Question

Suppose the annualized interest rate on 180-day Russian Ruble deposits is 4.3125 (bid) - 4.4375 (ask). At the same time, annualized interest rate on 180-day interest rate on 180-day Turkish Lira deposits is 9.125-9.375. Spot and 180-day forward quotes (TRY per RUB) are 0.07915-0.08820 (and 0.07450-0.07950, respectively. Find forward rate such that there is NO arbitrage? 180-day Russian Ruble bank rates 180-day Turkish Lira bank rates Spot (TRY/RUB) Forward (TRY/RUB) BID 4.3125 9.125 0.07915 0.07450 ASK 4.4375 9.375 0.08820 ?

Answer 1

Let us Simplify the said Spot rates and understand the meaning in simple mathematical form.

Spot Rates says

1 RUB = 0.07915 TRY.. Bid

1 RUB = 0.08820 TRY..Ask

Suppose you borrow 1 RUB @ russian interest rate of 4.4375 ( Since you are borrowing, you will have to pay interest and hense ask rate is applicable)

Now you sell this RUB and purchase TRY in Spot rates(Hence bid price since you are selling RUB)

You will get an amount equal to = 0.07915 TRY.

The interest you will have to pay for 6 months on 1 RUB = 1*0.044375*(6/12)

= 0.0221875 RUB.

the forward rate to eliminate must be equal to an amount that on purchasing and RUB the interest amount too must be covered.

To achieve no arbitage, 1.0221875 RUB = 0.07915 TRY

1 RUB = (0.07915/ 1.0221875) TRY

1 RUB = 0.07743

Hence a forward rate(TRY/RUB) = 0.07743 will create a position of no arbitage.

Tips: Remember the most important point to be remembered while solving these question is to remember the base currency during conversion.