Financial Policy Chapter 10
If the expected return on the market is 16%, then using the historical risk premium on large stocks of 8.6%, the current risk-free rate is:
Risk-free rate = 16% - 8.6% = 7.4%
The returns on your portfolio over the last 5 years were -5%, 20%, 0%, 10% and 5%. What is the standard deviation of your return?
Standard Deviation = √[(-.05 - .06)2 + (.20 - .06)2 + (0 - .06)2 + (.10 - .06)2 + (.05 - .06)2]/4 = √.0370/4 = √.00925 = .09617 = 9.62%
A capital gain occurs when:
the purchase price is less than the selling price
One year ago, you purchased a stock at a price of $32.50. The stock pays quarterly dividends of $.40 per share. Today, the stock is worth $34.60 per share. What is the total amount of your dividend income to date from this investment?
$1.60 Dividend income = $.40 × 4 = $1.60
Over the period of 1926 to 2011, small company stocks had an average return of ____%.
16.5
Over the period of 1926 to 2011, the average rate of inflation was _____%.
3.1
A stock had returns of 8%, 14%, and 2% for the past three years. Based on these returns, what is the probability that this stock will earn at least 20% in any one given year?
Average return = (.08 + .14 + .02) ÷ 3 = 8%; Total squared deviation = (.08 - .08)2 + (.14 - .08)2 + (.02 - .08)2 = .00 + .0036 + .0036 = .0072; Standard deviation = √(.0072 ÷ (3 - 1) = .06 = 6%; Upper end of the 95% probability range = 8% + (2 × 6%) = 20%; Probability of earning at least 20% in any one year is 2.5%
Which one of the following types of securities has tended to produce the lowest real rate of return for the period 1926 through 2011?
U.S. Treasury bills
The return earned in an average year over a multi-year period is called the _____ average return.
arithmetic
Over the period of 1926 through 2011, the annual rate of return on _____ has been more volatile than the annual rate of return on _____.
large company stocks; long-term corporate bonds
Estimates using the arithmetic average will probably tend to _____ values over the long-term while estimates using the geometric average will probably tend to _____ values over the short-term.
overestimate; underestimate
The standard deviation for a set of stock returns can be calculated as the:
positive square root of the variance.
The Zolo Co. just declared that it is increasing its annual dividend from $1.00 per share to $1.25 per share. If the stock price remains constant, then:
the dividend yield will increase
In estimating the future equity risk premium, it is important to include assumptions about:
the future risk environment and the amount of risk aversion of future investors
On average, for the period 1926 through 2011:
the risk premium on long-term corporate bonds has exceeded the risk premium on long-term government bonds.
The capital gains yield plus the dividend yield on a security is called the:
total return
The average squared difference between the actual return and the average return is called the:
variance.
What are the arithmetic and geometric average returns for a stock with annual returns of 4%, 9%, -6%, and 18%?
Arithmetic average = (.04 + .09 - .06 + .18) ÷ 4 = 6.25%; Geometric return = (1.04 × 1.09 × .94 × 1.18).25 - 1 = 5.89%
What are the arithmetic and geometric average returns for a stock with annual returns of 5%, 8%, -3%, and 16%?
Arithmetic average = (.05 + .08 - .03 + .16) ÷ 4 = 6.5%; Geometric return = (1.05 × 1.08 × .97 × 1.16).25 - 1 = 6.28%
A stock has returns of 3%, 18%, -24%, and 16% for the past four years. Based on this information, what is the 95% probability range for any one given year?
Average return = (.03 + .18 - .24 + .16) ÷ 4 = .0325; Total squared deviation = (.03 - .0325)2 + (.18 - .0325)2 + (-.24 - .0325)2 + (.16 - .0325)2 = .00000625 + .02175625 + .07425625 + .01625625 = .112275; Standard deviation = √(.112275 ÷ (4 - 1) = √.037425 = .19346 = 19.346%; 95% probability range = 3.25% ± (2 × 19.346%) = -35.4 to 41.9%
A stock had returns of 7%, 9%, -3%, and 5% over the past four years. What is the standard deviation of this stock for the past four years?
Average return = (.07 + .09 - .03 + .5) ÷ 4 = .045; Standard deviation = √{(.07 - .045)2 + (-.09 - .045)2 + (-.03 - .045)2 + (.05 - .045)2 }/(4 - 1) = 0.06656 = 6.7%
You have a sample of returns observations for the Malta Stock Fund. The 4 returns are 7.25%, 5.6%, 12.5%, 1.0%. What is the average return and variance of these returns?
Average return = (.0725 + .056 + .125 + .01)/4 = .2635/4 = .065875 = 6.6%; Variance = [(7.25 - 6.6)2 + (5.6 - 6.6)2 + (12.5 - 6.6)2 + (1 - 6.6)2]/3 = 67.5925/3 = 22.53
A stock had returns of 8%, -2%, 4%, and 16% over the past four years. What is the standard deviation of this stock for the past four years?
Average return = (.08 - .02 + .04 + .16) ÷ 4 = .065; Total squared deviation = (.08 - .065)2 + (-.02 - .065)2 + (.04 - .065)2 + (.16 - .065)2 = .000225 + .007225 + .000625 + .009025 = .0171; Standard deviation = √(.0171 ÷ (4 - 1) = √.0057 = .075498 = 7.5%
Over the past five years, a stock produced returns of 14%, 22%, -16%, 2%, and 10%. What is the probability that an investor in this stock will NOT lose more than 8% nor earn more than 21% in any one given year?
Average return = (.14 + .22 - .16 + .02 + .10) ÷ 5 = 6.4%; Total squared deviation = (.14 - .064)2 + (.22 - .064)2 + (-.16 - .064)2 + (.02 - 0.064)2 + (.10 - .064)2 = .005776 + .024336 + .050176 + .001936 + .001296 = .08352; Standard deviation = √.08352 ÷ (5 - 1) = √.02088 = 14.45%; 68% probability range = 6.4% ± 14.45% = -8.05% to 20.85%; Answer is 68%.
The long term inflation rate average was 3.2% and you invested in long term corporate bonds over the same period which earned 6.1%. What was the average risk premium you earned?
Average risk premium = 6.1% - 3.2% = 2.9%
Which of the following statements are correct concerning the variance of the annual returns on an investment? I. The larger the variance, the more the actual returns tend to differ from the average return. / II. The larger the variance, the larger the standard deviation. / III. The larger the variance, the greater the risk of the investment. / IV. The larger the variance, the higher the expected return.
I, II, III, and IV
A year ago, you purchased 300 shares of IXC Technologies, Inc. stock at a price of $10.05 per share. The stock pays an annual dividend of $.10 per share. Today, you sold all of your shares for $29.32 per share. What is your total dollar return on this investment?
Total dollar return = ($29.32 - $10.05 + $.10) × 300 = $8,811
In predicting the expected future return of the market, one of the dangers is that:
the past is not indicative of the future and the past period measured is too short to get a reasonable estimate of the future.
Excelsior share are currently selling for $25 each. You bought 200 shares one year ago at $24 and received dividend payments of $1.50 per share. What was your total rate of return?
% Total Return = [($25 + $1.50)/$24] - 1 = .1041667 = 10.42%
Excelsior shares are currently selling for $25 each. You bought 200 shares one year ago at $24 and received dividend payments of $1.50 per share. What was your percentage capital gain this year?
%CG = ($25 - $24)/$25 = .04167 = 4.17%
A year ago, you purchased 300 shares of IXC Technologies, Inc. stock at a price of $9.03 per share. The stock pays an annual dividend of $.10 per share. Today, you sold all of your shares for $28.14 per share. What is your total dollar return on this investment?
$5,763 Total dollar return = ($28.14 - $9.03 + $.10) × 300 = $5,763
You bought 100 shares of stock at $20 each. At the end of the year, you received a total of $400 in dividends, and your stock was worth $2,500 total. What was your total dollar capital gain and total dollar return?
$CG = $2,500 - $2,000 = $500; $Total Return = CG + DIV = $500 + $400 = $90
You bought 100 shares of stock at $20 each. At the end of the year, you received a total of $400 in dividends, and your stock was worth $2,500 total. What was your total return?
$Invest = $20(100) = $2,000; $Return = ($2,500 + $400 - $2,000)/$2,000 = .45 = 45%
Six months ago, you purchased 100 shares of stock in ABC Co. at a price of $43.89 a share. ABC stock pays a quarterly dividend of $.10 a share. Today, you sold all of your shares for $45.13 per share. What is the total amount of your capital gains on this investment?
$124.00 Capital gains = ($45.13 - $43.89) × 100 = $124
The dollar value of the world stock market capitalization, from largest to smallest is:
United States, Europe, Japan, United Kingdom
The average annual return on long-term corporate bonds for the period of 1926 to 2011 was ________%
6.4
The returns on your portfolio over the last 5 years were -5%, 20%, 0%, 10% and 5%. What is the arithmetic average return?
Arithmetic average = (-5 + 20 + 0 + 10 + 5)/5 = 6%
What are the arithmetic and geometric average returns for a stock with annual returns of 21%, 8%, -32%, 41%, and 5%?
Arithmetic average = (.21 + .08 - .32 + .41 + .05) ÷ 5 = 8.6%; Geometric return = (1.21 × 1.08 × .68 × 1.41 × 1.05).20 - 1 = 5.6%
Kids Toy Co. has had total returns over the past five years of 0%, 7%, -2%, 10%, and 12%. What was the arithmetic average return on this stock?
Arithmetic average = (0 + 7 - 2 + 10 + 12)/5 = 5.40%
A stock had returns of 8%, 39%, 11%, and -24% for the past four years. Which one of the following best describes the probability that this stock will NOT lose more than 43% in any one given year?
Average return = (.08 + .39 + .11 - .24) ÷ 4 = 8.5%; Total squared deviation = (.08 - .085)2 + (.39 - .085)2 + (.11 - .085)2 + (-.24 - .085)2 = .000025 + .093025 + .000625 + .105625 = .1993; Standard deviation = √.1993 ÷ (4 - 1) = √.06643333 = 25.7747%; Lower bound of the 95% probability range = 8.5% - (2 × 25.7747%) = -43.05; Probability of NOT losing more than 43% in any given year is 97.5%.
A stock had returns of 11%, 1%, 9%, 15%, and -6% for the past five years. Based on these returns, what is the approximate probability that this stock will earn at least 23% in any one given year?
Average return = (.11 + .01 + .09 + .15 - .06) ÷ 5 = 6%; Total squared deviation = (.11 - .06)2 + (.01 - .06)2 + (.09 - .06)2 + (.15 - .06)2 + (-.06 - .06)2 = .0025 + .0025 + .0009 + .0081 + .0144 = .0284; Standard deviation = √(0.284 ÷ (5 - 1) = √.0071 = .084; Upper end of the 95% probability range = .06 + (2 × .084) = 22.8%; Probability of earning more than 23% in any one year is just slightly less than 2.5%
The return pattern on your favorite stock has been 5%, 8%, -12%, 15%, 21% over the last five years. What has been your average return and holding period return over the last 5 years?
Average return = (5 + 8 - 12 + 15 + 21)/5 = 37/5 = 7.4%; HPR = [(1.05)(1.08)(.88)(1.15)(1.21)] - 1 = (1.3886) - 1 = .3886 = 38.9%
You just sold 200 shares of Langley, Inc. stock at a price of $38.75 a share. Last year you paid $41.50 a share to buy this stock. Over the course of the year, you received dividends totaling $1.64 per share. What is your capital gain on this investment?
Capital gain = ($38.75 - $41.50) × 200 = -$550 (capital loss)
Six months ago, you purchased 100 shares of stock in ABC Co. at a price of $43.26 a share. ABC stock pays a quarterly dividend of $.10 a share. Today, you sold all of your shares for $46.71 per share. What is the total amount of your capital gains on this investment?
Capital gains = ($46.71 - $43.26) × 100 = $345
One year ago, you purchased a stock at a price of $32 a share. Today, you sold the stock and realized a total return of 25%. Your capital gain was $6 a share. What was your dividend yield on this stock?
Capital gains yield = $6 ÷ $32 = 18.75%; Dividend yield = 25% - 18.75% = 6.25%
One year ago, you purchased a stock at a price of $60 a share. Today, you sold the stock and realized a total return of 30%. Your capital gain was $8 a share. What was your dividend yield on this stock?
Capital gains yield = $8 ÷ $32 = 25%; Dividend yield = 30% - 25% = 5%
You purchased 300 shares of Deltona, Inc. stock for $44.90 a share. You have received a total of $630 in dividends and $14,040 in proceeds from selling the shares. What is your capital gains yield on this stock?
Cost = 300 × $44.90 = $13,470; Capital gains yield = ($14,040 - $13,470) ÷ $13,470 = 4.23
One year ago, you purchased a stock at a price of $33. The stock pays quarterly dividends of $.60 per share. Today, the stock is worth $35.2 per share. What is the total amount of your dividend income to date from this investment?
Dividend income = $.60 × 4 = $2.40
Winslow, Inc. stock is currently selling for $40 a share. The stock has a dividend yield of 3.8%. How much dividend income will you receive per year if you purchase 500 shares of this stock?
Dividend income = $40 × .038 × 500 = $760
Winslow, Inc. stock is currently selling for $60 a share. The stock has a dividend yield of 2.5%. How much dividend income will you receive per year if you purchase 800 shares of this stock?
Dividend income = $60 × .025 × 800 = $1,200
You purchased 200 shares of stock at a price of $36.72 per share. Over the last year, you have received total dividend income of $322. What is the dividend yield?
Dividend per share = $322 ÷ 200 = $1.61; Dividend yield = $1.61 ÷ $36.72 = 4.4%
You purchased 300 shares of stock at a price of $37.23 per share. Over the last year, you have received total dividend income of $351. What is the dividend yield?
Dividend per share = $351 ÷ 300 = $1.17; Dividend yield = $1.17 ÷ $37.23 = 3.14%
Today, you sold 200 shares of SLG, Inc. stock. Your total return on these shares is 12.5%. You purchased the shares one year ago at a price of $28.50 a share. You have received a total of $280 in dividends over the course of the year. What is your capital gains yield on this investment?
Dividend yield = $280 ÷ (200 × $28.50) = 4.91%; Capital gains yield = 12.5% - 4.91% = 7.59%
A stock had returns of 6%, 13%, -11%, and 17% over the past four years. What is the geometric average return for this time period?
Geometric average = (1.06 × 1.13 × .89 × 1.17).25 - 1 = 5.7%
The prices for IMB over the last 3 years are given below. Assuming no dividends were paid, what was the 3-year holding period return? Given the following information: Year 1 return = 10%, Year 2 return = 15%, Year 3 return = 12%.
HPR = (1.10) (1.15) (1.12) = 1.4168 - 1 = 41.68%
The standard deviation on small company stocks: I. is greater than the standard deviation on large company stocks. / II. is less than the standard deviation on large company stocks. / III. had an average value of about 33% for the period 1926 to 2011. / IV. had an average value of about 20% for the period 1926 to 2011.
I and III only
Which of the following statements concerning the standard deviation are correct? I. The greater the standard deviation, the lower the risk. / II. The standard deviation is a measure of volatility. / III. The higher the standard deviation, the less certain the rate of return in any one given year. / IV. The higher the standard deviation, the higher the expected return.
II, III, and IV only
The total annual returns on large company common stocks averaged 12.3% from 1926 to 2011, small company stocks averaged 17.4%, long-term government bonds averaged 5.8%, while Treasury Bills averaged 3.8%. What was the average risk premium earned by long-term government bonds, and small company stocks respectively?
Long Term Government = 5.8% - 3.8% = 2.0%; Small Stocks = 17.5% - 3.8% = 13.7%
A stock has an expected rate of return of 8.3% and a standard deviation of 6.4%. Which one of the following best describes the probability that this stock will lose 11% or more in any one given year?
Lower bound of 99% probability range = .083 - (3 × .064) = -.109 = -10.9%; Probability of losing 11% or more is less than 0.5%
A stock had the following prices and dividends. What is the geometric average return on this stock? Year 1 price = $23.19 Year 2 price = $24.90/Dividend = $0.23 Year 3 price = $23.18/Dividend = $0.24 Year 4 price = $24.86/Dividend = $0.25
Return for year 2 = ($24.90 - $23.19 + $.23) ÷ $23.19 = 8.3657%; Return for year 3 = ($23.18 - $24.90 + $.24) ÷ $24.90 = -5.9438%; Return for year 4 = ($24.86 - $23.18 + $.25) ÷ $23.18 = 8.3261%; Geometric return = (1.083657 × .940562 × 1.083261).3333 - 1 = 3.4%
The market portfolio of common stocks earned 14.7% in one year. Treasury bills earned 5.7%. What was the real risk premium on equities?
Risk premium = 14.7% - 5.7% = 9.0%
Which one of the following is a correct statement concerning risk premium?
The greater the volatility of returns, the greater the risk premium
Six months ago, you purchased 1,200 shares of ABC stock for $21.20 a share. You have received dividend payments equal to $.60 a share. Today, you sold all of your shares for $22.20 a share. What is your total dollar return on this investment?
Total dollar return = ($22.20 - $21.20 + $.60) × 1,200 = $1,920
Eight months ago, you purchased 400 shares of Winston, Inc. stock at a price of $54.90 a share. The company pays quarterly dividends of $.50 a share. Today, you sold all of your shares for $49.30 a share. What is your total percentage return on this investment?
Total percentage return = ($49.30 - $54.90 + $.50 + $.50) ÷ $54.90 = -8.4% (loss)
Capital market history shows us that the average return relationship from lowest to highest between securities is:
Treasury bills, government bonds, corporate bonds, large common stocks, small company stocks.
Suppose you own a risky asset with an expected return of 12% and a standard deviation of 20%. If the returns are normally distributed, the approximate probability of receiving a return greater than 32% is approximately:
Z = (32 - 12)/20 = 1; 32 is 1 standard deviation above the mean. The probability of being within 1 standard deviation is approximately 68%; therefore, probability above the mean is approximately 32%/2 = 16%
The average compound return earned per year over a multi-year period is called the _____ average return.
geometric
A symmetric, bell-shaped frequency distribution that is completely defined by its mean and standard deviation is the _____ distribution.
normal
The excess return required from a risky asset over that required from a risk-free asset is called the:
risk premium.
The excess return you earn by moving from a relatively risk-free investment to a risky investment is called the:
risk premium.
Based on the period of 1926 through 2011, _____ have tended to outperform other securities over the long-term.
small company stocks
Which one of the following is a correct ranking of securities based on their volatility over the period of 1926 to 2011? Rank from highest to lowest.
small company stocks, large company stocks, long-term corporate bonds
The variance of returns is computed by dividing the sum of the:
squared deviations by the number of returns minus one
A portfolio of large company stocks would contain which one of the following types of securities?
stocks of firms included in the S&P 500 index
The risk premium is computed by ______ the average return for the investment.
subtracting the average return on the U.S. Treasury bill from
