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**6. Covered versus uncovered interest arbitrage**

On May 17, Manuel, an American investor, decided to buy three-month Treasury bills. He found that the per-annum interest rate on three-month Treasury bills is 8.00% in New York and 12.00% in London, Great Britain. Based on this information and assuming that tax costs and other transaction costs are negligible in the two countries, it is in Manuel’s best interest to purchase three-month Treasury bills in London , because it allows him to earn1.00% more for the three months.

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Explanation:

Manuel is better off purchasing three-month Treasury bills in London, because it allows him to earn 1.00% more for the three months than if he bought three-month Treasury bills in New York. You can calculate the interest-rate differential, or Manuel’s extra interest, as follows:

Extra InterestExtra Interest | = = | Foreign Interest Rate−Domestic Interest Rate12No. of Months for T-billForeign Interest Rate−Domestic Interest Rate12No. of Months for T-bill |

= = | 12.00%−8.00%12312.00%−8.00%123 | |

= = | 12.00%−8.00%412.00%−8.00%4 | |

= = | 1.00%1.00% |

Note that because of the assumption that transaction costs in London and New York are negligible, you can actually compare two country’s Treasury bill returns.

On May 17, the spot rate for the pound was $1.510, and the selling price of the three-month forward pound was $1.508. At that time, Manuel chose to ignore this difference in exchange rates. In three months, however, the spot rate for the pound fell to $1.450 per pound.

When Manuel converted the investment proceeds back into U.S. dollars, his actual return on investment was-2.97% .

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Explanation:

Uncovered interest arbitrage occurs when an investor does not obtain exchange-market cover to protect investment proceeds from foreign-currency fluctuations. In Manuel’s case, the dollar appreciated, and the spot rate for the pound fell from $1.510 to $1.450 per pound. This means that Manuel could not buy as many U.S. dollars per pound as he spent for pounds three months prior. So the new spot rate resulted in a loss of 3.97% of the investment proceeds. You can calculate Manuel’s uncovered discount as follows:

Uncovered InterestUncovered Interest | = = | New Spot Rate−Spot RateSpot Rate×100New Spot Rate−Spot RateSpot Rate×100 |

= = | $1.450−$1.510$1.510×100$1.450−$1.510$1.510×100 | |

≈ ≈ | −3.97% (discount)−3.97% (discount) |

Now you can calculate Manuel’s actual return on investment in British three-month Treasury bills:

Actual ReturnActual Return | = = | Extra Interest+Uncovered InterestExtra Interest+Uncovered Interest |

= = | 1.00%+(−3.97%)1.00%+−3.97% | |

= = | −2.97%−2.97% |

As a result of this transaction, Manuel realizes that there is great uncertainty about how many dollars he will receive when the Treasury bills mature. So, he decides to adjust his investment strategy to eliminate this uncertainty.

What should Manuel’s strategy be the next time he considers investing in Treasury bills?

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Explanation:

Manuel realizes that his actual return (-2.97%) is less than his expected return (1.00%) and decides to use a strategy known as covered interest arbitrage to eliminate the uncertainty over how many dollars he receives when the foreign currency is reconverted into dollars. That is, should he invest in foreign Treasury bills again while exchanging dollars for foreign currency to finance the investment, he would also contract in the forward market to sell the amount of foreign currency expected as proceeds from the investment with a delivery date to coincide with the maturity of the investment.

Had Manuel used the covered interest arbitrage strategy on May 17, his net return on investment (relative to purchasing the U.S. Treasury bills) in British three-month Treasury bills would be0.90% . (Note: Assume that the cost of obtaining the cover is zero.)

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Explanation:

Had Manuel used covered interest arbitrage, he would need to take into account not only information on foreign and domestic interest rates, but also all available information on spot and future exchange rates to calculate the net rate of return on investment in British three-month Treasury bills. To calculate Manuel’s net rate of return on investment, start with the following formula:

Net ReturnNet Return | = = | Extra Interest+Covered InterestExtra Interest+Covered Interest |

= = | Foreign Interest−Domestic InterestTime Periods in Year+Forward Rate−Spot RateSpot RateForeign Interest−Domestic InterestTime Periods in Year+Forward Rate−Spot RateSpot Rate | |

= = | 0.12−0.084+$1.508−$1.510$1.5100.12−0.084+$1.508−$1.510$1.510 | |

= = | 0.01+(−0.001)0.01+−0.001 | |

= = | 0.009, or 0.90%0.009, or 0.90% |

Therefore, using covered interest arbitrage, Manuel would have received a net return on investment in three-month Treasury bills of 0.90%, which is greater than the return with uncovered interest because, by using uncovered interest arbitrage, Manuel actually lost more than he had gained on the difference in interest rates in London and New York.

In addition, Manuel should have only invested in three-month British Treasury bills if the interest-rate differential in favor of British Treasury bills exceeded the cost of obtaining the forward cover. Here, it was assumed to be zero, but in real-world situations, it is costly.