FIN 3000 CH 12 HW

Calculate the geometric average return for the returns in the following table: S&P Returns 10.25 37.80 45.07 (8.10 ) (20.16) 15.11% 12.97% 20.16% 6.25% 10.09%

10.09%

Returns Year X Y 1 12 % 18 % 2 26 27 3 12 10 4 - 19 - 24 5 10 18 Using the returns shown above, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y.

8.20% 9.80% 0.027220 0.039320 16.50%. 19.83%

Suppose a stock had an initial price of $64 per share, paid a dividend of $1.35 per share during the year, and had an ending share price of $67. Compute the percentage total return. 8.44% 7.22% 6.80% 7.90% 9.92%

=(67-64+1.35)/64 =6.80%

A stock had returns of 19 percent, 14 percent, 12 percent, -4 percent, 10 percent, and 4 percent over the last six years. What is the arithmetic return for the stock? What is the geometric return for the stock? Arithmetic Return = 10.84%, Geometric Return = 10.21% Arithmetic Return = 9.17%, Geometric Return = 8.91% Arithmetic Return = 11.14%, Geometric Return = 10.86% Arithmetic Return = 9.83%, Geometric Return = 9.56% Arithmetic Return = 10.34%, Geometric Return = 9.87%

AAR=[19+14+12(-4)+10+4]/6 AAR=9.17% GAR== [(1+0.19) * (1+0.14) * (1+0.12) * (1+ (-0.04)) * (1+0.1) * (1+0.04)] 1/6 − 1 GAR= 8.91% Arithmetic Return = 9.17%, Geometric Return = 8.91%

A stock has had returns of 13 percent, 20 percent, 22 percent, −11 percent, 27 percent, and −5 percent over the last six years. What are the arithmetic and geometric average returns for the stock?

Arithmetic Return = 11.00% Geometric Return = 10.05%

Which of the following statements are true based on the historical record for 1926-2016? Risk and potential reward are inversely related. The normal distribution curve for large-company stocks is narrower than the curve for small-company stocks. Risk-free securities produce a positive real rate of return each year. Returns are more predictable over the short term than they are over the long term. Bonds are generally a safer, or less risky, investment than are stocks.

Bonds are generally a safer, or less risky, investment than are stocks.

Which one of the following correctly describes the dividend yield? This year's annual dividend divided by next year's expected stock price This year's annual dividend divided by today's stock price The increase in next year's dividend over this year's dividend divided by this year's dividend Next year's annual dividend divided by this year's annual dividend Next year's annual dividend divided by today's stock price

Next year's annual dividend divided by today's stock price

Which one of the following categories of securities had the highest average annual return for the period 1926-2016? Small-company stocks Long-term corporate bonds Large-company stocks Long-term government bonds U.S. Treasury bills

Small-company stocks

Which one of the following best defines the variance of an investment's annual returns over a number of years? The difference between the arithmetic average and the geometric average return for the period The average squared difference between the arithmetic and the geometric average annual returns The squared summation of the differences between the actual returns and the average geometric return The average squared difference between the actual returns and the arithmetic average return The average difference between the annual returns and the average return for the period

The average squared difference between the actual returns and the arithmetic average return

Stacy purchased a stock last year and sold it today for $4 a share more than her purchase price. She received a total of $1.15 per share in dividends. Which one of the following statements is correct in relation to this investment? The total dollar return per share is $2.85. The capital gain would have been less had Stacy not received the dividends. The dividend yield is greater than the capital gains yield. The capital gains yield is positive. The dividend yield is expressed as a percentage of the par value.

The capital gains yield is positive.

Suppose a stock had an initial price of $55 per share, paid a dividend of $1.90 per share during the year, and had an ending share price of $61. What was the dividend yield and the capital gains yield? Dividend Yield = 2.91%; Capital Gains Yield = 8.42% Dividend Yield = 3.45%; Capital Gains Yield = 9.46% Dividend Yield = 3.45%; Capital Gains Yield = 7.66% Dividend Yield = 2.91%; Capital Gains Yield = 10.91% Dividend Yield = 3.45%; Capital Gains Yield = 10.91%

The percentage total return (R) = [$1.90 + ($61-55)]/$55 = 14.36% The dividend yield = $1.90/$55 = 3.45% The capital gains yield = ($61-55)/$55 = 10.91%

Suppose a stock had an initial price of $90 per share, paid a dividend of $1.90 per share during the year, and had an ending share price of $89. Compute the percentage total return. 0.88% 1.00% 1.78% 2.11% 1.45%

Total Percentage Return = (Ending Price - Initial Price + Dividend)/Initial Price Total percentage return = ($89 - $90 + $1.90)/$90 Total percentage return = 1.00%

Suppose a stock had an initial price of $58 per share, paid a dividend of $1.90 per share during the year, and had an ending share price of $49. Compute the percentage total return, dividend yield, and capital gains yield.

Total Return -12.24% Dividend Yield 3.28% Capital Gain Yield -15.52%

Standard deviation is a measure of which one of the following? Risk premium Real returns Volatility Average rate of return Probability

Volatility

The geometric average return answers the question, What was your return in an average year over a particular period? What is the best method to use to calculate your average return? What was your average compounded return per year over a particular period? What was your average return per year over a particular period? What is the least amount of returns need to calculate an average?

What was your average compounded return per year over a particular period?

Suppose you bought a bond with an annual coupon rate of 7 percent one year ago for $860. The bond sells for $890 today. a. Assuming a $1,000 face value, what was your total dollar return on this investment over the past year? b. What was your total nominal rate of return on this investment over the past year? c. If the inflation rate last year was 1.5 percent, what was your total real rate of return on this investment?

a) =(1000x7%)+(890-860) = 70+30 = $100 b) =100/860 = 11.63% c) = 9.98%

Suppose you bought a bond with an annual coupon of 7 percent one year ago for $1,010. The bond sells for $985 today. a. Assuming a $1,000 face value, what was your total dollar return on this investment over the past year? b. What was your total nominal rate of return on this investment over the past year? c. If the inflation rate last year was 3 percent, what was your total real rate of return on this investment?

a) TDR=985-1010+70 TDR= $45 b) NR=(985-1,010+70)/(1,010) NR=4.46% c)[(1+0.0446)/(1+0.03)]-1 = 1.41%

Refer to Table 12.2. a. What was the average annual return on large-company stock from 1926 through 2016 in nominal terms? b. What was the average annual return on large-company stock from 1926 through 2016 in real terms?

a)Nominal return on large company stock=12.00% b)Approximate real return Real return on large company stock=12%-3% =8.74%

A stock has had returns of 8 percent, 26 percent, 14 percent, −17 percent, 31 percent, and −1 percent over the last six years. What are the arithmetic and geometric average returns for the stock?

arithmetic return=Total return/Total time period =(8+26+14-17+31-1)/6 =10.167% geometric average return=[(1+rate1)(1+rate2).......(1+rate6)]^(1/6)-1 =[(1+0.08)(1+0.26)(1+0.14)(1-0.17)(1+0.31)(1-0.01)]^(1/6)-1 =8.92%

According to the video, short-run projected wealth levels calculated using geometric averages are probably ______________. pessimistic optimistic. erroneous. confusing. foolish.

pessimistic