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In: Finance
Hull Consultants, a famous think tank in the Midwest, has provided probability estimates for the four...
Hull Consultants, a famous think tank in the Midwest, has provided probability estimates for the four potential economic states for the coming year. The probability of a boom economy is 12%, the probability of a stable growth economy is 18%, the probability of a stagnant economy is 45%, and the probability of a recession is 25%. 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? Investment Forecasted Returns for Each Economy Boom Stable Growth Stagnant Recession Stock 23% 14% 33% −15% Corporate bond 10% 7% 5% 4% Government bond 9% 6% 4% 3% 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. What is the variance of the stock investment? What is the standard deviation of the stock investment? What is the variance of the corporate bond investment? What is the standard deviation of the corporate bond investment? What is the variance of the government bond investment? What is the standard deviation of the government bond investment?
Solutions
Expert Solution
| Stock | |||||
| Scenario | Probability | Return | '=rate of return * probability | Actual return -expected return(A) | (A)^2* probability |
| Boom | 0.12 | 23.00% | 2.76% | 6.62% | 0.000526 |
| stable | 0.18 | 14.00% | 2.52% | -2.38% | 0.000102 |
| stagnant | 0.45 | 33.00% | 14.85% | 16.62% | 0.012430 |
| recession | 0.25 | -15% | -3.75% | -31.38% | 0.024618 |
| Expected return = | sum of weighted return = | 16.38% | Sum= | 0.037676 | |
| Standard deviation of Stock | '=(sum)^(1/2) | 19.41% | |||
| Coefficient of variation= | STD DEV/RETURN= | 1.18499348 | |||
| Govt bond | |||||
| Scenario | Probability | Return | '=rate of return * probability | Actual return -expected return(B) | (B)^2* probability |
| Boom | 0.12 | 9% | 1.08% | 4.29% | 0.000221 |
| stable | 0.18 | 6% | 1.08% | 1.29% | 0.000030 |
| stagnant | 0.45 | 4% | 1.80% | -0.71% | 0.000023 |
| recession | 0.25 | 3% | 0.75% | -1.71% | 0.000073 |
| Expected return = | sum of weighted return = | 4.71% | Sum= | 0.000347 | |
| Standard deviation of Govt bond | '=(sum)^(1/2) | 1.86% | |||
| Coefficient of variation= | STD DEV/RETURN= | 0.395263859 | |||
| corp bond | |||||
| Scenario | Probability | Return | '=rate of return * probability | Actual return -expected return(C) | (C)^2* probability |
| Boom | 0.12 | 10% | 1.20% | 5.29% | 0.000336 |
| stable | 0.18 | 7% | 1.26% | 2.29% | 0.000094 |
| stagnant | 0.45 | 5% | 2.25% | 0.29% | 0.000004 |
| recession | 0.25 | 4% | 1.00% | -0.71% | 0.000013 |
| Expected return = | sum of weighted return = | 5.71% | Sum= | 0.000447 | |
| Standard deviation of corp bond | '=(sum)^(1/2) | 2.11% | |||
| Coefficient of variation= | STD DEV/RETURN= | 0.370099407 |
choose corporate bond as it has lowest coefficient of variation
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