CH-7.3
Note: Bank One will notice a book imbalance (all the activity involves selling USD for JPY, selling
JPY for GBP, selling GBP for USD.) and will adjust quotes. Say:
S
JPY/USD,t
↓ (say, S
JPY/USD,t
= 93 JPY/USD).
S
USD/GBP,t
↓ (say, S
USD/GBP,t
= 1.56 USD/GBP).
S
JPY/GBP,t
↑ (say, S
JPY/GBP,t
= 145 JPY/GBP).
There is convergence between S
I
JPY,GBP,t
& S
JPY,GBP,t
:
S
I
JPY,GBP,t
↓ (= S
JPY,USD,t
↓ x S
USD/GBP,t
↓ ) ⇔ S
JPY,GBP,t
↑ ¶
Again, all the steps in the triangular arbitrage strategy should be done at the same time. Otherwise,
we’ll be facing risk and what we are doing should be considered pseudo-arbitrage.
It does not matter which currency you borrow (USD, GBP, JPY) in step (1). As long as the strategy
involves the step Sell JPY/Buy GBP (following the direction of the arrows in the triangle above!),
you should get the same profit as a %.
3. Covered Interest Arbitrage (Four instruments -two goods per market-, two markets)
Open the third section of the WSJ: Brazilian bonds yield 10% and Japanese bonds 1%.
Q: Why wouldn't capital flow to Brazil from Japan?
A: FX risk: Once JPY are exchanged for BRL (Brazilian reals), there is no guarantee that the BRL
will not depreciate against the JPY. The only way to avoid this FX risk is to be covered with a forward
FX contract.
Intuition: Suppose we have the following data:
= 1% for 1 year (T=1 year)
= 10% for 1 year (T=1 year)
= .025 BRL/JPY
We construct the following strategy, called carry trade, to “profit” from the interest rate differential:
Today, at time t=0, we do the following (1)-(3) transactions:
(1) Borrow JPY 1,000 at 1% for 1 year. (At T=1 year, we will need to repay JPY 1,010.)
(2) Convert to BRL at = .025 BRL/JPY. Get BRL 25.
(3) Deposit BRL 25 at 10% for 1 year. (At T=1 year, we will receive BRL 27.50.)
Now, we wait 1 year. At time T=1 year, we do the final step:
(4) Exchange BRL 27.50 for JPY at S
t+T
.
Problem with this carry trade: Today, we do not know S
t+T=1-year
. Note:
- If = .022 BRL/JPY, we will receive JPY 1250, for a profit of JPY 240.
- If = .025 BRL/JPY, we will receive JPY 1100, for a profit of JPY 90.
- If = .027 BRL/JPY, we will receive JPY 1019, for a profit of JPY 9.
- If = .030 BRL/JPY, we will receive JPY 916, for a profit of JPY -74.
We are facing FX risk. That is, (1)-(4) is not an arbitrage strategy.