1. An investment of $10,000 in a high-risk venture has a 50-50 chance over the next...

 

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1. An investment of $10,000 in a high-risk venture has a 50-50 chance over the next year of increasing to $14,000 or decreasing to $8,000. This means the net return can be either $4,000 or -$2,000. (a) Assuming a risk-neutral investor and a utility scale from O to 100, determine the utility of $0 net return on investment and the associated indifference probability. (b) Suppose that two investors A and B have exhibited the following indifference probabilities: Indifference probability Net Return ($) Investor A Investor B - 2,000 1.00 1.00 - 1,000 0.30 0.90 0.20 0.80 1,000 0.15 0.70 2,000 0.10 0.50 3,000 0.05 0.40 4,000 0.00 0.00 Graph the utility functions for investors A and B, and categorize the investors as either a risk-averse person or a risk seeker. (c) Suppose that investor A has the chance to invest in one of two ventures, I or II. Venture I can produce a net return of $3,000 with probability 0.40 or a net loss of $1,000 with probability 0.60. Venture Il can produce a net return of $2,000 with probability 0.60 and no return with probability 0.40. Based on the utility function in (b), use the expected utility criterion to determine the venture investor A should select. What is the expected monetary value associated with the selected venture (use the linear interpolation of the utility function)? (d) Repeat part (c) for investor B. 1. An investment of $10,000 in a high-risk venture has a 50-50 chance over the next year of increasing to $14,000 or decreasing to $8,000. This means the net return can be either $4,000 or -$2,000. (a) Assuming a risk-neutral investor and a utility scale from O to 100, determine the utility of $0 net return on investment and the associated indifference probability. (b) Suppose that two investors A and B have exhibited the following indifference probabilities: Indifference probability Net Return ($) Investor A Investor B - 2,000 1.00 1.00 - 1,000 0.30 0.90 0.20 0.80 1,000 0.15 0.70 2,000 0.10 0.50 3,000 0.05 0.40 4,000 0.00 0.00 Graph the utility functions for investors A and B, and categorize the investors as either a risk-averse person or a risk seeker. (c) Suppose that investor A has the chance to invest in one of two ventures, I or II. Venture I can produce a net return of $3,000 with probability 0.40 or a net loss of $1,000 with probability 0.60. Venture Il can produce a net return of $2,000 with probability 0.60 and no return with probability 0.40. Based on the utility function in (b), use the expected utility criterion to determine the venture investor A should select. What is the expected monetary value associated with the selected venture (use the linear interpolation of the utility function)? (d) Repeat part (c) for investor B.

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