Question

RETURNS ON CARRY TRADE

need the methodology/ explanation on how to calculate returns on a carry trade when using the interest rate and exchange rate as indicators. full method and formulas required.

Answer 1

Solution:-

Every country has a currency of its own and a central bank that decides interest rates in that country. Currency is just like any other asset which is traded in the markets and has a value. This value is expressed in other currencies. Just like a pen has a value (worth or price) in terms of USD of let's say $1, similarly a dollar has a certain value and currency markets express that value in terms of other currencies like GBP, EUR, YEN, etc.

A regular currency trade involves currency traders aiming at making profits by buying a currency whose value they believe would increase in relative to other currency. However, a carry trade works opposite. It's a trade where currency traders aim at making money by betting that the exchange rates between two currencies wouldn't change over a period of time. It sounds weird, so let's take a look at how such a trade can potentially yield profits for traders.

Logic behind currency carry trades:

An investor can invest in interest yielding bonds in any country. The interest rates in different countries sometimes differ a lot. Interest rates in one country could be lower than other country. This creates opportunities to make profits.

The strategy is that investor borrows money in the country where interest rates are low (in that country's currency), convert that borrowed money into currency of the country where interest rates are high and invest it into the interest-yielding bonds of that country. After making higher interest income on those bonds, he can liquidate his bonds, convert the proceeds back to the currency of original low interest country and pay back his borrowings & interest on the loan. Since, he made a higher rate of interest on his bonds than he had to pay on his borrowings, he ends up making a profit.

Example of a carry trade:

GBP and $ are trading at the rate of $2 per 1GBP, while the interest rates are 2% in the US are 4% in the UK. A trader can borrow $10 million ($10m) and convert that into GBP5 million [calculated as ($10million/2)]. He then invests GBP5m into UK bonds yielding 4% rate of interest. He holds the bonds for 1 year makes interest of GBP200,000. the bonds are liquidated and total proceeds of GBP5.2m (i.e. 5m + 200,000) are converted back to $10.4m (i.e. GBP5.2m*2). The US borrowing is then repaid along with interest totaling $10.2m (i.e. $10m + 2%), thus making profits of $200,000.

Method and formulas for calculating profits on a carry trade:

The steps and formulas involved in calculating profits on a carry trade are as follows:

1) Identify the two currencies whose pair is being traded, and which currency has lower interest yields and which one has higher interest yields.

Formula- as given in question

2) Identify the amount of money borrowed in the currency having low interest yields.

Formula- as given in question

3) Convert the amount of borrowing into currency of country that has higher interest yields. This will be the investment made in bonds/interest yielding securities of currency yielding higher interest rates

Formula- (Money borrowed in low interest currency*exchange rate of the pair)

4) Calculate the interest earned on bonds using holding period bonds and interest rate of the high interest currency

Formula- (Investment calculated as per step 3*Holding period in years*interest rate of high interest currency)

5) Calculate the total proceeds from liquidation of bonds (i.e. initial principal invested in bonds plus the interest earned)

Formula- (Investment calculated as per step 3 + interest calculated in step 4)

6) Convert the total liquidation proceeds back to the currency that was initially borrowed (low interest currency) using their exchange rates. This is the sale value in carry trade

Formula- (Proceeds as per step 5/exchange rate of the pair)

7) Calculate the interest expense payable on loan using holding period and interest rate of low interest currency.

Formula- (Sale value as per step 5*Holding period in years*interest rate of low interest currency)

8) Calculate the total loan repayment (i.e. money borrowed plus interest expense). This is the total cost of carry trade.

Formula- (Initial money borrowed + interest expense as per step 7)

9) Calculate the profit on currency trade as sale value (calculated in step 6) less total cost (calculated in step 8)

Formula- (Sales value as per step 6 - Cost as per step 8)