Question

Suppose the Kenyan shilling (KS) is currently traded at KS 1.4/$ and the Ethiopian Birr (EB) is traded at EB 1.39/$. Ignoring transaction costs:

A. Determine the KS/EB exchange rate consistent with these direct quotations.
A. KS 1.01/EB
B. KS 1.05/EB
C. KS 1.39/EB
D. KS 1.4/EB
B. Suppose the KS/EB exchange rate in the market was at KS 1.05/EB. Is there any arbitrage opportunity?
A. Yes, a profitable arbitrage opportunity exists.
B. No, there is no arbitrage opportunity.
C. It is uncertain; more information is needed.
D. The question is irrelevant to arbitrage.

C. How would you take advantage of any arbitrage situation?
A. Sell KS for EB at the market rate.
B. Buy KS at the market rate and sell EB at the direct quotation rate.
C. Buy EB at the market rate and sell KS at the direct quotation rate.
D. Hold the current positions without taking any action.


D. What is your profit?

A. KS 0.35/EB
B. KS 0.05/EB
C. The profit cannot be determined from the information provided.
D. There is no profit in the arbitrage situation.

Answer 1

The KS/EB exchange rate consistent with the given direct quotations is approximately KS 1.01/EB. Given a market rate of KS 1.05/EB, an arbitrage opportunity exists. Traders can buy EB at the market rate, exchange it for KS at the calculated rate, resulting in a profit of approximately KS 0.04/EB.Thus option a is the correct option.

Step-by-step explanation:

In order to determine the KS/EB exchange rate consistent with the given direct quotations, we need to find the cross rate between KS and EB. The cross rate is calculated by multiplying the exchange rates of the two currencies with respect to a common currency, which in this case is the US dollar (USD). The formula for the cross rate (CR) is given by:

[ CR = frac{Exchange Rate of Currency 1}{ExchangeRate of USD} times frac{Exchange Rate of USD}{Exchange Rate of Currency 2} ]

For KS/EB, the calculation is as follows:

[ CR_{KS/EB} = frac{1.4}{1} imes frac{1}{1.39} ]

[ CR_{KS/EB} approx 1.01 ]

Therefore, the KS/EB exchange rate consistent with the given direct quotations is approximately KS 1.01/EB.

Now, addressing the second part of the question, if the market exchange rate is KS 1.05/EB and the calculated rate is KS 1.01/EB, an arbitrage opportunity exists. Traders can buy KS at the market rate of KS 1.05/EB, exchange it for EB at the calculated rate of KS 1.01/EB, and make a risk-free profit.

Taking advantage of this arbitrage situation involves choosing option C: Buy EB at the market rate (KS 1.05/EB) and sell KS at the direct quotation rate (KS 1.4/EB). This strategy exploits the discrepancy in exchange rates.

As for the profit, it is the difference between the market and calculated rates:

[ Profit = Market Rate - Calculated Rate ]

[ Profit = 1.05 - 1.01]

[ Profit approx 0.04 ]

Therefore, the profit in this arbitrage situation is approximately KS 0.04/EB.

Therefore option a is the correct option.