Hi I need help explaining how you get to the answers for this problem. The answers are provided, but confusing to me.

HW2: Interest Rate Parity with bid-ask spreads

Suppose:

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 = 3.0% - 3.3%

With bid-ask rates and borrowing-lending rates, is arbitrage profit possible if you start with $1 million in part (a) and 1 million in part (b) ?

Do it both ways :

(a) borrow $ 1 million in US and invest overseas and

(b) borrow 1 million in UK and invest in US.

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HW #2: Answer

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

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(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) = 1,008,817.7

Repay 1,016,500.

After paying back the loan, you have a loss of 7,682