HW #2: Interest Rate Parity with bid-ask spreads

Spot rate St = $1.5080 - $1.5095 / £Six month Forward rate Ft,t+6 = $1.5280 – 1.5292/£Interest rate in US = 4.6 – 4.8%Interest rate in UK = 3 – 3.3%

Do it both ways : (a) borrow in US and invest overseas and (b) borrow overseas and invest in US.

Solution: (A) Borrow in US; invest in UK. Profit = $ 3,439

Step 1: Borrow $ 1mm in US at 4.8% / 2 = 2.4% for 6 months. Repay $1.024 million at t+6

Step 2: a) Convert $1mm to buy £ at ask spot quote (dealer sells at ask)Receive ( $1,000,000) divided by ($1.5095 / £) = £ 662,471

b) Invest £ at 3% / 2 = 1.5 % for 6 months. At t+6, receive £ 662,471 (1.015) = £ 672,408

c) Simultaneously, sell £ 672,408 in the forward market at bid (dealer buys £ at bid).At t+6 months, receive (£ 672,408) ($ 1.5280 per £) = $ 1,027,439

After paying back the $ loan, you have a gain of $3,439----------------------------------------------------------------------------------------------------

(B) If you Borrow in UK, invest in US. Profit = negative; loss & no arbitrage

Step 1: Borrow £ 1mm in UK at 3.3% / 2 = 1.65% for 6 months. Repay £ 1.0165 million at t+6

Step 2: a) Convert (sell) £1mm to buy $ at bid spot quote (dealer buys £ at bid)Receive (£ 1,000,000) ($1.5080 / £) = $ 1,508,000.

b) Invest $ at 4.6% / 2 = 2.3% for 6 months. At t+6, receive $ 1,508,000 (1.023) = $1,542,684.

c) Simultaneously, sell $ 1,542,684 (you buy £) in forward market at ask (dealer sells £ at ask).At t+6 months, receive ($1,542,684) (£ 1 / $1.5292) = £ 1,008,817.7Repay £ 1,016,500.After paying back the £ loan, you have a loss of £ 7,682