I need help I don't understand it

Question

if a stock gains 50 percent one year and then loses 50 percent of its value the next year is it accurate to say that its mean growth over the full two years period was 50+-50/2?

Answer 1

No it is not, because the 50% amount is different the second year compared to the first year.

 

Let's say a stock value is $100.

 

If it goes up 50%, then it goes up .50 x 100, which is $50, so the new value is $150 (100 + 50)

 

The next year if it goes down 50%, then it goes down .50 x 150, which is $75 dollars, so the new value is $75 (150 - 75)

 

So you can see the difference here is the 50% applies to $100 the first year but then applies to $150 the second year. 

 

 

Answer 2

v represents starting value

1.5v represents the gain

(0.5)(1.5)v represents the loss

The resulting value is 0.75v

The average would be 0.75v/2

Answer 3

Let the value of the stock initially be y

 

after the first year it gains 50%of x hence new value would be 1.5*y. The next year it loses 50% of the value that it started the year with. Hence the new value for the stock would be 50% of 1.5*y = 0.75*y

 

hence its average growth over the 2 year period would be (x - 0.75y) = 0.25y or 0.25y/2 = 0.125y per year. Since the initial stock was worth x

 

percent growth = 0.25y/y * 100% = 25% for 2 years or 0.125y/y *100% = 12.5 % per year 

 

Hence mean growth is 25% over the two-years period or 12.5% per year.