Finance Chapter 10

If the financial markets are efficient then:

stock prices should respond only to unexpected news and events.

Dan is a chemist for ABC, a major drug manufacturer. Dan cannot earn excess profits on ABC stock based on the knowledge he has related to his experiments if the financial markets are:

strong form efficient. If they are semi stong then he will.

One year ago, you purchased 100 shares of a stock. This morning you sold those shares and realized a total return of 8.2 percent. Given this information, you know for sure the:

sum of the dividend yield and the capital gains yield is 8.2 percent.

The average risk premium on long-term government bonds for the period 1926-2011 was equal to:

the rate of return on the bonds minus the T-bill rate.

Which one of the following had the lowest standard deviation of returns for the period of 1926-2011?

treasury bill

A stock has produced returns of 11 percent, 18 percent, -6 percent, -13 percent, and 21 percent for the past five years, respectively. What is the standard deviation of these returns?

Average return = (0.11 + 0.18 - 0.06 - 0.13 + 0.21)/5 = 0.062 σ2 = [(0.11 - 0.062)2 + (0.18 - 0.062)2 + (-0.06 - 0.062)2 + (-0.13 - 00.062)2 + (0.21 - 0.062)2]/(5 - 1) = 0.02247 σ = √0.02247 = 14.99 percent

Based on the period 1926-2011, what rate of return should you expect to earn over the long-term if you are unwilling to bear risk?

Between 3 and 4 percent

The stock of Southern United is priced at $40 a share and has a dividend yield of 2.1 percent. The firm pays constant annual dividends. What is the amount of the next dividend per share?

D = 0.021 × $40 = $0.84

Which one of the following combinations will always result in an increased dividend yield?

DECREASE in the stock price combined with a HIGHER dividend amount

Over the past four years, large-company stocks and U.S. Treasury bills have produced the returns stated below. During this period, inflation averaged 2.8 percent. Given this information, the average real rate of return on large-company stocks was ___ percent as compared to _____ percent for Treasury bills.

Divide by inflation!!! Large-company stocks: Average nominal return = (0.15 + 0.07 + 0.04 + 0.18)/4 = 0.11 Average real rate: r = (1.11/1.028) - 1 = 7.98 percent U.S. Treasury bills: Average nominal return = (0.06 + 0.03 + 0.02 + 0.04)/4 = 0.0375 Average real rate: r = (1.0375/1.028) - 1 = 0.92 percent

Which one of the following is defined as the average compound return earned per year over a multiyear period?

Geometric Average Return

Your portfolio has provided you with returns of 8.6 percent, 14.2 percent, -3.7 percent, and 12.0 percent over the past four years, respectively. What is the geometric average return for this period?

Geometric average return = (1.086 × 1.142 × 0.963 × 1.120)1/4 - 1 = 7.54 percent

Percentage returns

I. are easy to understand. II. relay information about a security more easily than dollar returns do. III. are not affected by the amount of the investment. IV. can be easily separated into dividend yield and capital gain yield

Which one of the following has the narrowest distribution of returns for the period 1926-2011?

Intermediate-terms government bonds

Which one of the following is defined as a bell-shaped frequency distribution that is defined by its average and its standard deviation?

Normal distribution

Which one of the following statements is correct concerning both the dollar return and the percentage return on a stock investment?

The dollar return is dependent on the size of the investment while the percentage return is not

New Labs just announced that it has received a patent for a product that will eliminate all flu viruses. This news is totally unexpected and viewed as a major medical advancement. Which one of the following reactions to this announcement indicates the market for New Labs stock is efficient?

The price of New Labs stock increases rapidly to a higher price and then remains at that price.

Assume the securities markets are strong form efficient. Given this assumption, you should expect which one of the following to occur?

The price of each security in that market will frequently fluctuate.

You bought a share of 8.5 percent preferred stock for $87.40 last year. The market price for your stock is now $88.10. What is your total return for last year?

Total return = ($88.10 - $87.40 + $8.50)/$87.40 = 10.53 percent

The rate of return on which one of the following is used as the risk-free rate?

Treasury bill

For the period 1926-2011, which one of the following had the smallest risk premium?

U.S. Treasury bills

The standard deviation measures the _____ of a security's returns over time.

Volatility

Semistrong form market efficiency states that the value of a security is based on:

all public-ally available information

The period 1926-2011 illustrates that U.S. Treasury bills:

can either outperform or underperform inflation on an annual basis.

A bond has an average return of 6.3 percent and a standard deviation of 3.8 percent. What range of returns would you expect to see 68 percent of the time on this security?

2.5 percent to 10.1 percent

Over the last four years, a stock has had an arithmetic average return of 8.8 percent. Three of those four years produced returns of 16.3 percent, 10.2 percent, and -14.1 percent, respectively. What is the geometric average return for this four-year period?

Arithmetic average return = 0.088 = (0.163 + 0.102 - 0.141 + x)/4 x = 22.8 percent Geometric average return = [1.163 × 1.102 × 0.859 × 1.228)1/4 - 1 = 7.83 percent

Over the last four years, the common stock of Plymouth Shippers has had an arithmetic average return of 9.3 percent. Three of those four years produced returns of 14.1 percent, 15.6 percent, and 3.4 percent, respectively. What is the geometric average return for this four-year period?

Arithmetic average return = 0.093 = (0.141 + 0.156 + 0.034 + x)/4 x = 0.041 Geometric average return = [1.141 × 1.156 × 1.034 × 1.041)1/4 - 1 = 9.16 percent

An efficient capital market is best defined as a market in which security prices reflect which one of the following?

Available information

A stock has yielded returns of 6 percent, 11 percent, 14 percent, and -2 percent over the past four years, respectively. What is the standard deviation of these returns?

Average return = (0.06 + 0.11 + 0.14 - 0.02)/4 = 0.0725 σ2 = [(0.06 - 0.0725)2 + (0.11 - 0.0725)2 + (0.14 - 0.0725)2 + (-0.02 - 00.0725)2 ]/(4 - 1) = 0.004892 σ = √0.004892 = 6.99 percent

A security produced returns of 13 percent, 18 percent, 9 percent, 23 percent, and -17 percent over the past five years, respectively. Based on these five years, what is the probability that this stock will earn more than 24.76 percent in any one given year?

Average return = (0.13 + 0.18 + 0.09 + 0.23 - 0.17)/5 = 0.092 σ2 = [(0.13 - 0.092)2 + (0.18 - 0.092)2 + (0.09 - 0.092)2 + (0.23 - 00.092)2 + (-0.17 - 00.092)2]/(5 - 1) = 0.024220 σ = √0.024220 = 0.155628 Upper end of 68 percent probability range = 0.092 + 0.155628 = 24.76 percent Probability of earning more than 24.76 percent = (1 - 0.68)/2 = 16 percent

Windsor stock has produced returns of 22.6 percent, 18.7 percent, 11.3 percent, -19.8 percent, and 2.4 percent over the past five years, respectively. What is the variance of these returns?

Average return = (0.226 + 0.187 + 0.113 - 0.198 + 0.024)/5 = 0.0704 σ2 = [(0.226 - 0.0704)2 + (0.187 - 0.0704)2 + (0.113 - 0.0704)2 + (-0.198 - 0.0704)2 + (0.024 - 0.0704)2]/(5 - 1) = 0.028453

One year ago, you bought a stock for $36.48 a share. You received a dividend of $1.62 per share last month and sold the stock today for $41.18 a share. What is the capital gains yield on this investment?

Capital gains yield = ($41.18 - $36.48)/$36.48 = 12.88 percent

Suppose a stock had an initial price of $74 per share, paid a dividend of $0.80 per share during the year, and had an ending share price of $77. What was the capital gains yield?

Capital gains yield = ($77 - $74)/$74 = 4.05 percent

Cox Footwear pays a constant annual dividend. Last year, the dividend yield was 2.5 percent when the stock was selling for $26 a share. What is the current price of the stock if the current dividend yield is 3.1 percent?

D = 0.025 × $26 = $0.65 P0 = $0.65/0.031 = $20.97 dividend yield= stock price/dividend

The Bermuda Triangle Store pays a constant dividend. Last year, the dividend yield was 5.4 percent when the stock was selling for $15 a share. What must the stock price be today if the market currently requires a 3.8 percent dividend yield on this stock?

D = 0.054 × $15 = $0.81 P0 = $0.81/0.038 = $21.32

Rocky Top pays a constant annual dividend. One year ago, when you purchased shares of that stock at $12 a share, the dividend yield was 2 percent. Over this past year, the inflation rate has been 2.6 percent. Today, the required return on this stock is 9 percent and you just sold all of your shares. What is your total nominal return on this investment? Round your answer to the nearest whole percentage.

Dividend = 0.02 × $12 = $0.24 P0 = $0.24/0.09 = $2.67 Nominal return = ($2.67 - $12 + $0.24)/$12 = -75.78 percent just like total return in this case

Which one of the following is the hypothesis that securities markets are efficient?

Efficient Markets hypothesis

The common stock of Hillshire Farms has yielded 16.3 percent, 7.2 percent, 11.8 percent, -3.6 percent, and 9.7 percent over the past five years, respectively. What is the geometric average return?

Geometric average return = (1.163 × 1.072 × 1.118 × 0.964 × 1.097)1/5 - 1 = 8.07 percent

A stock has produced returns of 16.6 percent, 3.4 percent, 11.7 percent, and -9.2 percent over the past four years, respectively. What is the geometric average return?

Geometric average return = (1.166 × 1.034 × 1.117 × 0.908)1/4 - 1 = 5.16 percent

Sarah earned a 2.9 percent real rate of return on her investments for the past year. During that time, the risk-free rate was 4.1 percent and the inflation rate was 3.6 percent. What was her nominal rate of return?

Nominal rate = (1.029 × 1.036) - 1 = 6.60 percent does not account for inflation

Assume large-company stocks returned 12.8 percent on average over the past 75 years. The risk premium on these stocks was 7.9 percent and the inflation rate was 3.6 percent. What was the average nominal risk-free rate of return for those 75 years?

Nominal risk-free rate = 12.8 percent - 7.9 percent = 4.9 percent

One year ago, Peyton purchased 3,600 shares of Broncos stock for $101,124. Today, he sold those shares for $26.60 a share. What is the total return on this investment if the dividend yield is 1.9 percent?

Purchase price = $101,124/3,600 shares = $28.09 a share Total return = [($26.60 - $28.09)/$28.09] + 0.019 = -3.40 percent Total return= cap gains yield+div yield

One year ago, Debra purchased 4,200 shares of KNF stock for $177,072. Today, she sold those shares for $48.50 a share. What is the capital gains yield on this investment if the dividend yield is 4.1 percent?

Purchase price = $177,072/4,200 shares = $42.16 a share Capital gains yield = ($48.50 - $42.16)/$42.16 = 15.04 percent

One year ago, LaTresa purchased 600 shares of Outland Co. stock for $3,600. The stock does not pay any regular dividends but it did pay a special dividend of $0.30 a share last week. This morning, she sold her shares for $7.25 a share. What was the total return on this investment?

Purchase price = $3,600/600 shares = $6 a share Total return = ($7.25 - $6 + $0.30)/$6 = 25.83 percent for special dividends just add to EQ

Which one of the following is the most apt to have the largest risk premium in the future based on the historical record for 1926-2011?

Small-company stocks

Which one of the following is the positive square root of the variance?

Standard deviation

Which one of the following statements is correct?

The higher the expected rate of return, the wider the distribution of returns.

According to the efficient markets hypothesis, professional investors will earn:

a dollar return equal to the value paid for an investment.

Over the period of 1926-2011:

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

The lower the standard deviation of returns on a security, the _____ the expected rate of return and the _____ the risk.

lower; lower

Over the period of 1926-2011, which one of the following investment classes had the highest volatility of returns?

small company stocks

The historical returns on large-company stocks, as reported by Ibbotson and Sinquefield and reported in your textbook, are based on the:

stocks of the 500 companies included in the S&P 500 index.

A stock has an average return of 19.2 percent and a standard deviation of 10.7 percent. In any one given year, you have a 95 percent chance that you will not lose more than _____ percent nor earn more than ____ percent if you invest in this security.

-2.2; 40.6 95 percent probability range = 0.192 ± (2 × 0.107) = -2.2 percent to 40.6 percent

What was the average annual risk premium on small-company stocks for the period 1926-2011?

12.9 percent

What is the probability associated with a return that lies in the upper tail when the mean plus two standard deviations is graphed?

2.5%

The variance is the average squared difference between which of the following?

Actual return- Avg. Return

Home Grown Tomatoes stock returned 28.7 percent, 2.6 percent, 13.1 percent, 12.2, and 11.8 percent over the past five years, respectively. What is the arithmetic average return for this period?

Arithmetic average = (0.287 + 0.026 + 0.131 + 0.122 + 0.118)/5 = 13.68 percent

Over the past five years, a stock returned 8.3 percent, -32.5 percent, -2.2 percent, 46.9 percent, and 11.8 percent, respectively. What is the variance of these returns?

Average return = (0.083 - 0.325 - 0.022 + 0.469 + 0.118)/5 = 0.0646 σ2 = [(0.083 - 0.0646)2 + (-0.325 - 0.0646)2 + (-0.022 - 0.0646)2 + (0.469 - 0.0646)2 + (0.118 - 0.0646)2]/(5 - 1) = 0.081504 Subtract avg and square, sum, and then divided by (n-1)

A security produced returns of 12 percent, -11 percent, -2 percent, 15 percent, and 9 percent over the past five years, respectively. Based on these five years, what is the probability that an investor in this stock will lose more than 17.06 percent in any one given year?

Average return = (0.12 - 0.11 - 0.02 + 0.15 + 0.09)/5 = 0.046 σ2 = [(0.12 - 0.046)2 + (-0.11 - 0.046)2 + (-0.02 - 0.046)2 + (0.15 - 0.046)2 + (0.09 - 0.046)2]/(5 - 1) = 0.01173 σ = √0.01173 = 0.108305 Lower end of 95 percent probability range = 0.046 - (2 × 0.108305) = -17.06 percent Probability of losing more than 17.06 percent = (1 - 0.95)/2 = 2.5 percent

Over the past six years, a stock had annual returns of 14 percent, -3 percent, 8 percent, 21 percent, -16 percent, and 4 percent, respectively. What is the standard deviation of these returns?

Average return = (0.14 - 0.03 + 0.08 + 0.21 - 0.16 + 0.04)/6 = 0.046667 σ2 = [(0.14 - 0.046667)2 + (-0.03 - 0.046667)2 + (0.08 - 0.046667)2 + (0.21 - 00.046667)2 + (-0.16 - 0.046667)2 + (0.04 - 0.046667)2]/(6 - 1) = 0.017027 σ = √0.017027 = 13.05 percent

Over the past four years, a stock produced returns of 15 percent, 6 percent, 11 percent, and 22 percent, respectively. Based on these four years, what range of returns would you expect to see 95 percent of the time?

Average return = (0.15 + 0.06 + 0.11 + 0.22)/4 = 0.135 σ2 = [(0.15 - 0.135)2 + (0.06 - 0.135)2 + (0.11 - 0.135)2 + (0.22 - 00.135)2]/(4 - 1) = 0.004567 σ = √0.004567 = 0.067577 95 percent probability range = 0.135 ± (2 × 0.067577) Range of returns = -0.02 percent to 27.02 percent

Five years ago, you purchased 600 shares of stock. The annual returns have been 7.2 percent, -19.4 percent, 3.8 percent, 14.2 percent, and 27.9 percent, respectively. What is the variance of these returns?

Average return = (0.226 + 0.187 + 0.113 - 0.198 + 0.024)/5 = 0.0704 σ2 = [(0.226 - 0.0704)2 + (0.187 - 0.0704)2 + (0.113 - 0.0704)2 + (-0.198 - 0.0704)2 + (0.024 - 0.0704)2]/(5 - 1) = 0.028453

A stock has returns for five years of 23 percent, -17 percent, 8 percent, 22 percent, and 3 percent, respectively. The stock has an average return of ______ percent and a standard deviation of _____ percent.

Average return = (0.23 - 0.17 + 0.08 + 0.22 + 0.03)/5 = 0.078 σ2 = [(0.23 - 0.078)2 + (-0.17 - 0.078)2 + (0.08 - 0.078)2 + (0.22 - 00.078)2 + (0.03 - 00.078)2]/(5 - 1) = 0.026770 σ = √0.026770 = 16.36 percent

over the past four years, a stock produced returns of 23 percent, -39 percent, 4 percent, and 16 percent, respectively. Based on these four years, what range of returns would you expect to see 99 percent of the time?

Average return = (0.23 - 0.39 + 0.04 + 0.16)/4 = 0.01 σ2 = [(0.23 - 0.01)2 + (-0.3 - 0.01)2 + (0.04 - 0.01)2 + (0.16 - 0.01)2]/(4 - 1) = 0.077267 σ = √0.077267 = 0.277969 99 percent probability range = 0.01 ± (3 × 0.277969) Range of returns = -82.39 percent to 84.39 percent

Kelly decided to accept the risk and purchased a high growth stock. Her returns for the past five years are 48 percent, 39 percent, -56 percent, 61 percent, and -24 percent, respectively. What is the standard deviation of these returns?

Average return = (0.48 + 0.39 - 0.56 + 0.61 - 0.24)/5 = 0.136 σ2 = [(0.48 - 0.136)2 + (0.39 - 0.136)2 + (-0.56 - 0.136)2 + (0.61 - 00.136)2 + (-0.24 - 0.136)2]/(5 - 1) = 0.258330 σ = √0.258330 = 50.83 percent

A stock produced returns of 19 percent, 27 percent, and -38 percent over three of the past four years, respectively. The arithmetic average for the past four years is 7 percent. What is the standard deviation of the stock's returns for the four-year period?

Average return = 0.07 = (0.19 + 0.27 - 0.38 + x)/4 x = 0.20 σ2 = [(0.19 - 0.07)2 + (0.27 - 0.07)2 + (-0.38 - 0.07)2 + (0.20 - 0.07)2]/(4 - 1) = 0.091267 σ = √0.091267 = 30.21 percent

A stock produced returns of 16 percent, 9 percent, and 21 percent over three of the past four years, respectively. The arithmetic average for the past four years is 10 percent. What is the standard deviation of the stock's returns for the four-year period?

Average return = 0.10 = (0.16 + 0.09 + 0.21 + x)/4 x = -0.06 σ2 = [(0.16 - 0.10)2 + (0.09 - 0.10)2 + (0.21 - 0.10)2 + (-0.06 - 0.10)2]/(4 - 1) = 0.0138 σ = √0.0138 = 11.75 percent

Suppose you bought a 6 percent coupon bond one year ago for $929. The bond sells today for $933. The face value is $1,000. If the inflation rate last year was 4.3 percent, what was your total real rate of return on this investment?

Nominal return = ($933 - $929 + $60)/$929 = 0.068891 Real rate = (1.068891/1.043) - 1 = 2.48 percent

You expect the inflation rate to be 3.8 percent and the U.S. Treasury bill yield to be 3.9 percent for the next year. The risk premium on small-company stocks is 12.6 percent. What nominal rate of return do you expect to earn on small-company stocks next year?

Nominal return on small-company stocks = 3.9 percent + 12.6 percent = 16.50 percent add T-bill return to small company stock bc the expected+what you will earn

Last year, Paul invested $38,000 in Oil Town stock, $11,000 in long-term government bonds, and $8,000 in U.S. Treasury bills. Over the course of the year, he earned returns of 12.1 percent, 7.2 percent, and 4.1 percent, respectively. What was the nominal risk premium on Oil Town's stock for the year?

Nominal risk premium = 12.1 percent - 4.1 percent = 8.0 percent subtract the return of the T-Bill to get nominal PREMIUM

Hercules Movers pays a constant annual dividend of $1.75 per share on its stock. Last year at this time, the market rate of return on this stock was 14.8 percent. Today, the market rate has fallen to 11.2 percent. What would your capital gains yield have been if you had purchased this stock one year ago and then sold the stock today?

P-1 = $1.75/0.148 = $11.8243 P0 = $1.75/0.112 = $15.6350 Capital gains yield = ($15.6250 - $11.8243)/$11.8243 = 32.14 percent

You purchased a zero coupon bond one year ago for $291.22. The market interest rate is now 8.75 percent. If the bond had 16 years to maturity when you originally purchased it, what was your total return for the past year if the face value of the bond is $1,000?

PV = $1,000/[1 + (0.0875/2)]30 = $276.76 Total return = ($276.76 - $291.22)/$291.22 = -4.97 percent coupon bonds are always compounded semiannually

Last year, Isaac earned 10.6 percent on her investments while U.S. Treasury bills yielded 3.8 percent and the inflation rate was 3.1 percent. What real rate of return did she earn on her investments last year?

Real return = (1.106/1.031) - 1 = 7.27 percent

You earned 26.3 percent on your investments for a time period when the risk-free rate was 3.8 percent and the inflation rate was 4.0 percent. What was your real rate of return for the period?

Real return = (1.263/1.040) - 1 = 21.44 percent

Which one of the following best describes an arithmetic average return?

Return earned in an AVERAGE year over a multi year period

Investors require a 4 percent return on risk-free investments. On a particular risky investment, investors require an excess return of 7 percent in addition to the risk-free rate of 4 percent. What is this excess return called?

Risk Premium

Which one of the following could cause the total return on an investment to be a NEGATIVE rate?

Stock prices that DECLINE over the investment period

One year ago, you purchased a 5 percent coupon bond with a face value of $1,000 when it was selling for 101.2 percent of par. Today, you sold this bond for 99.8 percent of par. What is your total dollar return on this investment?

Total dollar return = (0.998 × $1,000) - (1.012 × $1,000) + (0.05 × $1,000) = $36

One year ago, you purchased 500 shares of stock for $12 a share. The stock pays $0.22 a share in dividends each year. Today, you sold your shares for $28.30 a share. What is your total dollar return on this investment

Total dollar return = 500 × ($28.30 - $12 + $0.22) = $8,260

Which one of the following statements is true regarding the period 1926-2011?

U.S. Treasury bills had a positive average real rate of return.

The historical record for the period 1926-2011 shows that the annual nominal rate of return on:

U.S. Treasury bills have had a positive rate of return for every year in the period.

When, if ever, will the geometric average return exceed the arithmetic average return for a given set of returns?

never

If the financial markets are semistrong form efficient, then:

only individuals with private information have a marketplace advantage.

Which one of the following categories has the widest frequency distribution of returns for the period 1926-2011

small company stocks