. In total, the expected value is $1,100 + $7,500 + 12,500 = $21,100. Your initial investment is $16,000. To get the rate, you can also calculate the total expected value and divide by the initial investment. $21,100/$16,000 = 1.31875. 3) Here is an example of how a topic addressed in the previous question might be presented as a multiple choice problem: You have decided that in the future you would like your expected rate of return on your diversified portfolio to be 45%.
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