A bank purchases a six month 1 million euro dollar deposit at an interest rate o

Question

A bank purchases a six month 1 million euro dollar deposit at an interest rate of 6.5 percent per year. It invests the funds in a six-month Swedish krona bond paying 7.5 percent per year. The current spot rate of U.S. dollars for Swedish krona is $0.18/SKr.

a. The six-month forward rate on the Swedish krona is being quoted at $0.18/SKr. What is the net spread earned on this investment if the bank covers its foreign exchange exposure using the forward market?

b. At what forward rate will the spread be only 1 percent per year?

Explanation / Answer

A bank purchases a six-month, $1 million Eurodollar deposit at an annual interest rate of 6.5 percent. It invests the funds in a six-month Swedish krone bond paying 7.5 percent per year. The current spot rate is $0.18/SK. ============================================================================================================================================ a. The six-month forward rate on the Swedish krone is being quoted at $0.1810/SK. What is the net spread earned on this investment if the bank covers its foreign exchange exposure using the forward market? ================================================================================================== Interest plus principal expense on six-month CD = $1m x (1 + 0.065/2) = $1,032,500 ---------------------------------------------------------------------------------------------------------------------------------------- Principal of Swedish bond = $1,000,000/0.18 = SK5,555,555.56 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Interest and principle = SK5,555,555.56 x (1 + 0.075/2) = SK 5,763,888.89 =----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Interest and principle in dollars if hedged: SK 5,763,888.89 x 0.1810 = $1,043,263.89 ------------------------------------------------------------------------------------------------------------------------------------ Spread = $1,043,263.89-1,032,500 = $10,763.89/1 million = 0.010764, or 2.15 percent p.a. ========================================================================================================================================================================================================================= b. What forward rate will cause the spread to be only 1 percent per year? ----------------------------------------------------------------------------------------------------------------------------------------- Net interest income should be = 0.005 x 1,000,000 = $5,000 -------------------------------------------------------------------------------------------------------------------------------------------------- Therefore, interest income should be = $1,032,500 + $5,000 = $1,037,500 ------------------------------------------------------------------------------------------------------------------------------------ Forward rate = SK 5,763,888.89/$1,037,500 = $0.18/SK ----------------------------------------------------------------------------------------------------------------------------------------- For the spread to remain at 1% the spot and the forward will have to be the same.

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