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Compute the (a) expected return, (b) standard deviation, and (c) coefficient of variation for investments with the following probability distributions: Probability           r/A                r/B 0.3                    30.0%             5.0% 0.2                     10.0              15.0 0.5                     -2.0               25.0

Compute the (a) expected return, (b) standard deviation, and (c) coefficient of variation for investments with the following probability distributions: Probability           r/A                r/B 0.3                    30.0%             5.0% 0.2                     10.0              15.0 0.5                     -2.0               25.0

Essentials Of Investments
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Compute the (a) expected return, (b) standard deviation, and (c) coefficient of variation for investments with the following probability distributions:

Probability           r/A                r/B

0.3                    30.0%             5.0%

0.2                     10.0              15.0

0.5                     -2.0               25.0

### Exercise 8-3 **Objective:** Compute the following for investments with the given probability distributions: - (a) Expected return - (b) Standard deviation - (c) Coefficient of variation #### Probability Distributions Table The table below provides the data needed to perform the calculations: | Probability | \( r_A \) | \( r_B \) | |-------------|-----------|-----------| | 0.3 | 30.0% | 5.0% | | 0.2 | 10.0% | 15.0% | | 0.5 | -2.0% | 25.0% | **Notes:** - \( r_A \) and \( r_B \) represent the return rates for two different scenarios or investment options. - The probability column indicates the likelihood of each return outcome occurring. **Instructions:** 1. **Expected Return:** Calculate the weighted average of all possible returns using the probabilities. 2. **Standard Deviation:** Measure the dispersion or variability of the returns. 3. **Coefficient of Variation:** Determine the ratio of the standard deviation to the expected return to assess risk per unit of return. These calculations will aid in understanding the risk and potential profitability of the investments based on their probability distributions.
Transcribed Image Text:### Exercise 8-3 **Objective:** Compute the following for investments with the given probability distributions: - (a) Expected return - (b) Standard deviation - (c) Coefficient of variation #### Probability Distributions Table The table below provides the data needed to perform the calculations: | Probability | \( r_A \) | \( r_B \) | |-------------|-----------|-----------| | 0.3 | 30.0% | 5.0% | | 0.2 | 10.0% | 15.0% | | 0.5 | -2.0% | 25.0% | **Notes:** - \( r_A \) and \( r_B \) represent the return rates for two different scenarios or investment options. - The probability column indicates the likelihood of each return outcome occurring. **Instructions:** 1. **Expected Return:** Calculate the weighted average of all possible returns using the probabilities. 2. **Standard Deviation:** Measure the dispersion or variability of the returns. 3. **Coefficient of Variation:** Determine the ratio of the standard deviation to the expected return to assess risk per unit of return. These calculations will aid in understanding the risk and potential profitability of the investments based on their probability distributions.
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