Tsumugi, a foreign exchange trader at P$.$J$.$ Worgani Investment and Assets Management Corporation, is exploring interest arbitrage possibilities. She wants to borrow $10,000,000$ or its equivalent in an interest arbitrage between US dollar and Japanese Yen. She has to state his arbitrage proceeds in Yen in the end of any trade. She faced the following exchange rate and interest rates quotes. Spot rate $1-$Month forward rate $1-$Month US dollar interest rate $1-$Month China Yuan yen interest rate $143\mathrm{.}960/$$ $143\mathrm{.}586/$$ $5\mathrm{.}33\%$ per annum $1\mathrm{.}50\%$ per annum

Based on the scenario mentioned in the previous page, answer the following questions:

$($a$)$ Calculate and show the profit potential of covered interest arbitrage. Explain the steps involved in the arbitrage activity, with the help of carry$-$trade diagram as illustration.

$($b$)$ Assuming that Tsumigi$$s research associates, who have good reputation in predicting the future movements of exchange rates, predict that due to the brighter economic outlook of Japan in the following month, Yen spot rate will weaken to $150\mathrm{.}00/$$$.$ Show how Marianne could have uncovered interest arbitrage opportunity. Explain the steps involved in the arbitrage activity, with the help of carry$-$trade diagram as illustration.

$($c$)$ Based on your answers in Part $($a$)$ and $($b$)$ above, do you think Tsumugi should engage in covered or uncovered interest arbitrage? Justify your answer.