Question $1$

Currency carry trade involves buying a high$-$yielding currency and funding it with a low$-$yielding currency, without any hedging. Generally, Japanese Yen and Swiss Franc have been popular funding currencies for the carry trade $($due to the low interest rate in these countries$),$ while British Pound and Australian Dollar have been popular investment currencies due to their high interest rates. Say currently, $1$ Australian Dollar $($AUD$)$ is equivalent to $84\mathrm{.}25$ Japanese Yen $($JPY$),$ the interest rate in Australia is $0\mathrm{.}1\%,$ and the interest rate in Japan is $-0\mathrm{.}1\%.$ You decide to borrow JPY and invest in AUD for a year, and consider transaction costs to be nil.

a$)$ What must be the expected exchange rate $($AUD$/$JPY$)$ for the carry trade to be profitable?

b$)$ Half a year after you have initialized your carry trade, Australia announces that they will cut interest rates. How are these rate cuts going to hamper$/$benefit your trading strategy?

c$)$ Instead of investing in AUD for a year and exchanging it back to yen at the spot rate at that time, you venture into a forward deal with the forward exchange rate being $83$ AUD$/$JPY $($assume that this forward exchange rate is the fair$/$correct price$).$ Comment on the riskiness of the Japanese Bond Market.

d$)$ Explain when the currency carry trade strategy fails to be profitable, and should investors go for such strategies during times of volatility?