Trans-Atlantic Arbitrage

CHAPTER 6
QUESTIONS : 8,13,14,15

QUESTION 8

Akira Numata –UIA Japan

Assumptions | Value $ | Yen equivalent | Arbitrage funds | 5,000,000 | 593,000,000 | Spot Rate (¥/$) | 118.60 | | 180-days forward Rate | 117.80 | | Expected spot Rate | 118.00 | | 180-days U.S dollar interest rate | 4.80% | | 180-days Japanese Yen Interest Rate | 3.400% | |

Calculations
Calculating forward Rate (i= interest rate)
F180 sf/$ = S sf/$*1+ (isF*180/360)/ (i$*180/360) =118.60*1+ (0.034*180/360)/ 1+ (0.048*180/360) =118.60*1.017/1.024 =117.789 = 117.80

Difference in interest Rate i¥ - i$
=3.400% -4.800%
= -1.400%

Expected gain (loss) on the Spot Rate
Fsf =(S-F)/ (F)*(360/no.of days) = (118.60-118.00)/ (118.00)*(360/180) = 0.6/118.00*2*100 = 1.0169 =1.017%

UIA potential profit (loss)

Difference in interest rate | -1.400% | Expected gain (loss) on spot rate | 1.017% | UIA profit potential | -383% | | |

In accordance to the arbitrage rule of thumb, given the difference in the interest rate is greater than the expected change in spot rate, it is advisable that Akira Numata should borrow yen and invest in the higher yielding currency which is, in this case the U.S dollar. By doing so, she would be able to gain an uncovered investment arbitrage.

U.S Dollar interest rate (180 days) I$=4.800% per annum (2.400% per 180 days)

=U.S $5,000,000 *1.0240 $5120, 000

Spot (¥/$) forward -180days (¥/$)
(118.60/¥593000000)