Question

The USD appreciates 4% versus the JPY. The MXN depreciates 4% versus the USD. What is the approximate appreciation or depreciation we might see in the JPY/MXN exchange rate?

Answer 1

As per the question, we have two currency pairs to work with,

1. USD - JPY

2. USD - MXN

So, let's take the current market rates for both the currency pairs, which are as below

1USD = 110.77 JPY

1USD = 19.27 MXN

(Rates are as per 22 Feb 2019, 6:00 AM UTC market value)

Now, consider the currency movements as per the question in steps.

STEP 1

USD appreciates 4% versus JPY.

Since we know, that if any currency A appreciates as compared to currency B, then we need more amount of currency B for purchasing a similar amount of currency A.

So in this case, USD appreciates with respect to JPY. Hence, now for the same 1USD, we will require more JPY. It is calculated as below

Previous

1USD = 110.77 JPY

After USD appreciation by 4% Vs JPY

New exchange rate value is calculated as 1USD = [110.77 + (110.77 * 4%)] JPY = [110.77 + (110.77*0.04)] JPY

1USD = 115.201 JPY

STEP 2

MXN depreciates 4% versus USD.

Since we know, that if any currency A depreciates as compared to currency B, then the same amount of currency B will purchase a lesser amount of currency A.

So in this case, MXN depreciates with respect to USD. Hence, now for the same 19.27 MXN, we will get less USD. It is calculated as below

Previous

1USD = 19.27 MXN

After MXN depreciation by 4% Vs USD

New exchange rate value is calculated as 19.27 MXN = [1- (1*0.04)] USD = 0.96 USD

19.27 MXN = 0.96 USD

Now the relation between JPY and MXN rates before and after.

Before

1USD = 110.77 JPY

1USD = 19.27 MXN

So, for calculating JPY/MXN, we use the below formula

(JPY/MXN) = (JPY/USD) * (USD/MXN)

JPY/MXN = (1/110.77) * 19.27 = 0.1740

i.e. 1JPY = 0.1740 MXN

After

1USD = 115.201 JPY

0.96 USD = 19.27 MXN

So, for calculating JPY/MXN, we use the below formula

(JPY/MXN) = (JPY/USD) * (USD/MXN)

JPY/MXN = (1/115.201) * (19.27/0.96) = 0.1742

i.e. 1JPY = 0.1742 MXN

So, the appreciation/depreciation is calculated by the below method,

= [ (R₁ - R₂)/ R₂ ] *100

where, R₁ = Starting Value of the Quote currency (which is MXN here) as compared to Base currency (which is JPY here)

R₂ = Final Value of the Quote currency

= [ (0.1740-0.1742)/0.1742] * 100

= - 0.11481 %

So, MXN has depreciated by 0.11481% versus JPY