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Wize University Introduction to Finance Textbook > Risk, Return & Portfolio Theory

Ex-Post Risk and Return

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Return on Investment

The total return on investment is made up of 2 components: the income yield and the capital gain yield.

Income Yield

Income yield represents the return earned on income generated through owning an asset. Here are some examples of incomes that an investor earns with different types of assets:
  • Buildings: Rent
  • Stocks: Dividends
  • Bonds: Coupons
Use the following formula to measure the Income Yield of an investment

Where:
CF = Cash flows received (coupons, dividends, rent, etc)
P0= Purchase price
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Capital Gain Yield
Capital gains and losses represent the changes to the market value of the asset. Use the following formula to compute the capital gain yield:


Where:
CF = Cash flows received (coupons, dividends, rent, etc)
P0 = Purchase price
P1 = Current price or Selling price

Holding Period Return (Total Return)
The total return is the sum of the income yield and the capital gain yield:

Periodic Average Return (Geometric Average)

  • The average return earned period period.
  • Considers thats returns compound periodically

Where:
TR = Total return
t = Length of holding period
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Example: Return on Investment

a) A share of ABC Inc. was selling for $32.16 one year ago. The stock paid an annual dividend of $3.45 during the year. Compute the total return on the stock if the current stock price is $37.74.






b) Steve purchased a bond of MPT Company for $985 three years ago. The bond paid a coupon of $2.52 per year. What is the annualized holding period return on the bond if its current market value is $989?

Practice: Return on Investment

You purchased stock in ABC Inc. for $31.44 two years ago and sell today for $43.56. The company issued annual dividends of $2 per share.

Compute the income yield, capital gain yield, holding period return and annualized holding period return.

Round your final answers to 2 decimal places and enter in % form.
Extra Practice
You made an investment in your 401k account of $5,000 in a mutual fund that pays quarterly dividends. The price of each unit the day you made the investment is $100. The following year you invested another $7,000 in your 401k account at a price of $35 per unit. How much would you have in your account two years after your initial investment if you know that the annual income yield of the mutual fund is 9% and a mutual fund unit is trading at $80 today?
You purchased a stock for $34 three years ago. The price of the stock increased by $1.88 in the first year, then decreased by $2.89 in the second year, and today is trading at $43.90.
You received a dividend of $0.15 in year 1, $0.20 in year 2 and $0.25 in year 3.
What was your income yield in the third year?
You purchased a stock for $34 three years ago. The price of the stock increased by $1.88 in the first year, then decreased by $2.89 in the second year, and today is trading at $43.90.
You received a dividend of $0.15 in year 1, $0.20 in year 2 and $0.25 in year 3.
What was your return in the second year?
Karla bought shares of ABC Company for $88.22 two years ago. The stock paid quarterly dividends of $0.48. What is her annualized total return if she can sell the stock today for $94.55?
Karla bought shares of ABC Company for $88.22 two years ago. The stock paid quarterly dividends of $0.48. What is the total return if she can sell the stock today for $94.55?
Karla bought shares of ABC Company for $88.22 two years ago. The stock paid quarterly dividends of $0.48. What is the capital gain yield if she can sell the stock today for $94.55?
Karla bought shares of ABC Company for $88.22 two years ago. The stock paid quarterly dividends of $0.48. What is the income yield if she can sell the stock today for $94.55?
Which of the following is a true statement?
Use the following two statements to answer this question:
I. Risk is the possibility of losing money in your investments.
II. Ex post returns are future returns while ex ante returns are actual returns.
Suppose you have earned a total return of 12% on the 400 shares of ABC Company that you purchased for $7,500 last year. ABC has paid out five equal dividends over this period. What is the amount of the dividend if the current price per share of ABC stock is $10.00?
What will be the selling price in one year of a stock that is currently selling for $10.00, expected to pay a $2.00 dividend, and have a capital gain of 10%.
Meghan paid $53.44 for one share of SOS Company one year ago. The stock paid twelve monthly dividends of $0.10 each during the year, and is selling for $34.66 now. What are the income yield and capital gain yield for SOS over the past year?
Sean bought shares in PMP Company for $27.89 three years ago. Since then, he collected three dividends of $2.40 and today the stock is trading at $33.41. What is his holding period return?
What is the holding period return on a bond that was purchased 4 years ago for $890.44 and sold today for $1,000. The bond has a coupon rate of 8% paid semi-annually and a face value of $1,000.
Cyrus bought a share of WIZE Company for $58.90 one year ago. The stock paid a semi-annual dividend of $1.80. What is the return on investment if the stock is selling for $64.40 today?
Cyrus bought a share of WIZE Company for $58.90 one year ago. The stock paid a semi-annual dividend of $1.80. What is the capital gain yield if the stock is selling for $64.40 today?
Cyrus bought a share of WIZE Company for $58.90 one year ago. The stock paid a semi-annual dividend of $1.80. What is the income yield if the stock is selling for $64.40 today?
What is the holding period return on a bond that was purchased 4 years ago for $890.44 and sold today for $1,000. The bond has a coupon rate of 8% paid semi-annually and a face value of $1,000.