Why ‘percentage fall required to loss from percentage profit calculator’ need?

Suppose a stock or fund up by 100% then value will be double. Now if this available value decreases by 50% then the old value will be same. Thus, a calculator is needed to find out how much percentage of fall is happen for any percentage of profit than we can hedge our portfolio.

Example- Calculator’s value:

Calculation steps:

What is the ‘percentage fall required to loss from percentage profit calculator’ formula?

a= percentage profit in percentage
let percentage fall required to loss, b in percentage
Now we suppose that, any value is x and after profit is y
then, y= x+x*a*0.01 …..eq1
then, x= y-y*b*0.01 …..eq2
put the value of x in …..eq1
y= (y-y*b*0.01)*(1+a*0.01)
1= (1-b*0.01)*(1+a*0.01)
1= 1+a*0.01-b*0.01+a*b*0.01*0.01
1-1-a*0.01= -b*0.01*(1+a*0.01)
b= a/(1+a*0.01)
b= 100*a/(100+a)%