PPP, also known as the law of one price, states that the same goods should be have the same price independent of location purchased (after adjusting for exchange rate). Due to market frictions, PPP has not been seen to hold in reality.
A modified version of PPP called absolute PPP compares the average price of a basket of goods between 2 countries instead of comparing individual goods. However, this still is unobserved reality due to differing consumption patterns between counties.
Relative PPP states that changes in exchange rate should offset the price effect of inflation differences between two counties.
%ΔS(A/B) = Inflation(A) − Inflation(B)
%ΔS(A/B) = change in spot price (Currency A/Currency B)
Finally the ex-ante PPP is the same as relative PPP except that it uses expected inflation as a factor instead of actual inflation.
In the short run, deviations from PPP happen frequently as there aren’t true arbitrage opportunities to hold prices in line with the rule, but in the long run there is evidence that relative PPP holds.