Assume the following information:

·        An Italian investor has €125,000 to invest.

·        The current spot rate of Pakistani Rupee is €0.0051

·        The 60-day forward rate of the Pakistani Rupee is €0.0050.

·        The 60-day interest rate in Italy is 1.74 percent.

·        The 60-day interest rate in Pakistan is 3.8 percent.

What is the yield to an Italian investor who conducts covered interest arbitrage? Did covered interest arbitrage work for the investor in this case? 

Answer:

A covered interest arbitrage is a form of arbitrage in which an investor invests the money in the high yielding currencies and use forward contract to cover the exchange rate risk. That is why it is named as covered as all the risks are covered using the derivative instrument. Interest Arbitrage would mean that we are exploiting the difference between the interest rates between diferent currencies. But as per this theory interest arbitrage would not be possible in long run as the cost to cover the risk would offset the extra returns from the difference in interest rates.

Now, since the Italian investor is conducting interest rate arbitrage, it would mean that he would invest the money in high yielding currency i.e. PKR and cover that with forward contract. But as per this theory, the return by doing all that would be almost equal to the return of directly investing in the Italian Market.

Amount to Invest =  125,000

Current Spot Rate =  0.0051 / PKR

60 Day Forward Rate =  0.0050 / PKR

60 Day Interest Rate in Italy = 1.74% p.a. Continuously Compounded

60 Day Interest Rate in Pakistan = 3.8% p.a. Continuously Compounded

Time = 60 Days

Now, below would be the steps an investor needs to take for the covered interest arbitrage:

1. Convert the amount to be invested in PKR at the current spot Rate.

Converted Amount = Amount to Invest / Current Spot Rate

Converted Amount = 125,000 / 0.0051

Converted Amount = 24,509,803.92 PKR

2. Invest the converted amount in PKR at the higher interest rate for 60 days.

Amount to be received after 60 Days = Converted Amount * e^{60 Days Interest Rate in Pakistan * Time in Years}

Amount to be received after 60 Days = 24,509,803.92 * e^{3.80% * 60 / 365}

Amount to be received after 60 Days = 24,663,385.44 PKR

3. Enter into a forward contract to covert these PKRs into Euro at a future date.

Amount in Euro after 60 days = Amount to be received after 60 Days / Forward Rate

Amount in Euro after 60 days = 24,663,385.44 * 0.0050

Amount in Euro after 60 days = 123,316.93

Yield for Italian Investor = (Amount in Euro after 60 Days / Amount to Invest) - 1

Yield for Italian Investor = (123,316.93 / 125,000) - 1

Yield for Italian Investor = (123,316.93 / 125,000) - 1

Yield for Italian Investor = - 1.35%

Thus, yield to italian investor in conducting the covered interest arbitrage would be - 1.35%.

Since the Italian Interest Rate (1.74% * 60 / 365) > Yield of Covered Interest Arbitrage (- 1.35%),

Covered interest rate arbitrage has made the position of investor worse than what it could have been if he would have invested in the italian market in first place. Thus, Covered interest arbitrage has not worked for investor in this case.

* Since nothing was given against the interest rate, we have used the general conventions followed in quoting these rates. Generally these rates are quoted in per annum terms and in derivatives trades it is generally quoted in continuously compounded terms.