f ch 11
Is volatility a reasonable measure of risk when evaluating the investment in a single stock?
No. In the case of an investment in a single stock, the volatility does not explain the size of its average return, because the stock has its own unique risk that can be diversified away.
What care, if any, should be taken when selecting stocks for an investment portfolio?
Stocks should be selected such that their returns are inversely correlated, so that the risks get cancelled out as we pool more stocks in the portfolio.
In the United States over the long term, small stocks have provided the highest return followed by the large stocks in the S&P 500.
TRUE
Independent risks can be diversified by holding a large number of uncorrelated assets with independent risks.
TRUE
On average, stocks have delivered higher returns than bonds in the long run.
TRUE
The risk that inflation rates are likely to increase in the next year is an example of common risk.
TRUE
What is the diversification achieved by an investor if he invests in Exxon Mobil, Dell, and Bank of America?
The three stocks Exxon Mobil, Dell, and Bank of America belong to three different sectors and should have a high level of independent risk. Thus, the portfolio of these three stocks should have considerable diversification benefits.
Ford Motor Company had realized returns of 20%, 30%, 30%, and 20% over four quarters. What is the quarterly standard deviation of returns for Ford calculated from this sample?
A) 5.77% A) Average return = (20%+ 30% + 30% + 20%) / 4 = 25%; standard deviation = ((20% - 25%)2 + (30% - 25%)2 + (30% - 25%)2 + (20% - 25%)2 ) / (4 - 1) = 5.77%
A portfolio of stocks can achieve diversification benefits if the stocks that comprise the portfolio are ________.
A) not perfectly positively correlated
There is an overall relationship between ________ and ________. Larger stocks have a lower volatility overall.
A) size, risk
Which of the following investments had the largest fluctuations overall return over the past eighty years?
A) small stocks
Suppose you invested $79 in the Ishares Dividend Stock Fund (DVY) a month ago. It paid a dividend of $0.41 today and then you sold it for $66. What was your return on the investment?
B) -$15.94% B) $(66 + 0.41) - 79 = -12.59 ; -12.59 /79 = -15.94%
Consider an economy with two types of firms, S and I. S firms always move together, but I firms move independently of each other. For both types of firms there is a 20% probability that they will have a 20% return and a 80% probability that they will have a -30% return. What is the expected return for an individual firm?
B) -20% B) expected return = 0.2 × (20%) + 0.8 × (-30%) = -20%
IGM Realty had stock prices of $33, $33, $38, $36, and $28 at the end of the last five quarters. If IGM pays a dividend of $1 at the end of each quarter, what is the annual realized return on IGM?
B) -4.49%
The average annual return over the period 1926-2009 for the S&P 500 is 12.8%, and the standard deviation of returns is 21.4%. Based on these numbers, what is a 67% confidence interval for 2010 returns?
B) -8.6%, 34.2% B) 12.8% - (1 × 21.4%) = -8.6%; 12.8% + (1 × 21.4%) = 34.2%
The S&P 500 index delivered a return of 25%, 15%, -35%, and -5% over four successive years. What is the arithmetic average annual return for four years?
B) 0% B) (25 + 15 - 35 - 5) / 4 = 0%
The risk that is linked across outcomes is called ________.
B) common risk
When investing for a long term, investors care about the volatility of ________ returns and not the volatility of ________ returns.
B) cumulative, average
The average annual return for the S&P 500 from 1886 to 2006 is 9.5%, with a standard deviation of 18%. Based on these numbers, what is a 95% confidence interval for 2007ʹs returns?
C) -26.5%, 45.5% C) 9.5% - (2 × 18%) = -26.5%; 9.5% + (2 × 18%) = 45.5%
Which of the following statements is FALSE?
C) Smaller stocks have lower volatility than larger stocks C) Smaller stocks have higher volatility than larger stocks.
If returns on stock A are more volatile than the returns on stock B, the geometric average return of stock A will be ________ the geometric average return of stock B when their arithmetic average returns are same.
C) lower than
Which of the following investments offered the highest overall return over the past eighty years?
C) small stocks
Suppose you invested $100 in the Ishares High Yield Fund (HYG) a month ago. It paid a dividend of $2 today and then you sold it for $100. What was your dividend yield and capital gains yield on the investment?
D) 2%, 0% D) Dividend yield = $2 / $100 = 2%; cap gains yield = $100 - $100 = 0
The S&P 500 index delivered a return of 10%, 15%, 15%, and -30% over four successive years. What is the arithmetic average annual return for four years?
D) 2.50% D) (10 + 15 + 15 - 30) / 4 = 2.50%
You purchase a 30-year, zero-coupon bond for a price of $25. The bond will pay back $100 after 30 years and make no interim payments. The annual compounded return (geometric average return) on this investment is ________.
D) 4.73% D) Using a financial calculator: N = 30, PV = -25, FV = 100; CPT = I/Y; I/Y = 4.73%
McCoy paid a one-time special dividend of $3.40 on October 18, 2010. Suppose you bought McCoy stock for $47.00 on July 18, 2010, and sold it immediately after the dividend was paid for $63.52 . What was your realized return from holding McCoy?
D) 42.38% D) ($3.40 + $63.52 - $47.00 ) / $47.00 = 42.38%
What is the excess return for the S&P 500?
D) 9.3%
The probability mass between two standard deviations around the mean for a normal distribution is ________.
D) 95%
The risk premium of a stock is NOT affected by its ________.
D) unsystematic risk
Amazon.com stock prices gave a realized return of 5%, -5%, 11%, and -11% over four successive quarters. What is the annual realized return for Amazon.com for the year?
A) -1.46% A) (1 + 0.05) × (1 - 0.05) × (1 + 0.11) × (1 - 0.11) = 0.9854 ; 0.9854 - 1 = -1.46%
What is the excess return for Treasury bills?
A) 0%
What is the excess return for corporate bonds?
A) 2.6%
The average annual return on the S&P 500 from 1996 to 2005 is closest to ________.
A) 8.68%
The geometric average annual return for a large capitalization stock portfolio is 10% for ten years and 6% per year for the next five years. The geometric average annual return for the entire 15 year period is ________.
B) 8.65% B) Compound return for first ten years = (1 + 0.1)10 = 2.5937 ; compound return for next 5 years = (1 + 0.06)5 = 1.3382 ; total return over 15 years = 2.5937 × 1.3382 = 3.4710 ; geometric average annual return = (3.4710 )1/15 - 1= 0.0865 ; geometric average annual return = 8.65%
What is the excess return for the portfolio of small stocks?
C) 19.5%
A stock whose return does not depend on overall economic conditions has a low systematic risk.
FALSE
Investors should earn a risk premium for bearing unsystematic risk.
FALSE
What are the two components of realized return from a stock investment?
The total realized return earned from a stock investment comprises two components: dividend yield and capital gains yield.
What is the diversification achieved by an investor if he invests in Dell, IBM, and Microsoft?
There will not be much diversification achieved by investing in Dell, IBM, and Microsoft, because all three have similar business and thus, high common risk.
Comment on the accuracy of the statement that as we put more stocks in a portfolio, its risk gets eliminated to zero.
This is an inaccurate statement as the portfolio risk does not get eliminated, but the portfolio is left with only systematic risk. The unsystematic risk gets eliminated.
When looking at investment portfolios historically, was there a pattern between returns and volatility?
Yes, there is a direct relationship between return and volatility, i.e., high volatility investments have generally yielded higher returns.
Is volatility a reasonable measure of risk when evaluating large portfolios?
Yes, volatility is a reasonable measure of risk for large portfolios, once it is fully diversified.
blockbuster drug before the Food and Drug Administration (FDA) waiting for approval. If approved, Big Cureʹs blockbuster drug will produce $1 billion in net income for Big Cure. Little Cure has ten separate, less important drugs before the FDA waiting for approval. If approved, each of Little Cureʹs drugs would produce $50 million in net income. The probability of the FDA approving a drug is 50%. What is the expected payoff for Little Cureʹs ten drugs?
A) $250 million A) expected payoff = prob of payoff × amount if successful = 0.5 × $50 = $25 million for each drug $25 million × 10 drugs = $250 million
The average annual return for the S&P 500 from 1886 to 2006 is 15%, with a standard deviation of 25%. Based on these numbers, what is a 95% confidence interval for 2007ʹs returns?
A) -35%, 65% A) 15% - (2 × 25%) = -35%; 15% + (2 × 25%) = 65%
Amazon.com stock prices gave a realized return of 15%, 15%, -15%, and -15% over four successive quarters. What is the annual realized return for Amazon.com for the year?
A) -4.45% A) (1 + 0.15) × (1 + 0.15) × (1 - 0.15) × (1 - 0.15) = 0.9555 ; 0.9555 - 1 = -0.0445 or -4.45%
Greg purchased stock in Bear Stearns and Co. at a price of $88 per share one year ago. The company was acquired by JP Morgan at a price of $11 per share. What is Gregʹs return on his investment?
A) -87.50% A) $(11 - 88) = -$77; -$77 / $88 = -87.50%
Suppose you invested $100 in the Ishares High Yield Fund (HYG) a month ago. It paid a dividend of $2 today and then you sold it for $95. What was your dividend yield and capital gains yield on the investment?
A) 2%, -5% A) $2 / $100 = 2%; -$5 / $100 = -5%
Consider an economy with two types of firms, S and I. S firms always move together, but I firms move independently of each other. For both types of firms there is a 40% probability that the firm will have a 20% return and a 60% probability that the firm will have a -30% return. The standard deviation for the return on an individual firm is closest to ________.
A) 24.49% A) expected return = 0.4(20%) + 0.6(-30%) = -10.00% standard deviation = 0.4(0.20 - -0.1)2 + 0.6(-0.30 - -0.1)2 = 0.24494897
You own shares in Supernova Inc. that were purchased at a price of $23 per share. Quicksilver Inc. has offered to purchase Supernova Inc. and buy your shares at a price of $34 per share. What will be your return if you tender your shares to Quicksilver Inc. and the deal is completed?
A) 47.83% A) $34 - $23 = $11; $11 / $23 = 47.83%
If the returns on a stock index can be characterized by a normal distribution with mean 12%, the probability that returns will be lower than 12% over the next period equals ________.
A) 50%
The standard deviation of returns of ________. I. small stocks is higher than that of large stocks II. large stocks is lower than that of corporate bonds III. corporate bonds is higher than that of Treasury bills Which statement is true?
A) I and III
Two slot machines offer to double your money 3 times out of 5. Machine A takes $10 bets and Machine B takes $100 bets on each occasion. A risk-averse investor prefers to bet on ________.
A) Machine A
Which of the following statements is FALSE?
A) On average, larger stocks have higher volatility than smaller stocks.
If a stock pays dividends at the end of each quarter, with realized returns of R1, R2, R3, and R4 each quarter, then the annual realized return is calculated as ________.
A) Rannual = (1 + R1) (1 + R2) (1 + R3)( 1 + R4) - 1
Rational investors ________ fluctuations in the value of their investments
A) are averse to
Because investors can eliminate unsystematic risk for free by diversifying their portfolios, they ________.
A) do not require a risk premium for bearing it
Stocks with high returns are expected to have ________.
A) high variability
Historically, stocks have delivered a ________ return on average compared to Treasury bills but have experienced ________ fluctuations in values.
A) higher, higher
Which of the following is NOT a diversifiable risk?
A) the risk that oil prices rise, increasing production costs
Investors demand a higher return for investments that have larger fluctuations in values because ________.
A) they do not like risk
In general, it is possible to eliminate ________ risk by holding a large portfolio of assetsA) unsystematic
A) unsystematic
Many former employees at AlphaEnergy, an energy trading and supply company, had a large part of their portfolio invested in AlphaEnergyʹs stock. These employees were bearing a high degree of ________ risk.
A) unsystematic
Independent risk is more closely related to ________.
A) unsystematic risk
While ________ seems to be a reasonable measure of risk when evaluating a large portfolio, the ________ of an individual security does not explain the size of its average return.
A) volatility, volatility
Assume that you purchased Quicksilverʹs stock at the closing price on December 31, 2004 and sold it after the dividend had been paid at the closing price on January 26, 2005. Your total return rate (yield) for this period is closest to ________.
B) -4.00% B) (P1 + D1 - P0) / P0 = ($13.78 + $0.14 - $14.50 ) / $14.50 = -0.04000 or -4%
Assume that you purchased Quicksilverʹs stock at the closing price on December 31, 2004 and sold it at the closing price on December 30, 2005. Your realized annual return for the year 2005 is closest to ________.
B) -45.1%
Suppose you invested $93 in the Ishares High Yield Fund (HYG) a month ago. It paid a dividend of $0.53 today and then you sold it for $94. What was your dividend yield and capital gains yield on the investment?
B) 0.57%, 1.08% B) Dividend yield = $0.53 / $94 = 0.57%; cap gain = $94 - $93 = $1; capital gains yield $1 / $93 = 1.08%
Suppose the quarterly arithmetic average return for a stock is 10% per quarter and the stock gives a return of 15% each over the next two quarters. The arithmetic average return over the six quarters is ________.
B) 11.67% B) (10 + 10 + 10 + 10 + 15 + 15) / 6 = 11.67%
The average annual return on IBM from 1996 to 2005 is closest to ________.
B) 16.07%
If asset Aʹs return is exactly two times asset Bʹs return, then following risk return tradeoff, the standard deviation of asset A should be ________ times the standard deviation of asset B.
B) 2
Consider an economy with two types of firms, S and I. S firms always move together, but I firms move independently of each other. For both types of firms there is a 70% probability that the firm will have a 20% return and a 30% probability that the firm will have a -30% return. The standard deviation for the return on an portfolio of 20 type S firms is closest to ________.
B) 22.91% B) expected return = 0.7(20%) + 0.3(-30%) = 5% standard deviation = 0.7(0.20 - 0.05)2 + 0.3(-0.30 - 0.05)2 = 0.22912878 Since all these firms move the same, there is no adjustment to the standard deviation.
Amazon.com stock prices gave a realized return of 15%, 15%, 15%, and 10% over four successive quarters. What is the annual realized return for Amazon.com for the year?
B) 67.30% B) (1 + 0.15) × (1 + 0.15) × (1 + 0.15) × (1 + 0.1) = 1.6730 ; 1.6730 - 1 = 0.673 or 67.30%
Which of the following statements is TRUE?
B) Portfolios of smaller stocks are typically less volatile than individual small stocks
Which of the following statements is FALSE?
B) The geometric average return will always be above the arithmetic average return, and the difference grows with the volatility of the annual returns. B) The geometric average return will always be below the arithmetic average return, and the difference grows with the volatility of the annual returns.
Which of the following investments offered the lowest overall return over the past eighty years?
B) Treasury bills
Fluctuations of a stockʹs return that are due to market-wide news representing common risk is the ________.
B) systematic risk
If the Federal Reserve were to change from an expansionary to a contractionary monetary policy, this would be an example of ________.
B) systematic risk
The risk premium of a security is determined by its ________ risk and does not depend on its ________ risk.
B) systematic, unsystematic
A companyʹs stock price jumped when it announced that its revenue had decreased because of the quality issues of its products. This is an example of ________
B) unsystematic risk
Your investment over one year yielded a capital gains yield of 5% and no dividend yield. If the sale price was $114 per share, what was the cost of the investment?
C) $108.57 C) $114 / (1 + 0.05) = $108.57
Bear Stearnsʹ stock price closed at $98, $103 , $58, $29, $4 over five successive weeks. The weekly standard deviation of the stock price calculated from this sample is ________.
C) $42.96 C) Average return = $(98 + 103 + 58 + 29 + 4) / 5 = $58.4; standard deviation = (($98 - 58.4)2 + (103 - 58.4)2 + (58 - 58.4)2 + (29 - 58.4)2 + (4 - 58.4)2) / (5 - 1)1/2 = $42.96
The average annual return for the S&P 500 from 1886 to 2006 is 5%, with a standard deviation of 15%. Based on these numbers, what is a 95% confidence interval for 2007ʹs returns?
C) -25%, 35% C) 5% - (2 × 15%) = -25%; 5% + (2 × 15%) = 35%
Assume that you purchased Quicksilverʹs stock at the closing price on December 31, 2004 and sold it after the dividend had been paid at the closing price on January 26, 2005. Your capital gains rate (yield) for this period is closest to ________.
C) -3.85% C) (P1 - P0) / P0 = ($13.47 - $14.01 ) / $14.01 = -0.0385 or -3.85%
The average annual return over the period 1926-2009 for the S&P 500 is 12.0%, and the standard deviation of returns is 21.3%. Based on these numbers, what is a 95% confidence interval for 2010 returns?
C) -30.6%, 54.6% C) 12.0% - (2 × 21.3%) = -30.6%; 12.0% + ( 2 × 21.3%) = 54.6%
The Ishares Bond Index fund (TLT) has a mean and annual standard deviation of returns of 5% and 10%, respectively. What is the 66% confidence interval for the returns on TLT?
C) -5%, 15% C) 66% confidence interval = from mean - standard deviation to mean + standard deviation; from 5% - 10% = -5% to 5% + 10% = 15%
Assume that you purchased Quicksilverʹs stock at the closing price on December 31, 2004 and sold it after the dividend had been paid at the closing price on January 26, 2005. Your dividend yield for this period is closest to ________.
C) 0.74% C) div / P0 = $0.11 / $14.88 = 0.007 or 0.7%
Suppose you invested $59 in the Ishares Dividend Stock Fund (DVY) a month ago. It paid a dividend of 0.38 today and then you sold it for $66. What was your return on the investment?
C) 12.51% C) $(66 + 0.38) - 59 = 7.38; 7.38 / 59 = 12.51%
Ford Motor Company had realized returns of 15%, 30%, -15%, and -30% over four quarters. What is the quarterly standard deviation of returns for Ford?
C) 27.39% C) Average return = (15% + 30% + -15% + -30%) / 4 = 0%; standard deviation = ((15%)2 + (30%)2 + (-15%)2 + (-30%)2 ) / (4 - 1)1/2 = 27.39%
McCoy paid a one-time special dividend of $3.20 on October 18, 2010. Suppose you bought McCoy stock for $47.00 on July 18, 2010, and sold it immediately after the dividend was paid for $62.93 . What was your capital gain yield from holding McCoy?
C) 33.89% C) ($62.93 - $47.00 ) / $47.00 = 33.89%
Consider an economy with two types of firms, S and I. S firms always move together, but I firms move independently of each other. For both types of firms there is a 60% probability that the firm will have a 20% return and a 40% probability that the firm will have a -30% return. The standard deviation for the return on a portfolio of 20 type I firms is closest to ________.
C) 5.48% C) expected return = 0.6(20%) + 0.4(-30%) = 0% standard deviation = 0.6(0.20 - 0)2 + 0.4(-0.30 - 0)2 = 0.24494897 Since all these firms move independently, stdev = stdev(single firm) / number of obs = 0.24494897 / 20 = 0.05477226
The S&P 500 index delivered a return of 20%, -10%, 20%, and 5% over four successive years. What is the arithmetic average annual return for four years?
C) 8.75% C) (20 - 10 + 20 + 5) / 4 = 8.75%
Suppose you invested $60 in the Ishares Dividend Stock Fund (DVY) a month ago. It paid a dividend of $0.63 today and then you sold it for $65. What was your return on the investment?
C) 9.38% C) $(65 + 0.63) - 60 = 5.63; 5.63 / 60 = 9.38%
Which of the following statements is FALSE?
C) Fluctuations of a stockʹs return that are due to firm-specific news are common risks. C) Fluctuations of a stockʹs return that are due to firm-specific news are not common risks.
Which of the following statements is FALSE?
C) Volatility seems to be a reasonable measure of risk when evaluating returns on large portfolios and the returns of individual securities C) Volatility seems to be a reasonable measure of risk when evaluating returns on large portfolios and the volatility does not explain the size of returns of individual securities.
As we increase the number of stocks in a portfolio, the standard deviation of returns of the portfolio ________.
C) decreases
Which of the following is NOT a systematic risk?
C) the risk that your new product will not receive regulatory approval
Big Cure and Little Cure are both pharmaceutical companies. Big Cure presently has a potential blockbuster drug before the Food and Drug Administration (FDA) waiting for approval. If approved, Big Cureʹs blockbuster drug will produce $1 billion in net income for Big Cure. Little Cure has ten separate, less important drugs before the FDA waiting for approval. If approved, each of Little Cureʹs drugs would produce $100 million in net income. The probability of the FDA approving a drug is 40%. What is the expected payoff for Big Cureʹs blockbuster drug?
D) $400 million D) expected payoff = prob of payoff × amount if successful = 0.4 × $1 billion = $400 million
You purchased Alpha Innovative Inc. stock at a price of $25 per share. Its price was $15 after six months and the company declared bankruptcy at the end of the next six months. The realized return over the last year is ________.
D) -100% D) 0 - 25 / 25 = -100%
The average annual return over the period 1926-2009 for small stocks is 21.2%, and the standard deviation of returns is 21.2%. Based on these numbers, what is a 95% confidence interval for 2010 returns?
D) -21.2%, 63.6% D) 21.2% - (2 × 21.2%) = -21.2%; 21.2% + ( 2 × 21.2%) = 63.6%
Treasury bill returns are 4%, 3%, 2%, and 5% over four years. The standard deviation of returns of Treasury bills is ________.
D) 1.29% D) Average return = (4% + 3% + 2%+ 5%) / 4 = 3.5%; standard deviation = ((4% - 3.5%)2 + (3% - 3.5%)2 + (2% - 3.5%)2 + (5% -3.5%)2 ) / (4 - 1) = 1.29%
Ford Motor Company had realized returns of 10%, 20%, -10%, and -10% over four quarters. What is the quarterly standard deviation of returns for Ford?
D) 15.00% D) Average return = (10% + 20% - 10% - 10%) / 4 = 2.5%; standard deviation = ((10% - 2.5)2 + (20% - 2.5)2 + (-10% - 2.5)2 + (-10% - 2.5)2 ) / (4 - 1)1/2 = 15.00%
Suppose that a stock gave a realized return of 20% over a two-year time period and a 10% return over the third year. The geometric average annual return is ________.
D) 16.57% D) (1 + 0.2) × (1 + 0.2) × (1 + 0.1) = 1.584 ; geometric average = (1.584 )(1/3) = 1.1657 ; hence 16.57%
The excess return is the difference between the average return on a security and the average return for ________.
D) Treasury bills
The risk premium of a stock is not affected by its ________.
D) unsystematic risk
Rational investors may be willing to choose an investment that has additional risk but does not offer additional reward.
FALSE
There is a clear link between the volatility of returns for individual stocks and the returns for individual stocks.
FALSE
Which type of investment has historically had the lowest volatility?
Investments in Treasury bills have historically witnessed the lowest volatility
Which type of investment has historically had the highest volatility?
Investments in small stocks have historically witnessed the highest volatility.
A portfolio of stocks where each stock has a large component of independent risk benefits when such stocks are held in a portfolio, because the independent risks are averaged out. This is also referred to as diversification of risks.
TRUE
Historical evidence on the returns of large portfolios of stock and bonds shows that investments with higher volatility have rewarded investors with higher returns.
TRUE
