# Trans-Atlantic Arbitrage

Topics: United States dollar, Investment, ISO 4217 Pages: 9 (1378 words) Published: September 26, 2011
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) (118.00*5120,000)
¥604,160,000

¥593,000,000 *1.0170 (¥ 603,081,000) Japanese yen interest rate (180 days) ¥107900 i¥=3.400% per annum (1.700% per 180 days)

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a) Akira Numata can make an uncovered investment arbitrage profit/gain of ¥107900 if her expectations about the future rate is correct.

b) Future rates are difficult to predict. Akira is taking the risk of playing the game of “luck and chance”. There is no guarantee/certainty that the predicted future rate will be the actual future rate at the end of the period. There is the possibility that the future rate is actually a different rate, far from the rate Akira predicted which may or may not be favorable to him. Even a small movement in the expected rate could cost him a lot of money. If the spot rate at the end of 180 days was ¥106.oo/\$, Akira would experience a loss of ¥60361000.

QUESTION 13

Assumptions | Value \$| Swiss Franc equivalent |
Arbitrage funds | 1,000,000| 1,281,000|
Spot Rate (SFr./\$)| 1.2810| |
90-days forward Rate | 1.2740| |
90-days U.S dollar interest rate| 4.800%| |
90-days Swiss Franc Interest Rate | 3.200%| |

Calculations

Difference in interest rate
Equation= isfr - i\$
=3.200%-4.800%
= -1.600%

90-days interest rate for Swiss Franc...