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Many analysts use past data on stock and government security returns to estimate a historical risk premium
Many analysts use past data on stock and government security returns to estimate a historical risk premium. Assume that the arithmetic (geometric) average of annual stock returns is 10% (9%) and that the arithmetic (geometric) average of annual treasury bond returns is 5% (4.5%) over a hundred-year period. If the annualized standard deviation in stock returns over this period was 20%, which of the following is your fairest characterization of the historical risk premium (which you plan to use in your long term hurdle rate)?
Select one:
a. Historical risk premium is 5%, standard error is 20%
b. Historical risk premium is 4.5%, standard error is 2%
c. Historical risk premium is 5.5%, standard error is 2%
d. Historical risk premium is 4%, standard error is 2%
e. None of the above
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Which of the following statements best describes what the R—squared of 52.6% in the regression that estimates the Beta for Goldman Sachs is telling you about the risk?
Select one:
a. None of the above
b. 52.6% of the total risk in the firm is market risk
c. 52.6% of the total risk in the firm can be diversified away
d. 52.6% of the total risk in the firm is firm specific risk
e. 52.6% of the beta can be attributed to market risk
Expert Solution
1.
A risk premium will get compounded over time and geometric averages is better measure of compounding. Therefore, risk premium = 9% - 4.5% = 4.5%
The standard error is computed by dividing the standard deviation by the square root of number of period. In this case, Standard devation is 20% and number of period is 100
Standard error = 20% / (100)^(1/2) = 2%
Ans: Historical risk premium is 4.5%, standard error is 2%.
2.
R-sqaure is the proportion (fraction) of the total variance that is "explained" by the regression model. Bets ia measure of market risk.
Ans: 52.6% of the total risk in the firm is market risk.
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