Question

The recent market data on the U.S. and UK are shown as:

    the spot rate of the UK pound                      $1.27/£

     the 90-day forward rate                               $1.29/£

     the 180-day forward rate                             $1.30£

        

     interest rate (TB) in the U.S.:                      3% (per year)                                         

     interest rate (TB) in the UK.:                       1% (per year)

If you have $1 million available for 6 months, where do you want to invest (assume no transaction costs)? Explain why. Please apply all three decision making rules, as discussed in class, and show that your answers are consistent. (Rule 3 will be covered on Oct. 20)

Answer 1

Amount available for Investment = $1 Million

Option : I Invest in USD

Interest Rate in US = 3% per year

If $1 Million is invested in USD for 6 Months,

Amount after 6 Months = $1 Million(1+(0.03*(6/12)))

Amount after 6 Months = $1.015 Million

Option : II Invest in UK by Converting $1 Million to Pounds.

Spot Rate of UK Pound = $1.27/£

Amount in UK Pound available for Investment = $1 Million/$1.27 = £787,401.57

Amount after 6 Months = £787,401.57 (1+(0.01*(6/12)))

Amount after 6 Months = £791,338.58

If Such Amount is reconverted to US$,

the 180-day forward rate                             $1.30£

Amount after 6 Months = £791,338.58 * $1.30/£

Amount after 6 Months = $1,028,740 = $1.029 Million

As Amount after 6 Months is higher in case of Option II, i.e., it is better to invest in UK

Alternatively,

Fair Forward Exchange Rate£ = Spot$ ( 1 + I$) / ( 1 + I£)

Fair Forward Exchange Rate£ = $1.27 ( 1 + (0.03*6/12)) / ( 1 + (0.01*6/12))

Fair Forward Exchange Rate£ = $1.2826

Actual Forward Rate = $1.30/£

As Actual Forward Rate is higher than Fair forward rate, Forwards are Over Priced. As the forwards are overpriced, It is advisable to sell forwards which can be done by purchasing Pounds in spot investing and Converting back to US$ after 6 Months.