Going from ¥103/$1 to ¥149/$1 is a 30.9% loss in value. A 50% loss in value would be going from (eg) ¥100/$1 to ¥200/$1.

I'm trying to reverse engineer your thinking. Did you do 150 - 100 = 50, then use 100 as the denominator to get 50%? Because that's not what "losing 50% of value" means.