Investment Expected Return Expected RiskReturn/risk ratio Current investments10.00%5.00%2.00
German Tools 15.00% 8.00%1.88
Japanese Tools 13.00% 9.00%1.44
Local Manufacturer 11.00% 7.00%1.57
a. If Jonathon were risk-indifferent, which investments would he select? Explain why.
Answer: Risk indifferent investors don’t require a change in return in exchange for an increase in risk. Jonathon would pick the local manufacturer. b. If he were risk-averse, which investments would he select? Why?
Answer: Risk-averse investors require the return to grow proportionally to the risk. The German Tools investment has the highest return/risk ratio, therefore Jonathon would pick that company. c. If he were risk-seeking, which investments would he select? Why?
Answer: Risk-seeking investors’ attitudes allow an increase in risk with a decrease in return. Jonathon would pick Japanese Tools in this case, since it has the lowest return/risk ratio. d. Given the traditional risk preference behavior exhibited by financial managers, which investment would be preferred? Why?
Answer: Traditionally, managers are risk-averse, meaning they need returns to grow as risk increases. Technically speaking, the firm’s current investments have the least amount of risk for the returns offered (ratio of 2.00, or 1% risk per 2% return). But, the firm wants to increase its returns, so of the new options, the most risk-averse option is German Tools (ratio of 1.88, or 1% risk per 1.88% return).
Problem 2: Big Bank, Inc., is considering the purchase of one of two high speed servers, R and S. Both should provide benefits over a 10-year period, and each requires an initial investment of $4,000. Management has constructed the table (at the top of the facing page) of estimates of rates of return and probabilities for pessimistic, most likely, and optimistic results. a. Determine the range for the rate of return for each of the two servers.
Answer: The range for the rate of return on each server is the values between the pessimistic and optimistic return expectations. For Server R, the range is 20-30%. For Server S, the range is 15-35%. b. Determine the expected value of return for each server.
Answer: The expected value of return is calculated by adding together the products of each option’s probability X return. See the tables below:
| Possible outcomes| Probability| Returns| Weighted value| Server R| Pessimistic| 0.25| 20| 5|
| Most Likely| 0.5| 25| 12.5|
| Optimistic| 0.25| 30| 7.5|
| | | Expected| 25|
| Possible outcomes| Probability| Returns| Weighted value| Server S| Pessimistic| 0.2| 15| 3|
| Most Likely| 0.55| 25| 13.75|
| Optimistic| 0.25| 35| 8.75|
| | | Expected| 25.5|
c. Purchase of which server is riskier? Why?
Answer: The range illustrates the probability for investments to earn a specific return, since the broader the range, the less certain the returns. For Server R, the difference in the high and low end of the range is only 10 points. For Server S, the difference in the high and low end of the range is 20 points, indicating less probability of a specific return. While Server S has a higher probability of a most-likely or optimistic return, the uncertainty is doubled, while the expected return is only increased by 0.5%. Server R is the less risky of the two investments.
Problem 3: You have been given the return data shown in the first table on three countries—China, India, and South Korea—over the period 2009–2012....