| Table 1 Estimated Total Returns | |||||
| State of the Economy | Probability | T-Bond | SETX | Golden | S&P 500 |
| Recession | 5% | 5% | -19% | 20% | -14% |
| Below Average | 15% | 5% | 2% | 13% | 3% |
| Average | 45% | 5% | 9% | 10% | 11% |
| Above Average | 25% | 5% | 34% | 5% | 22% |
| Boom | 10% | 5% | 25% | -5% | 33% |
Calculate the standard deviations and coefficients of variation of returns for the four alternatives. What type of risk do these statistics measure? Is the standard deviation or the coefficient of variation the better measure? How do the alternatives compare when risk is considered?
We need to calculate the mean and standard deviation using the following formula:
Mean of a probability distribution = E(X) = probability * X
Standard deviation = square root ( probability * [X-E(X)]2 )
Coefficient of variation = mean / standard deviation
For T-Bond, the mean = 5% and standard deviation = 0 because the returns do not change. There is no variation because of constant returns, hence coefficient of variation is undefined and this can be confirmed with the formula too. which is 5% / 0 = undefined.
Calculate the mean and standard deviation of SETX, Golden and S&P500 as follows:
E (SETX) = 0.05 * -19 + 0.15 * 2 + 0.45 * 9 + 0.25 * 34 + 0.10 * 0.25 = 14.40%
E (Golden) = 0.05 * -20 + 0.15 * 13 + 0.45 * 10 + 0.25 * 5 + 0.10 * -5 = 8.20%
E (S&P500) = 0.05 * -14 + 0.15 * 3 + 0.45 *11 + 0.25 * 22 + 0.10 * 0.33 = 13.50%
Standard deviation = square root ( probability * [X-E(X)]2 )
Substituting the values for SETX, Golden and S&P500 in the formula above, we get the following values for standard deviation:
Standard deviation (SETX) = 14.12%
Standard deviation (Golden) = 5.64%
Standard deviation (S&P500) = 10.64%
Coefficient of variation (SETX) = Mean / Standard deviation = 14.40 / 14.12 = 0.9802
Coefficient of variation (Golden) = Mean / Standard deviation = 8.20 / 5.64 = 0.6883
Coefficient of variation (S&P500) = Mean / Standard deviation = 13.50 / 10.64 = 0.7883
What type of risk do these statistics measure?
Both Standard deviation and coefficient of variation measures the variability of the data set or dispersion of data around the mean.
Is the standard deviation or the coefficient of variation the better measure?
The coefficient of variation is a relative measure as it encapsulates both mean and standard deviation whereas standard deviation is an absolute measure. When one has to compare two or more distributions then co-efficient of variation is a better measure than standard deviation because an absolute measure comparison is meaningless.
How do the alternatives compare when risk is considered?
SETX is most risky with standard deviation of 14.12%, whereas TBond is risk free. Golden ranks 2nd in risk and S&P500 is 3rd in risk.
Table 1 Estimated Total Returns State of the Economy Probability T-Bond SETX Golden S&P 500 Recession 5% 5% -19% 20% -14% Below Average 15% 5% 2% 13% 3% Average 45% 5% 9% 10% 11% Above Average 25% 5% 34% 5% 22% Boom 10% 5% 25% -5% 33% Why is the T-bond return in table 1 shown to be independent of the state of the economy? Is the return on a 1-year T-bond risk-free?
Table 1 Estimated Total Returns State of the Economy Probability T-Bond SETX Golden S&P 500 Recession 5% 5% -19% 20% -14% Below Average 15% 5% 2% 13% 3% Average 45% 5% 9% 10% 11% Above Average 25% 5% 34% 5% 22% Boom 10% 5% 25% -5% 33% SETX expects to have $2.72 in earnings next year. SETX had $1.95 in earnings 4 years ago. What should SETX sell for? If it sells for $25, should you buy?
Table 1 Estimated Total Returns State of the Economy Probability T-Bond SETX Golden S&P 500 Recession 5% 5% -19% 20% -14% Below Average 15% 5% 2% 13% 3% Average 45% 5% 9% 10% 11% Above Average 25% 5% 34% 5% 22% Boom 10% 5% 25% -5% 33% Golden expects to have $1.45 in earnings next year. Golden had $1.30 in earnings 3 years ago. What should Golden sell for?
Table 1 Estimated Total Returns State of the Economy Probability T-Bond SETX Golden S&P 500 Recession 5% 5% -19% 20% -14% Below Average 15% 5% 2% 13% 3% Average 45% 5% 9% 10% 11% Above Average 25% 5% 34% 5% 22% Boom 10% 5% 25% -5% 33% SETX's A-Rated bonds yield 7.35%. What is the required return on SETX's stock using the bond risk premium method? (Assume 6% premium)
Table 1 Estimated Total Returns State of the Economy Probability T-Bond SETX Golden S&P 500 Recession 5% 5% -19% 20% -14% Below Average 15% 5% 2% 13% 3% Average 45% 5% 9% 10% 11% Above Average 25% 5% 34% 5% 22% Boom 10% 5% 25% -5% 33% Golden's AA-Rated bonds yield 5.95%. What is the required return on Golden's stock using the bond risk premium method? (Assume 6% premium)
Table 1 Estimated Total Returns State of the Economy Probability T-Bond SETX Golden S&P 500 Recession 5% 5% -19% 20% -14% Below Average 15% 5% 2% 13% 3% Average 45% 5% 9% 10% 11% Above Average 25% 5% 34% 5% 22% Boom 10% 5% 25% -5% 33% Golden expects to pay $0.85 in dividends next year. Golden paid $0.67 in dividends 5 years ago. What should Golden sell for? If it sells for $14, should you buy? If Value Line...
Table 1 Estimated Total Returns State of the Economy Probability T-Bond SETX Golden S&P 500 Recession 5% 5% -19% 20% -14% Below Average 15% 5% 2% 13% 3% Average 45% 5% 9% 10% 11% Above Average 25% 5% 34% 5% 22% Boom 10% 5% 25% -5% 33% Notwithstanding the Value Line report, suppose SETX's long-term debt ratio (Long-term debt/Total assets) decreased during the period 2002 through 2012. Further, suppose this ratio was projected to continue decreasing in 2013 and beyond....
Table 1 Estimated Total Returns State of the Economy Probability T-Bond SETX Golden S&P 500 Recession 5% 5% -19% 20% -14% Below Average 15% 5% 2% 13% 3% Average 45% 5% 9% 10% 11% Above Average 25% 5% 34% 5% 22% Boom 10% 5% 25% -5% 33% Value Line indicates that non-utility businesses will account for much of SETX's earnings growth. Suppose Value Line specified that an increasing portion of SETX's assets would be devoted to non-regulated businesses in the...
Table 1 Estimated Total Returns State of the Economy Probability T-Bond SETX Golden S&P 500 Recession 5% 5% -19% 20% -14% Below Average 15% 5% 2% 13% 3% Average 45% 5% 9% 10% 11% Above Average 25% 5% 34% 5% 22% Boom 10% 5% 25% -5% 33% 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? Based on the coefficient of...
5 investment alternatives have the following returns and standard deviations of returns. AlternativeReturns: Expected ValueStandardDeviationA$1,550$880B3,3301,360C3,3301,140D5,5402,660E14,6004,860 Rank the five alternatives from lowest risk to highest risk using the coefficient of variation. (Round the final answers to 2 decimal places.) AlternativesCoefficient ofVariationA B C D E RankingAlternativeLowest risk (Click to select) A C B D E | (Click to select) A C B D E to (Click to select) A C B D E | (Click to select) A C B D E Highest risk (Click to select) A C B D E