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Chapter 17: Q5. (page 368)

Corporations often distribute profits to their shareholders in the form of dividends, which are quarterly payments sent to shareholders. Suppose that you have the chance to buy a share in a fashion company called Rogue Designs for \(35 and that the company will pay dividends of \)2 per year on that share. What is the annual percentage rate of return? Next, suppose that you and other investors could get a 12 percent per year rate of return on the stocks of other very similar fashion companies. If investors care only about rates of return, what should happen to the share price of Rogue Designs? (Hint: This is an arbitrage situation.)

Short Answer

Expert verified

The annual percentage rate of return is 12%.

If the investors care only about rates of return, the share price of Rogue Designs and the other very similar fashion companies will be the same.

Step by step solution

01

Step 1. Annual percentage rate of return

The annual percentage rate of return is the percentage gain or loss (relative to the buying price) over a given period of time, typically a year. The dividends of $2 per year are divided by the price of share $35 and multiplied by 100 to get the annual percentage return of 12%.

02

Step 2. Arbitrage

The other investor could also get a 12% per year rate of return on the stocks of other very similar fashion companies. The share price of Rogue Designs and the other fashion company will become equal. According to the concept of arbitrage, if the rate of returns on the shares of products simultaneously differs, the share price will change to equate the rate of returns.

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Most popular questions from this chapter

An investment has a 50 percent chance of generating a 10 percent return and a 50 percent chance of generating a 16 percent return. What is the investment’s average expected rate of return?

  1. 10 percent

  2. 11 percent

  3. 12 percent

  4. 13 percent

  5. 14 percent

  6. 15 percent

  7. 16 percent

Next, consider another pair of assets, C and D. Asset C will make a single payment of \(150 in one year while D will make a single payment of \)200 in one year. Assume that the current price of C is \(120 and that the current price of D is \)180.

c. What are the rates of return of assets C and D at their current prices? Given these rates of return, which asset should investors buy and which asset should they sell?

d. Assume that arbitrage continues until C and D have the same expected rate of return. When arbitrage ends, will C and D have the same price?

Compare your answers to questions a through d before answering question e.

e. We know that arbitrage will equalize rates of return. Does it also guarantee to equalize prices? In what situations will it equalize prices?

If an investment has 35 percent more non-diversifiable risk than the market portfolio, its beta will be:

  1. 35

  2. 1.35

  3. 0.35

The U.S. government issues longer-term bonds with horizons of up to 30 years. Why do 20-year bonds issued by the U.S. government have lower rates of return than 20-year bonds issued by corporations? And which do you think has the higher rate of return, longer-term U.S. government bonds or short-term U.S. government bonds? Explain.

What are mutual funds? What different types of mutual funds are there? And why do you think they are so popular with investors?
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