Question
In: Finance
Investment Forecasted Returns for Boom Economy Forecasted Returns for Stable Growth Economy Forecasted Returns for Stagnant...
| Investment | Forecasted Returns for Boom Economy | Forecasted Returns for Stable Growth Economy | Forecasted Returns for Stagnant Economy | Forecasted Returns for Recession Economy |
| Stock | 26% | 11% | 7% | -15% |
| Corporate bond | 9% | 7% | 5% | 4% |
| Government bond | 8% | 6% | 4% | 3% |
Variance and standard deviation
(expected).
Bacon and Associates, a famous Northwest think tank, has provided probability estimates for the four potential economic states for the coming year in the following table: The probability of a boom economy is 21%, the probability of a stable growth economy is 45%, the probability of a stagnant economy is 24%, and the probability of a recession is 10%. Calculate the variance and the standard deviation of the three investments: stock, corporate bond, and government bond. If the estimates for both the probabilities of the economy and the returns in each state of the economy are correct, which investment would you choose, considering both risk and return?
Hint: Make sure to round all intermediate calculations to at least seven (7) decimal places. The input instructions, phrases in parenthesis after each answer box, only apply for the answers you will type.
*Please show work in Excel*
Solutions
Expert Solution
Stock variance is 2.86916667 and standard deviation is 16.93861466
Corporate bond variance is 0.04916667 and standard deviation is 2.217355783
and government bond variance is 0.0491667 and standard deviation is 2.217355783
the following is the steps of calculation variance and standard deviation in excel also at the end of this explanation excel sheet will be attached for further clarification.
| Particulars | Forcasted return | ||||
| Investment | Boom Economy | Stable Economy | Stagnant Economy | Recession Economy | |
| Stock | 26% | 11% | 7% | -15% | |
| Corporate bond | 9% | 7% | 5% | 4% | |
| Government bond | 8% | 6% | 4% | 3% | |
|
Variance and standard deviation |
|||||
| Stock | Forcasted return | Mean | Variance | Standard deviation | |
| Boom Economy | 26% | ||||
| Stable Economy | 11% | ||||
| Stagnant Economy | 7% | ||||
| Recession Economy | -15% | ||||
| Avg(Mean) | 7.25% | 7.25% | 2.86916667 | 16.93861466 | |
| Formula | average(B9:B12) | var(B9:B12)*100 | stdev(B9:B12)*100 | ||
| Corporate bond | Forcasted return | Mean | Variance | Standard deviation | |
| Boom Economy | 9% | ||||
| Stable Economy | 7% | ||||
| Stagnant Economy | 5% | ||||
| Recession Economy | 4% | ||||
| Avg(Mean) | 6.25% | 6.25% | 0.04916667 | 2.217355783 | |
| average(B17:B20) | var(B17:B20)*100 | stdev(B17:B20)*100 | |||
| Government Bond | Forcasted return | Mean | Variance | Standard deviation | |
| Boom Economy | 8% | ||||
| Stable Economy | 6% | ||||
| Stagnant Economy | 4% | ||||
| Recession Economy | 3% | ||||
| Avg(Mean) | 5.25% | 5.25% | 0.0491667 | 2.217355783 | |
| average(B25:B28) | var(B25:B28)*100 | stdev(B25:B28)*100 |
Now the return of different investment opportunity according to the probability of economic situation.
| Stock | Forcasted return | Probability | Return probability | ||
| Boom Economy | 26% | 21% | 5% | I9*J9 | |
| Stable Economy | 11% | 45% | 5% | ||
| Stagnant Economy | 7% | 24% | 2% | ||
| Recession Economy | -15% | 10% | -2% | ||
| 10.59% | sum(K9:K12) | ||||
| Corporate bond | Forcasted return | Probability | Return probability | ||
| Boom Economy | 9% | 21% | 2% | I17*J17 | |
| Stable Economy | 7% | 45% | 3% | ||
| Stagnant Economy | 5% | 24% | 1% | ||
| Recession Economy | 4% | 10% | 0% | ||
| 6.64% | Sum(K17:K20) | ||||
| Goverment bond | Forcasted return | Probability | Return probability | ||
| Boom Economy | 8% | 21% | 2% | ||
| Stable Economy | 6% | 45% | 3% | ||
| Stagnant Economy | 4% | 24% | 1% | ||
| Recession Economy | 3% | 10% | 0% | ||
| 5.64% | sum(K25:K28) | ||||
Now as we have to determine the best investment opportunity according to risk reward ration therefore,
| Stock | Forcasted return | Probability | Return probability | Risk reutrn ratio | ||
| Boom Economy | 26% | 21% | 5% | I9*J9 |
potential risk/return |
|
| Stable Economy | 11% | 45% | 5% |
it determine per unit of return we are getting for per unit of risk |
||
| Stagnant Economy | 7% | 24% | 2% | |||
| Recession Economy | -15% | 10% | -2% | |||
| 10.59% | sum(K9:K12) | 1.598677998 | 16.93/10.59 | |||
| Corporate bond | Forcasted return | Probability | Return probability | |||
| Boom Economy | 9% | 21% | 2% | I17*J17 | ||
| Stable Economy | 7% | 45% | 3% | |||
| Stagnant Economy | 5% | 24% | 1% | |||
| Recession Economy | 4% | 10% | 0% | |||
| 6.64% | Sum(K17:K20) | 0.3338855422 | 2.217/6.64 | |||
| Goverment bond | Forcasted return | Probability | Return probability | |||
| Boom Economy | 8% | 21% | 2% | |||
| Stable Economy | 6% | 45% | 3% | |||
| Stagnant Economy | 4% | 24% | 1% | |||
| Recession Economy | 3% | 10% | 0% | |||
| 5.64% | sum(K25:K28) | 0.3918439716 | 2.21/5.64 |
after this ration we decided to invest in "Corporate bond"with the given economic situation as its risk to reward ratio is lowest ie 0.3338855422. and risk to reward ration help to determine per unit of risk we are getting for per unit of return.
Please refer to attached file for steps, explanation and calculation along with formula and cell referred.
jeff jeffy answered 2 years agoRelated Solutions
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