Purchasing power parity (PPP) is an economics theory which proposes that the exchange rate of any two currencies will remain equal to the ratio of their respective purchasing powers. Purchasing power of a currency is measured as the amount of the currency needed to buy a selected product or basket of goods commonly available in different countries.

Purchasing power parity theory states that, in the long run, the price paid for a product in two countries using different currencies will be same after the exchange rate differences have been accounted for. This itself is based on the law of one price i.e. price of a given commodity is same no mater what currency is used to purchase it.

It also suggests that a change in purchasing power of the two currencies will induce readjustment of the exchange rate towards new equilibrium point.

Purchasing power parity assumes similar market conditions and absence of costs such as transportation and duties etc.

## Formula

Let's say we have two currencies A and B. Then,

$$\text{Exchange Rate}\ (\text{A per 1 unit of B}) \\= \frac{\text{Purchasing Power of A}}{\text{Purchasing Power of B}}$$

Purchasing power of a currency is a function of inflation which means that high rate of inflation of one currency relative to another will reduce the purchasing power of the currency and vice versa. This means that the exhange rate between two currencies will change in proportion to the ratio of inflation rates between the two currencies as shown in the following equation:

$$\frac{\text{Forward Rate}}{\text{Spot Rate}}=\left(\frac{\text{1}+\text{i} _ {\text{quot}}}{\text{1}+\text{i} _ {\text{base}}}\right)^\text{n}$$

Where iquot is the inflation rate of quote currency, ibase is the inflation rate for base currency and n are the number of years until the date of foraward rate.

Let's say the exchange rate is quoted as USD/GBP i.e. GBP per 1 USD. In this case the USD is the base currency and GBP is the quote currency.

The above equation may be rearraged to obtain the following formula for the estimated of forward exhange rate:

$$\text{Forward Rate}\\=\text{Spot Rate}\times\left(\frac{\text{1}+\text{i} _ {\text{quot}}}{\text{1}+\text{i} _ {\text{base}}}\right)^\text{n}$$

## Example

For the sake of simplicity we are going to ignore the bid-ask spread in the following example. The price of a standardized basket of goods is 18,000 USD or 13,000 GBP. Let us test whether purchasing power parity exists if the current USD/GBP exchange rate is 1.3800 USD.

The estimated exhange rate as per PPP is 1.3846 [=18,000/13,000], which is quite near the 1.3800 meaning that PPP exists. This example is just for understanding purpose only. Real life spot rates may be quite different than the rate estimated using PPP because currency exhange rates are determined by a number of market conditions.