This question will compare two different arbitrage situations. Recall that arbitrage should equalize rates of return. We want to explore what this implies about equalizing prices. In the first situation, two assets, $A$ and $B$, will each make a single guaranteed payment of $100$dollars in 1 year. But asset $A$ has a current price of $80$dollars while asset $B$ has a current price of 90 dollars.
a. Which asset has the higher expected rate of return at current prices? Given their rates of return, which asset should investors be buying and which asset should they be selling?
b. Assume that arbitrage continues until A and B have the same expected rate of return. When arbitrage ceases,
will $\mathrm{A}$ and $\mathrm{B}$ have the same price?
Next, consider another pair of assets, $\mathbf{C}$ and $\mathbf{D}$. Asset $\mathbf{C}$ will make a single payment of $150$dollars in one year while D will make a single payment of $200$dollars in one year. Assume that the current price of $\mathrm{C}$ is $120$dollars and that the current price of $\mathrm{D}$ is $180$dollars
c. Which asset has the higher expected rate of return at current prices? Given their rates of return, which asset should investors be buying and which asset should they be selling?
d. Assume that arbitrage continues until $\mathrm{C}$ and $\mathrm{D}$ have the same expected rate of return. When arbitrage ceases, will $\mathrm{C}$ and $\mathrm{D}$ 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 also equalize prices?