Interest Rate Parity Recall Covered Interest Arbitrage Example
Interest Rate Parity
Recall Covered Interest Arbitrage Example 1 • Foreign Currency = French Francs • Investable Amount = $ 1, 000 • Sj : Spot rate = $ 0. 10 = ff 1 • Fj : Forward rate = $ 0. 10 = ff 1 • In US @ interest = 5% • In France @ interest = 6%
If you Deposited in France CALCULATION Step 1 : Convert $ into ff @ spot rate of $ 0. 10 $ 1, 000 / 0. 10 = ff 10, 000 Step 2 : Deposit on interest of 6% in France ff 10, 000 * 6 % = ff 600, 000 Total = ff 10, 600, 000 Step 3 : Convert ff into $ @ forward rate 0. 10 ff 10, 600, 000 * 0. 10 = $ 1, 060, 000
IF YOU DEPOSITED IN US US INTEREST @ = 5 % CALCULATION : • Investment: $ 1, 000 * 5 % • Profit = $ 50000 • Total = $ 1, 050, 000
RESULT : Profit from France is more than US • From France $ 1, 060, 000 So invest in France • From US $ 1, 050, 000
Interest Rate Parity (IRP) Definition • “If there is a difference in the interest rate of the two countries, • The forward rate will have a premium / discount equal to the interest rate differential , • Then there will be no difference in profit to invest in home or foreign country”
Calculating Premium/Discount Formula: P = (1+ih) / (1+if) – 1 Where • P = Forward Premium • ih = Home Interest Rate • if = Foreign Interest Rate
Calculation DATA interest rate in France = if = 6% Interest rate in US = ih = 5% P / D = (1+5%)/(1+6%) – 1 * 100 D = approx - 0. 94% • It shows forward discount • It means US investors will receive 0. 94% Less when they will convert the currency on forward Rate
FORWARD RATE CALCULATION FORMULA Fj = Sj ( 1 + p) Where • Fj = Forward rate • Sj = Spot rate • P = Premium or Discount
DATA • Fj : Forward rate =? • Sj : Spot rate = $ 0. 10 = ff 1 • D : Discount = - 0. 94 %
CALCULATION Formula Fj = Sj ( 1 + D) Fj = 0. 10 ( 1 + (- 0. 94 %) ) Fj = $ 0. 09906
Example 2 You have two options for investment 1. In US @ interest = 5% 2. In France @ interest = 6%
DATA • Foreign Currency = French Francs • Investable Amount = $ 1, 000 • Sj : Spot rate = $ 0. 10 • Fj : Forward rate = $ 0. 09906 = ff 1 • In US @ interest = 5% • In France @ interest = 6% = ff 1
IF YOU DEPOSITED IN FRANCE Calculation Step 1 : Convert $ into ff @ Spot of $ 0. 10 $ 1, 000 / 0. 10 = ff 10, 000 Step 2 : Deposit on interest of 6% in France. ff 10, 000 * 6 % = ff 600, 000 Total = ff 10, 600, 000 Step 3 : Convert ff into $ @ forward $0. 09906 ff 10, 600, 000 * 0. 09906 = $ 1, 050, 036
IF YOU DEPOSITED IN US US INTEREST @ = 5 % CALCULATION : • Investment: $ 1, 000 * 5 % • Profit = $ 50000 • Total = $ 1, 050, 000
RESULT : It is approx equal profit From US & France • From France $ 1, 050, 036 • From US $ 1, 050, 000
CONCLUSION Therefore • we can say that IRP exists because • Investing in home country or foreign country provides the same profit • Even there was a difference in the interest rate
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