Macroeconomics 20th Edition by Campbell McConnell ,Stanley Brue ,Sean Flynn

Exercise 22

Suppose initially that two assets, A and B, will each make a single guaranteed payment of $100 in 1 year. But asset A has a current price of $80 while asset B has a current price of $90. LO3
a. What are the rates of return of assets A and B at their current prices? Given these rates of return, which asset should investors buy and which asset should they sell?
b. Assume that arbitrage continues until A and B have the same expected rate of return. When arbitrage ends, will A and B have the same price?
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?