Carry Trade problem - is my Logic Correct?

[Rasec]

I can’t seem to understand why the return is 1.033 % on the JPY/ AUD currency rate!!! can you find a hole in my logic?

Carry Trade Problem:

Tokyo based baller enters into a carry trade position based on borrowing in yen and investing in one-year
australian dollar.

After one year, the all in return in JPY is?


JPY: 0.10% (1mon LIBOR); JPY/USD ; 81.30 (spot); 80.00 (1yr fwd)
AUD: 4.50% (1mon LIBOR); USD/AUD ; 1.0750 (spot); 1.0803 (1yr fwd)

Logic: the strategy requires to go long the high yield currency and short the low yield currency.

1) Borrow cheap currency (Yen)

2) Convert to investment currency at the spot exchange rate
-given the two currency pairs, we need to find either JPY/AUD or AUD/JPY. In this case, JPY/AUD
is 87.40 (1.0750 x 81.30).

JPY/AUD = 87.50 –> need to convert to AUD by taking the inverse, since we are investing in AUD
AUD/JPY = 0.01144

3) Invest investment currency at high risk-free rate.
- 0.01144 x (1+.0450) = 0.012

Wait. Patiently.

4) Convert investment currency (plus interest) to cheap currency at the (current) spot exchange rate
- calculate the 1 year spot

80 x 1.0803 = 86.42 * remember this is JPY/AUD, you have AUD and need to convert back to JPY, since we are
going from AUD to JPY we multiply.

86.42 x 0.012 = 1.033 AUD


Pay off cheap currency loan

1.033 - 0.10 = 3.23


Question:

I can’t see how there is a 3.3% return change. Based on implied fwd rates the (87 vs 86), the Yen is strengething
vs the australian dollar. If 1.033 is the curreny rate, how is 3.3% a return?

 

[afilippi]

you added 1 to 4.5% in order to calculate the gain, so once you get the 1.033 you have to subtract the 1 out again

 

[Rasec]

1.033 is the current exchange rate ( AUD/JPY). i’m not seeing how taking 1 from the fx rate is a return. This is just the price at time T+1.

 

[afilippi]

I think it’d be easier if you used a notional principal amount to figure out the return

 

[afilippi]

I think that’s where you’re getting confused..
Imagine borrowing 1,000,000 JPY and converting it to AUD
You’d get 11,441.97 AUD, invest at 4.50% and in one year you’d have 11,956.86. Convert that BACK to AUD and you get around 1,033,359.67 AUD. Pay the 0.10% interest rate on the 1,000,000 JPY which is 1,000 JPY that you can subtract from 1,033,359.67. This gives you 1,032,359.67. Now just use the HPR formula:
1,032,359 - 1,000,000 / 1,000,000 = 3.23%