Question

Suppose initially that two assets, A and B, will each make a single guaranteed payment of $200 in 1 year. But asset A has a current price of $160 while asset B has a current price of $180.

Instructions: Round your answers to 2 decimal places.

a. What are the rates of return of assets A and B at their current prices?

     Return on asset A =

     Return on asset B =

Given these rates of return, which asset should investors buy, and which asset should they sell?

     Buy asset: A or B and Sell asset: A or B.

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?

There is insufficient data to determine the prices.

Yes, they will have the same price.

No, they will have different prices.

Next, consider another pair of assets, C and D. Asset C will make a single payment of $300 in 1 year, while D will make a single payment of $400 in 1 year. Assume that the current price of C is $240 and that the current price of D is $360.

c. What are the rates of return of assets C and D at their current prices?

     Return on asset C =

     Return on asset D =

Given these rates of return, which asset should investors buy, and which asset should they sell?

     Buy asset: C or D and Sell asset: C or D.

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?

No, they will have different prices.

There is insufficient data to determine the prices.

Yes, they will 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?

Yes or No

In what situations will it also equalize prices?

When payoffs are the same.

Under no situation.

When payoffs are different.

Answer 1

(a) ROR on A = (payment - price / price)*100

= ((200-160)/160)*100 = 25%

ROR on B = ((200 -180)/180)*100 = 11.11%

Since the ROR on A is higher, buy A and sell B

(b)Yes, they will have the same price when arbitrage ends. Buying A increases A's price and selling B decreases B's price till they are equal.

(c) ROR on C = ((300-240)/240)*100 = 25

ROR on D = ((400-360)/360)*100 = 11.11%

Since the ROR on C is higher, buy C and sell D

(d) No, they will have different prices when arbitrage ends as the final payment is different. Thus, the price that equalizes their ROR will be different.

(e) No, equal ROR does not guarantee equal prices as seen in (d)

(f) It can only happen when the final payoffs are the same.