Interest Rate Parity

Recall Covered Interest Arbitrage Example 1 Foreign Currency = French Francs Investable Amount = $ 1,000,000 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 $ 1,000,000 / 0.10 = ff 10,000,000 Step 2 : Deposit on interest of 6% in France ff 10,000,000 * 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 CALCULATION : Investment: $ 1,000,000 * 5 % US INTEREST @ = 5 % CALCULATION : Investment: $ 1,000,000 * 5 % Profit = $ 50000 Total = $ 1,050,000

RESULT : Profit from France is more than US From US $ 1,050,000 From France $ 1,060,000 So invest in France

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 Interest rate in US = ih = 5% It shows forward discount 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 Fj = 0.10 ( 1 + (- 0.94 %) ) Fj = $ 0.09906 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 = $ 1,000,000 Sj : Spot rate = $ 0.10 = ff 1 Fj : Forward rate = $ 0.09906 = ff 1 In US @ interest = 5% In France @ interest = 6%

IF YOU DEPOSITED IN FRANCE Calculation Step 1 : Convert $ into ff @ Spot of $ 0.10 $ 1,000,000 / 0.10 = ff 10,000,000 Step 2 : Deposit on interest of 6% in France. ff 10,000,000 * 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 CALCULATION : Investment: $ 1,000,000 * 5 % US INTEREST @ = 5 % CALCULATION : Investment: $ 1,000,000 * 5 % Profit = $ 50000 Total = $ 1,050,000

RESULT : It is approx equal profit From US & France $ 1,050,000 From France $ 1,050,036

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