E 44. E 45. D 46.
E 47.
E 48.
D 49.
E) None of the above
Rationale: HPR = .40 (22%) + .35 (11%) + .25 (-9%) = 10.4% What is the expected standard deviation for the stock? A) 2.07% B) 9.96% C) 7.04% D) 1.44%
E) None of the above
Rationale: s = [.40 (22 - 10.4)2 + .35 (11 - 10.4)2 + .25 (-9 - 10.4)2]1/2 = 12.167% What is the expected variance for the stock? A) 142.07% B) 189.96% C) 177.04% D) 128.17%
E) None of the above
Rationale: s = [ .40 (22 - 10.4)2 + .35 (11 - 10.4)2 + .25 (-9 - 10.4)2] = 148.04% Which of the following measures of risk best highlights the potential loss from extreme negative returns? A) Standard deviation B) Variance
C) Upper partial standard deviation D) Value at Risk (VaR) E) None of the above
Over the past year you earned a nominal rate of interest of 3.6 percent on your money. The inflation rate was 3.1 percent over the same period. The exact actual growth rate of your purchasing power was A) 3.6%. B) 3.1%. C) 0.5%. D) 6.7%.
E) none of the above
Rationale: r = (1+R) / (1+I) - 1; 1.036/ 1.031% - 1 = 0.328%.
A year ago, you invested $1,000 in a savings account that pays an annual interest rate of 4.3%. What is your approximate annual real rate of return if the rate of inflation was 3% over the year? A) 4.3%. B) -1.3%. C) 7.3%. D) 3%.
E) none of the above.
Rationale: 4.3% - 3% = 1.3%.
If the annual real rate of interest is 3.5% and the expected inflation rate is 3.5%, the nominal rate of interest would be approximately A) 0%.
E 50.
Use the following to answer questions 51-53:
You have been given this probability distribution for the holding period return for GM stock:
B) 3.5%. C) 12.25%. D) 7%.
E) none of the above.
Rationale: 3.5% + 3.5% = 7%.
You purchased a share of CSCO stock for $20. One year later you received $2 as dividend and sold the share for $31. What was your holding period return? A) 45% B) 50% C) 60% D) 40%
E) none of the above
Rationale: ($2 + $31 - $20)/$20 = 0.65, or 65%.
E 51. E 52. B 53.
What is the expected holding period return for GM stock? A) 10.4% B) 11.4% C) 12.4% D) 13.4% E) 14.4%
Rationale: HPR = .40 (30%) + .40 (11%) + .20 (-10%) = 14.4% What is the expected standard deviation for GM stock? A) 16.91% B) 16.13% C) 13.79% D) 15.25% E) 14.87%
Rationale: s = [.40 (30 - 14.4)2 + .40 (11 - 14.4)2 + .20 (-10 - 14.4)2]1/2 = 14.87% What is the expected variance for GM stock? A) 200.00% B) 221.04% C) 246.37% D) 14.87% E) 16.13%
Rationale: s = [.40 (30 - 14.4)2 + .40 (11 - 14.4)2 + .20 (-10 - 14.4)2] = 221.04%
B 54. You purchase a share of CAT stock for $90. One year later, after receiving a
dividend of $4, you sell the stock for $97. What was your holding period return?
A) 14.44% B) 12.22% C) 13.33% D) 5.56% E) none of the above Rationale: HPR = ([97 - 90] + 4) / 90 = 12.22%
B 55. When comparing investments with different horizons the ____________
provides the more accurate comparison.
A) arithmetic average B) effective annual rate C) average annual return D) historical annual average E) none of the above
B 56. Annual Percentage Rates (APRs) are computed using A) simple interest. B) compound interest. C) either A or B can be used. D) best estimates of expected real costs. E) none of the above.
D 57. An investment provides a 2% return semi-annually, its effective annual rate is A) 2%. B) 4%. C) 4.02% D) 4.04% E) none of the above Rationale: (1.02)2 -1 = 4.04%
D 58. An investment provides a 3% return semi-annually, its effective annual rate is A) 3%. B) 6%. C) 6.06% D) 6.09% E) none of the above Rationale: (1.03)2 -1 = 6.09%
D 59. An investment provides a 2.1% return quarterly, its effective annual rate is A) 2.1%. B) 8.4%. C) 8.56% D) 8.67% E) none of the above Rationale: (1.021)4 -1 = 8.67%
C 60. Skewnes is a measure of ____________.
A) how fat the tails of a distribution are B) the downside risk of a distribution C) the normality of a distribution D) the dividend yield of the distribution E) None of the above
C 61. Kurtosis is a measure of ____________. A) how fat the tails of a distribution are B) the downside risk of a distribution C) the normality of a distribution D) the dividend yield of the distribution E) A and C
A 62. When a distribution is positively skewed, ____________. A) standard deviation overestimates risk B) standard deviation correctly estimates risk C) standard deviation underestimates risk D) the tails are fatter than in a normal distribution E) none of the above
C 63. When a distribution is negatively skewed, ____________. A) standard deviation overestimates risk B) standard deviation correctly estimates risk C) standard deviation underestimates risk D) the tails are fatter than in a normal distribution E) none of the above
D 64. If a distribution has “fat tails” it exhibits A) positive skewness B) negative skewness C) a kurtosis of zero D) kutrosis E) A and D Essay Questions
65. Discuss the relationships between interest rates (both real and nominal),
expected inflation rates, and tax rates on investment returns.
The nominal interest rate is the quoted interest rate; however this rate is approximately equal to the real rate of interest plus the expected rate of inflation. Thus, an investor is expecting to earn the real rate in terms of the increased purchasing power resulting from the investment. In addition, the investor should consider the after-tax returns on the investment. The higher the inflation rate, the lower the real after-tax rate of return. Investors suffer an inflation penalty equal to the tax rate times the inflation rate.
The rationale for this question is to ascertain that the student understands the relationships among these basic determinants of the after-tax real rate of return.
66. Discuss why common stocks must earn a risk premium.
Most investors are risk averse; that is, in order to accept the risk involved in
investing in common stocks, the investors expect a return from the stocks over and above the return the investors could earn from a risk-free investment, such as U. S. Treasury issues. This excess return (the return in excess of the risk-free rate) is the risk premium required by the investors to invest in common stocks.
The purpose of this question is to ascertain that the students understanding the basic risk-return relationship, as the relationship applies to investing in common stocks vs. a risk-free asset (i.e., why would investors be willing to assume the risk of common stock as investment vehicles)?
67. Discuss the law of one price and how this concept relates to the
possibility of earning arbitrage profits?
The law of one price states that equivalent securities are equally (or almost equally) priced when sold on different markets. As a result, risk-free arbitrage profits should not be possible.
The purpose of this question to introduce the student to arbitrage profits and market efficiency.
68. Discuss the historical distributions of each of the following in terms of
their average return and the dispersion of their returns: U. S. small company stocks, U. S. large company stocks, U. S. long-term
government bonds, and U.S. T-bills. Would any of these investments cause a loss in purchasing power during a 1926-2005 holding period?
Whether the averages are measured on a geometric basis or an arithmetic basis, the ranking is always the same, with small company average>large company average>government bond average>T-bill average. With regard to risk, the relationships among the standard deviations are small
company>large company>government bonds>T-bills. These ranks indicate that the ex-post data confirm what would be expected - higher returns are earned to compensate for the increased risk. None of these investments would have caused a loss in purchasing power during the 1926-2002 period, because all had average returns higher than the average inflation rate. The goal of this question is to see if students have a general idea of the
historical relationships among the returns and risk levels of various categories of investments relative to each other and to the level of inflation.
69. Discuss some reasons why an investor with a long time horizon might
choose to invest in common stocks, even though they have historically been riskier than government bonds or T-bills.
Common stocks can be expected to provide for the best growth in purchasing
power based on historical data. An investor with a long time horizon can tolerate fluctuations in stock returns because of the long-term upward trend in stock returns. How much common stock an investor is willing to hold and what types of stocks he chooses for his portfolio will depend on his level of risk aversion.