Sample Case Answers
SAMPLE CASE ANSWER
2. Calculate the expected rate of return on each of the four alternatives listed in Table 1. Based solely on expected returns, which of the potential investments appears best?
The expected return is the weighted average of the estimated returns in the different states of the world, where the probabilities of each outcome are the weights. Each outcome is multiplied by its probability and all products are then summed together. Expected Return can be calculated with the following formula:
[pic]
where:
[pic]: The expected rate of return - E(r)
Pi : The probability of the i-th outcome. ri : The i-th possible outcome. n : The number of possible outcomes.
The charts below show the calculation of the expected returns for the 1-Year Bond, TECO, Gold Hill and S&P 500, based on the above equation. This shows that the XYZ Corp has the highest expected return of XX%, and thus, appears to be the best potential investment based solely on expected rate of return.
|Expected rate of Return Calculations | | | | | |
| | | | | | | | | |T-bond | | | | |Goldhill | | | | | | | | | | | | | | | | | | | | | | | | |State |Pi |ri |Piri | |State |Pi |ri |Piri | | | | | | | | | | | |Recession |0.10 |8.0 | | |Recession |0.10 |18.0 | | |Below Average |0.20 |8.0 | | |Below Average |0.20 |23.0 | | |Average |0.40 |8.0 | | |Average |0.40 |7.0 | | |Above Average |0.20 |8.0 | | |Above Average |0.20 |-3.0 | | |Boom |0.10 |8.0 | | |Boom |0.10 |2.0 | | | | | | | | | | | | | | Σ ’ |E(r) = | | | | Σ ’ |E(r) = | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |TECO | | | | |S&P 500 | | | | | | | | | | | | | | | | | | | | | | | | |State |Pi |ri |Piri | |State |Pi |ri |Piri | | | | | | | | | | | |Recession |0.10 |-8.0 | | |Recession |0.10 |-15.0 | | |Below
2. Calculate the expected rate of return on each of the four alternatives listed in Table 1. Based solely on expected returns, which of the potential investments appears best?
The expected return is the weighted average of the estimated returns in the different states of the world, where the probabilities of each outcome are the weights. Each outcome is multiplied by its probability and all products are then summed together. Expected Return can be calculated with the following formula:
[pic]
where:
[pic]: The expected rate of return - E(r)
Pi : The probability of the i-th outcome. ri : The i-th possible outcome. n : The number of possible outcomes.
The charts below show the calculation of the expected returns for the 1-Year Bond, TECO, Gold Hill and S&P 500, based on the above equation. This shows that the XYZ Corp has the highest expected return of XX%, and thus, appears to be the best potential investment based solely on expected rate of return.
|Expected rate of Return Calculations | | | | | |
| | | | | | | | | |T-bond | | | | |Goldhill | | | | | | | | | | | | | | | | | | | | | | | | |State |Pi |ri |Piri | |State |Pi |ri |Piri | | | | | | | | | | | |Recession |0.10 |8.0 | | |Recession |0.10 |18.0 | | |Below Average |0.20 |8.0 | | |Below Average |0.20 |23.0 | | |Average |0.40 |8.0 | | |Average |0.40 |7.0 | | |Above Average |0.20 |8.0 | | |Above Average |0.20 |-3.0 | | |Boom |0.10 |8.0 | | |Boom |0.10 |2.0 | | | | | | | | | | | | | | Σ ’ |E(r) = | | | | Σ ’ |E(r) = | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |TECO | | | | |S&P 500 | | | | | | | | | | | | | | | | | | | | | | | | |State |Pi |ri |Piri | |State |Pi |ri |Piri | | | | | | | | | | | |Recession |0.10 |-8.0 | | |Recession |0.10 |-15.0 | | |Below