Chapter 10 Finance

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.

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%

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%

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

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%

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%

You bought a stock three months ago for $77.82 per share. The stock paid no dividends. The current share price is $82.09. What is the APR and EAR of your investment?

The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the initial price. This stock paid no dividend, so the return was: R = ($82.09 - 77.82) / $77.82 R = .0549, or 5.49% This is the return for three months, so the APR is: APR = 4(5.49%) APR = 21.95% And the EAR is: EAR = (1 + .0549)4 - 1 EAR = .2382, or 23.82%

You bought one of Rocky Mountain Manufacturing Co.'s 9 percent coupon bonds one year ago for $1,049.80. These bonds make annual payments and mature seven years from now. Suppose that you decide to sell your bonds today, when the required return on the bonds is 8.5 percent. If the inflation rate was 4.4 percent over the past year, what would be your total real return on investment?

To find the return on the coupon bond, we first need to find the price of the bond today. Since the bond has 7 years to maturity, the price today is: P1 = $90.00(PVIFA8.5%,7) + $1,000 / 1.0857 P1 = $1,025.59 You received the coupon payments on the bond, so the nominal return was: R = ($1,025.59 - 1,049.80 + 90.00) / $1,049.80 R = .0627, or 6.27% And using the Fisher equation to find the real return, we get: r = (1.0627 / 1.044) - 1 r = .0179, or 1.79%

You purchased a zero-coupon bond one year ago for $282.83. The market interest rate is now 7 percent. Assume semiannual compounding periods. If the bond had 19 years to maturity when you originally purchased it, what was your total return for the past year?

To find the return on the zero-coupon bond, we first need to find the price of the bond today. We need to remember that the price for zero-coupon bonds is calculated with semiannual periods. Since one year has elapsed, the bond now has 18 years to maturity, so the price today is: P1 = $1,000 / 1.03536 P1 = $289.83 There are no intermediate cash flows on a zero-coupon bond, so the return is the capital gain, or: R = ($289.83 - 282.83) / $282.83 R = .0248, or 2.48%

Suppose you bought a bond with an annual coupon rate of 7.8 percent one year ago for $901. The bond sells for $934 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 4.3 percent, what was your total real rate of return on this investment?

a. The total dollar return is the change in price plus the coupon payment, so: Total dollar return = $934 - 901 + 78 Total dollar return = $111 b. The nominal percentage return of the bond is: R = ($934 - 901 + 78) / $901 R = .1232, or 12.32% Notice here that we could have simply used the total dollar return of $111 in the numerator of this equation. c. Using the Fisher equation, the real return was: (1 + R) = (1 + r)(1 + h) r = (1.1232 / 1.043) - 1 r = .0769, or 7.69%