Question

IRP arbitrage2

**a.**

If the interest rate in the United Kingdom is 5 percent, the
interest rate in the United States is 4 percent, the spot exchange
rate is $1.6789/£1, and interest rate parity holds, what must be
the one-year forward exchange rate? |

One-year forward exchange rate | $ per £ |

**b.**

If the forward rate is actually $1.6617/£1, would you borrow in dollars or pounds to make an arbitrage profit? |

Dollars | |

Pounds |

**c.**

If you can borrow either $1 million or £1 million (borrow in
currency identified in previous part) to capitalize on the
arbitrage profit using the actual forward rate of $1.6617/£1, what
is your arbitrage profit at the end of the year expressed in
$dollars? |

Arbitrage profit in $ | $ |

Answer #1

As per Interest rate parity, forward rate = Spot Rate(1+Interest Rate US)/(1+Interest rate UK)

= 1.6789(1.04)/(1.05)

= $1.6629/Pound

b.Actual Rate 1 Pound = $1.6617 (Less dollars per pound than it should be)

Borrow in Pounds

c.Borrow Pound1,000,000

Convert into Pound at Spot rate = 1,000,000*1.6789= $1,678,900

Invest and get 1,678,900(1.04) = $1,746,056

Convert Back into USD at forward rate 1,746,056/1.6617 = Pound 1,050,764.8793

Repay Loan 1,000,000*1.05 = Pound 1,050,000

Arbitrage Profit = Pound 764.8793 or 764.8793*1.6617 = $1,271

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