Question

BL lives in the US and has $800,000 surplus funds that he wants to invest for one year in any currency. He receives the following quotes from a commercial bank:

Spot rate= 1 British Pound: $50-55

One-year forward rate= 1 British Pound: $58-64

One-year US interest rate= 6%

One year UK interest rate= 1%

(i) With supporting calculations, advise BL whether covered interest arbitrage is worthwhile.

(ii) Would your advice differ, if transaction costs in respect of the covered interest arbitrage amount to $5,000?

(iii) Using the interest rate parity model, calculate the interest differential between the two countries.

Answer 1

(i) BL has $ 800,000 with an option to invest in UK market. He can convert he dollar amount to GBP using the spot price. He can convert it at offer price of 55. Therefore, GBP he has post converting $ 800,000 -

800,000 / 55 = 14545.45 GBP

Investing in UK market will earn him 1 % per year. Yherefore, ath the end of the year amount earned by BL -

14545.45 * (1+1%) = GBP 14,690.91

Using the forward rate we will convert this GBP into USD at bid price  of 58, to avoid any foreign exchange risk-

USD = 14690.91 * 58 = $ 852,072

Therefore there is an arbitrage opportunity of $ 52,072.

Additionally, if the same amount was not converted and kept in US, BL would have earned -

800,000 * 6% = $ 48,000

Therefore covered interest arbitrage would effectively help BL to earn more ie earn more by $ 4,072 (52072 - 48000).

ii) In case the total transaction cost in covered interest arbitrage is $ 5,000/- still BL would earn less

Therefore earnings from covered interest arbitrage option = 52,072 - 5000 = USD 47,052

And interest earnd from US without any conversion option is $48,000 more than the above. hence with transaction cost of $5,000 involved, it is not recommendable to go for covered interest arbitrage option.

III) Using interest rate parity model, we can calcuate the interest rates so that the conversion rate is at par

For calculations we will compute Mid rate for spot and forward

Therefore, spot rate = (50+55) / 2 = 52.5

Forward rate = (58+64)/2 = 61

As per Interest rate parity, we will find both the interest rates -

Forward rate = spot rate * [(1+ overseas country interest rate) / (1+domestic country rate)]

61=52.5 * (1+GBP int rates) / 1.06

Therefore, GBP = 23%

also, calculating the dollar interest rate,

61 = 52.5 *[(1.01) / (1+$ rate)

Therefore, USD = 13%

Hence the interest rate differentials should be, 23-13 = 10%