Ta Session 1

TA-Session 1

Triangular Arbitrage in real life:

| BID | ASK |

USD/GBP | 1,5322 | 1,5431 |

USD/EUR | 1,2647 | 1,2649 |

| | |

GBP/USD | 0,6480 | 0,6527 |

EUR/USD | 0,7906 | 0,7907 |

a)

Converting EUR into GBP:

EUR1000 x USD1,2647/EUR = USD1264,7

USD1264,7 x GBP0,6480/USD = GBP819,5256

Reverse, convert back into EUR:

GBP 819,5256 x USD1,5322/GBP * 0,7906 EUR/USD = 992,78

Percentage loss = 0.722%

b)

S(GBP/EUR)BID =S(USD/EUR)BID x S(GBP/USD)BID = 1,2647 x 0,6480 = 0,8195

S(GBP/EUR)ASK =S(GBP/USD)ASK x S(USD/EUR)ASK = 0,6527 x 1,2649 = 0,8256

S(EUR/GBP)BID = 1/S(GBP/EUR)ASK = 1/0,8256 = 1,2112

S(EUR/GBP)ASK = 1/S(EUR/GBP)ASK = 1/0,8195 = 1,2203

Ratio: S(GBP/EUR)BID- S(GBPEUR)ASKS(GBPEUR)ASK= 0,8195-0,82560,8256=-0,00739

c)

We would ask for the quotes of EUR/GBP from another bank.

d)

EUR/GBPBID = 1,3612

EUR/GBPASK = 1,3698

Yes, there is an arbitrage opportunity. We can buy USD, sell USD and buy GBP, sell GBP and buy EUR.

EUR1000000*USD1.2647/EUR*1/USD1.5431/GBP*EUR1.3612/GBP = EUR1115617.68

Arbitrage profit = EUR115617.68

e)

implied bid < bank’s ask ; bank’s bid < implied ask

The Forward Market

Effective interest rates:

i(CHF) = 0,08 x180360 = 0,04

i(EUR) = 0,10 x180360 = 0,05

Investing in EUR deposits:

EUR10 000 000 x (1+i(EUR)) = EUR10 000 000 x (1 + 0,05) = EUR10 500 000

Investing in covered CHF deposits:

1S(EURCHF)x (1+iCHF x F(EURCHF))

EUR100000001,1960x 1+0,04 x 1,2024=EUR10 455 652,17

The payoff is larger when investing in EUR deposits. If this was real, investors would borrow in CHF and invest the money in EUR deposits and make an arbitrage profit.

PPP

a)

SPPP(JPYEUR)=JPY2175 000EUR15 000=JPY145/EUR

b)

The EUR is undervalued by 145-135135=7.4%

c)

Because the actual exchange rate is less than the implied PPP exchange rate, the EUR is undervalued on the foreign exchange market and will have to strengthen from JPY135/EUR to JPY145/EUR.

d)

Relative PPP states that...