Chapter 10

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 = $900

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%

You earned a total return of -5% on NoDotCom this year, earned -40% last year, and earned 30% two years ago. Calculate both the three-year holding period return and the average three year return.

3-year holding period return = (0.95) (0.60) (1.30) = 0.741 - 1 = -25.9% Average three-year return = (-.05 + - .40 + .30)/3 = -.15/3 = -5%.

A stock has produced returns of 11.9 percent, 5.6 percent, 16.4 percent, and -4.2 percent over the past four years, respectively. What is the geometric average return?

7.14% (1.119 x 1.056 x 1.164 x .958)^1/4 -1 = 7.14

minimum variance portfolio.

A dominant portfolio within an opportunity set that has the lowest possible level of risk is referred to as the:

yielded a higher return than expected for the level of risk assumed.

A stock with an actual return that lies above the security market line has:

risk, opportunities, accounting practices

A stock's PE ratio is primarily affected by which three factors?

normal distribution

A symmetric, bell-shaped frequency distribution that is completely defined by its mean and standard deviation is the

the dominant portion of the opportunity set.

An efficient set of portfolios is comprised of:

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%

total; systematic

As we add more diverse securities to a portfolio, the ____ risk of the portfolio will decrease while the _____ risk will not.

may be less than the variance of the least risky stock in the portfolio.

If a stock portfolio is well diversified, then the portfolio variance:

long-term U.S. Treasury bonds

In 2008, which asset class had the highest rate of return in the U.S.?

dividend yield.

Next year's annual dividend divided by the current stock price is called the:

systematic

Risk that affects a large number of assets, each to a greater or lesser degree, is called _____ risk.

A stock has had returns of −18.4 percent, 28.4 percent, 16.8 percent, −9.5 percent, 34.2 percent, and 26.4 percent over the last six years. What are the arithmetic and geometric returns for the stock?

The arithmetic average return is the sum of the known returns divided by the number of returns, so: Arithmetic average return = (-.184 + .284 + .168 - .095 + .342 + .264) / 6 Arithmetic average return = .1298, or 12.98% Using the equation for the geometric return, we find: Geometric average return = [(1 + R1) × (1 + R2) × ... × (1 + RT)]1/T - 1 Geometric average return = [(1 - .184)(1 + .284)(1 + .168)(1 - .095)(1 + .342)(1 + .264)](1/6) - 1 Geometric average return = .1108, or 11.08% Remember, the geometric average return will always be less than the arithmetic average return if the returns have any variation.

variance

The average squared difference between the actual return and the average return is called the:

total return

The capital gains yield plus the dividend yield on a security is called the:

can be used to compute a stock price at any point in time.

The constant dividend growth model:

risk premium

The excess return you earn by moving from a relatively risk-free investment to a risky investment is called the

a weighted

The expected return on a portfolio is best described as ____ average of the expected returns on the individual securities held in the portfolio.

is limited by the returns on the individual securities within the portfolio.

The expected return on a portfolio:

the risk-free rate of return.

The intercept point of the security market line is the rate of return which corresponds to:

eliminate asset-specific risk.

The primary purpose of portfolio diversification is to:

price-sales ratio

Which one of these stock valuation methods is used for a non-dividend paying firm that is experiencing accounting losses?

26% 20.55%

You find a certain stock that had returns of 17 percent, −24 percent, 25 percent, and 8 percent for four of the last five years. The average return of the stock over this period was 10.40 percent.

move perfectly in sync with one another.

You have a portfolio comprised of two risky securities. This combination produces no diversification benefit. The lack of diversification benefits indicates the returns on the two securities:

36. 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? A. $1.24 B. $1.64 C. $40.00 D. $124.00 E. $164.00 Capital gains ($45.13 - $43.89) × 100 = $124

37. 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? A. $5,703 B. $5,733 C. $5,753 D. $5,763 E. $5,853 Total dollar return = ($28.14 - $9.03 + $.10) × 300 = $5,763

40. 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? A. 1.25% B. 3.75% C. 6.25% D. 18.75% E. 21.25% Capital gains yield = $6 ÷ $32 = 18.75%; Dividend yield = 25% - 18.75% = 6.25%

46. 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? A. 6.3% B. 6.6% C. 7.1% D. 7.5% E. 7.9% 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%

47. 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? A. less than 0.5% B. less than 1.0% C. less than 1.5% D. less than 2.5% E. less than 5% Lower bound of 99% probability range = .083 - (3 × .064) = -.109 = -10.9%; Probability of losing 11% or more is less than 0.5%.

53. What are the arithmetic and geometric average returns for a stock with annual returns of 4%, 9%, -6%, and 18%? A. 5.89%; 6.25% B. 6.25%; 5.89% C. 6.25%; 8.33% D. 8.3%; 5.89% E. 8.3%; 6.25% Arithmetic average = (.04 + .09 - .06 + .18) ÷ 4 = 6.25%; Geometric return = (1.04 × 1.09 × .94 × 1.18)(.25) - 1 = 5.89%

58. 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? A. $400; $500 B. $400; $900 C. $500; $900 D. $900; $2,500 E. None of these $CG = $2,500 - $2,000 = $500 $Total Return = CG + DIV = $500 + $400 = $900

61. 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%. A. 12.3% B. 13.9% C. 15.8% D. 41.7% E. 46.5% HPR = (1.10) (1.15) (1.12) = 1.4168 - 1 = 41.68%

64. 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: A. 4.6% B. 7.4% C. 8.4% D. 10.6% E. 12.6% Risk-free rate = 16% - 8.6% = 7.4%

71. 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? A. 6.50%; 16.9 B. 6.60%; 22.5 C. 6.60%; 4.75 D. 26.35%; 67.6 E. None of these. 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

represent the smallest twenty percent of the companies listed on the NYSE.

A portfolio of small-company common stocks is best described as the stocks of the firms which:

9.7

A stock had returns of 9 percent, -9 percent, 7 percent, and 13 percent over the past 4 years. What is the standard deviation of this stock for the past four years?

11.33% 10.33%

A stock has had returns of 16 percent, 23 percent, 15 percent, −11 percent, 30 percent, and −5 percent over the last six years. What are the arithmetic and geometric returns for the stock?

-31 to 40

A stock has returns of 18 percent, 15 percent, -21 percent, and 6 percent for the past four years. Based on this information, what is the 95 percent probability range of returns for any one given year?

-25.4 to 37.4

A stock has returns of 3 percent, 19 percent, −15 percent, and 17 percent for the past 4 years. Based on this information, what is the 95 percent probability range for any one given year?

the risk-free rate.

A stock with a beta of zero would be expected to have a rate of return equal to:

market values of all stocks to decrease.

Assume you are using the dividend growth model to value stocks. If you expect the market rate of return to increase across the board on all equity securities, then you should also expect the:

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.

B. overestimate; underestimate

small-company stocks

Based on the period of 1926 through 2014, _____ have tended to outperform other securities over the long-term.

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%

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

Little John Industries sold for $1.90 on January 1 and ended the year at a price of $2.50. In addition, the stock paid dividends of $0.20 per share. Calculate Little John's dividend yield, capital gains yield, and total rate of return for the year.

Dividend yield = $0.20/$1.90 = 10.53% Capital gain = $0.60/$1.90 = 31.58% Total return = 10.53% + 31.58% = 42.11%

You find a certain stock that had returns of 12.4 percent, -21.2 percent, 27.2 percent, and 18.2 percent for four of the last five years. Assume the average return of the stock over this period was 10.4 percent. What was the stock's return for the missing year? What is the standard deviation of the stock's returns?

Here, we know the average stock return, and four of the five returns used to compute the average return. We can work the average return equation backward to find the missing return. The average return is calculated as: .1040 = (.124 - .212 + .272 + .182 + R) / 5 .52 = .124 - .212 + .272 + .182 + R R = .1540, or 15.40% The missing return has to be 15.40 percent. Now we can use the equation for the variance to find: Variance = 1/4[(.124 - .104)2 + (-.212 - .104)2 + (.272 - .104)2 + (.182 - .104)2 + (.154 - .104)2] Variance = .034266 And the standard deviation is: Standard deviation = .0342661/2 Standard deviation = .1851, or 18.51%

move perfectly opposite to one another.

If the correlation between two stocks is -1, the returns on the stocks:

was conducted in the primary market.

If the issuer of a stock receives the proceeds from a sale of that issuer's stock, then the sale:

37

In 2008, the S&P 500 Index lost approximately what percent of its value?

the risk premium on long-term corporate bonds has exceeded the risk premium on long-term government bonds.

On average, for the period 1926 through 2014

large-company stocks; long-term corporate bonds

Over the period of 1926 through 2014, the annual rate of return on _____ has been more volatile than the annual rate of return on _____.

unsystematic

Risk that affects at most a small number of assets is called _____ risk.

$8008

Six months ago, you purchased 2,600 shares of ABC stock for $30.33 a share. You have received dividend payments equal to $0.40 a share. Today, you sold all of your shares for $33.01 a share. What is your total dollar return on this investment?

11.39%

Suppose a stock had an initial price of $86 per share, paid a dividend of $1.80 per share during the year, and had an ending share price of $94.

Use the following returns for X and Y. Returns Year X Y 1 22.5 % 28.5 % 2 - 17.5 -4.5 3 10.5 30.5 4 21.0 -16.0 5 5.5 34.5 Calculate the average returns for X and Y. Calculate the variances for X and Y. Calculate the standard deviations for X and Y.

The average return is the sum of the returns, divided by the number of returns. The average return for each stock was: X=(.225+.......+.055)/5=8.4% y=(.285.....+.345)/5=14.6% Remembering back to "sadistics," we calculate the variance of each stock as: x=(.225-.0830)^2+.....(.055-.0840)^2)= .026030 y= (.85-.1460)^2+....(.345-.1460)^2)=.053580 The standard deviation is the square root of the variance, so the standard deviation of each stock is: σX = .0260301/2 σX = .1613, or 16.13% σY = .0535801/2 σY = .2315, or 23.15%

spreading an investment across many diverse assets will eliminate idiosyncratic risk.

The principle of diversification tells us that:

capital gains

The rate at which a stock's price is expected to appreciate (or depreciate) is called the _____ yield.

You bought a share of 6.60 percent preferred stock for $97.68 last year. The market price for your stock is now $102.42. What is your total return for last year?

The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the initial price. Since preferred stock is assumed to have a par value of $100, the dividend was $6.60, so the return for the year was: R = ($102.42 - 97.68 + 6.60) / $97.68 R = .1161, or 11.61%

Suppose a stock had an initial price of $121 per share, paid a dividend of $3.30 per share during the year, and had an ending share price of $153. Compute the percentage total return. What was the dividend yield? What was the capital gains yield?

The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the initial price. The return of this stock is: R = [($153 - 121) + 3.30] / $121 R = .2917, or 29.17% The dividend yield is the dividend divided by the initial price, so: Dividend yield = $3.30 / $121 Dividend yield = .0273, or 2.73% And the capital gains yield is the increase in price divided by the initial price, so: Capital gains yield = ($153 - 121) / $121 Capital gains yield = .2645, or 26.45%

market risk premium

The slope of an asset's security market line is the:

positive square root of the variance.

The standard deviation for a set of stock returns can be calculated as the:

is over ten times as large as the standard deviation of U.S. Treasury bills.

The standard deviation of small-company stocks:

dividend yield plus the dividend growth rate.

The total return on a stock is equal to the:

the present value of the future income that the stock is expected to generate.

The underlying assumption of the dividend growth model is that a stock is worth:

You purchased 270 shares of a particular stock at the beginning of the year at a price of $76.33. The stock paid a dividend of $1.45 per share, and the stock price at the end of the year was $82.84. What was your dollar return on this investment?

To calculate the dollar return, we multiply the number of shares owned by the change in price per share and the dividend per share received. The total dollar return is: Dollar return = 270($82.84 - 76.33 + 1.45) Dollar return = $2,149.20

9 to 8.64

What are the arithmetic and geometric average returns for a stock with annual returns of 18 percent, 9 percent, -5 percent, and 14 percent? List the arithmetic answer first.

market value of the total shares held in each stock.

When computing the expected return on a portfolio of stocks the portfolio weights are based on the

small-company stocks, large-company stocks, long-term corporate bonds

Which one of the following is a correct ranking of securities based on their volatility over the period of 1926 to 2014? Rank from highest to lowest.

the Federal Reserve increases interest rates

Which one of the following is the best example of systematic risk?

The standard deviation of a portfolio can often be lowered by changing the weights of the securities in the portfolio.

Which one of the following statements is correct concerning the standard deviation of a portfolio?

U.S. Treasury bills

Which one of the following types of securities has tended to produce the lowest real rate of return for the period 1926 through 2014?

a decrease in the portfolio standard deviation

Which one of the following would indicate a portfolio is being effectively diversified?

The growth rate must be less than the discount rate.

Which one of these applies to the dividend growth model of stock valuation?

future opportunities

Which one of these factors generally has the greatest impact on a firm's PE ratio?

2.23% 4.75%

You've observed the following returns on Crash-n-Burn Computer's stock over the past five years: 18 percent, -3 percent, 16 percent, 11 percent, and 10 percent. Suppose the average inflation rate over this period was 3.2 percent and the average T-bill rate over the period was 5.5 percent. What was the average real risk-free rate over this time period?