Finance Chapter 3
Consider a portfolio of two securities: one share of Johnson and Johnson (JNJ) stock and a bond that pays $100 in one year. Suppose this portfolio is currently trading with a bid price of $141.65 and an ask price of $142.25, and the bond is trading with a bid price of $91.75 and an ask price of $91.95. In this case, what is the no-arbitrage price range for JNJ stock?
According to the law of one price, the price that portfolio of securities is trading is equal to the sum of the price of securities within the portfolio. If the portfolio, composed of a bond and JNJ stock is currently trading with a bid price of $141.65 and an ask price of $142.25, and the bond is trading at a bid price of $91.75 and an ask price of $91.95, then the no-arbitrage price of the stock should be between $(141.65 - 91.95) and $(142.25 - 91.75) or between $49.70 and $50.50. At any price below $49.90 or above $50.30 an arbitrage opportunity would exist. For example, if the stock were currently trading at $49, an investor could purchase the stock and the bond for $49 + $91.95 = $140.95 and then immediately sell the portfolio for $141.65 and have an arbitrage of $141.65 - 140.95 = $0.70. If the price of the stock was $50.60, then an investor could purchase the portfolio for $142.25 and sell the bond and stock individually for $91.75 and $50.60 respectively. The investor would gain an arbitrage of $91.75 + $50.60 - $142.25 = $0.10.
b. Suppose that if you receive the stock bonus, you are required to hold it for at least one year. What can you say about the value of the stock bonus now? What will your decision depend on?
Because you could buy the stock today for $6,300 if you wanted to, the value of the stock bonus cannot be more than $6,300. But if you are not allowed to sell the company's stock for the next year, its value to you could be less than $6,300. Its value will depend on what you expect the stock to be worth in one year, as well as how you feel about the risk involved. You might decide that it is better to take the $5,000 in cash then wait for the uncertain value of the stock in one year.
b. How can your firm turn this NPV into cash today?
The firm can borrow $18.18 million today, and pay it back with 10% interest using the $20 million it will receive from the government (18.18 × 1.10 = 20). The firm can use $10 million of the 18.18 million to cover its costs today and save $4.55 million in the bank to earn 10% interest to cover its cost of 4.55 × 1.10 = $5 million next year. This leaves 18.18 - 10 - 4.55 = $3.63 million in cash for the firm today.
Throughout the 1990s, interest rates in Japan were lower than interest rates in the United States. As a result, many Japanese investors were tempted to borrow in Japan and invest the proceeds in the United States. Explain why this strategy does not represent an arbitrage opportunity.
There is exchange rate risk. Engaging in such transactions may incur a loss if the value of the dollar falls relative to the yen. Because a profit is not guaranteed, this strategy is not an arbitrage opportunity.
Suppose the risk-free interest rate is 4%. a. Having $200 today is equivalent to having what amount in one year? b. Having $200 in one year is equivalent to having what amount today? c. Which would you prefer, $200 today or $200 in one year? Does your answer depend on when you need the money? Why or why not?
a. Having $200 today is equivalent to having 200 × 1.04 = $208 in one year. b. Having $200 in one year is equivalent to having 200 / 1.04 = $192.31 today. c. Because money today is worth more than money in the future, $200 today is preferred to $200 in one year. This answer is correct even if you don't need the money today, because by investing the $200 you receive today at the current interest rate, you will have more than $200 in one year.
Suppose your employer offers you a choice between a $5000 bonus and 100 shares of the company stock. Whichever one you choose will be awarded today. The stock is currently trading for $63 per share. a. Suppose that if you receive the stock bonus, you are free to trade it. Which form of the bonus should you choose? What is its value?
a. Stock bonus = 100 × $63 = $6,300 Cash bonus = $5,000 Since you can sell (or buy) the stock for $6,300 in cash today, its value is $6,300 which is better than the cash bonus.
Suppose Bank One offers a risk-free interest rate of 5.5% on both savings and loans, and Bank Enn offers a risk-free interest rate of 6% on both savings and loans. a. What arbitrage opportunity is available? b. Which bank would experience a surge in the demand for loans? Which bank would receive a surge in deposits? c. What would you expect to happen to the interest rates the two banks are offering?
a. Take a loan from Bank One at 5.5% and save the money in Bank Enn at 6%. b. Bank One would experience a surge in the demand for loans, while Bank Enn would receive a surge in deposits. c. Bank One would increase the interest rate, and/or Bank Enn would decrease its rate.
