# â€‹Change in Future Stock Price

- The following formula that relates the up and down changes to the standard deviation of stock returns:
- 1 + upside change = u = e
^{Ïƒâˆšh} - 1 + downside change = d = 1/ u
- Where, e = base of natural logarithms = 2.718
- Ïƒ = standard deviation of (continuously compounded) stock returns
- h = time interval as fraction of year

- 1 + upside change = u = e
- In our example, standard deviation of stock returns, Ïƒ = 40.69%, h = 0.5
- u= e
^{0.4069âˆš0.5}= 1.3333, => upside change = 33% - d= 1/u = 1/1.3333 = 0.75, => downside change = 25%

- u= e
- Thus stock price takes the following two values
- Rs. 85 x 1.3333 = Rs. 113.33
- Rs. 85 x 0.75 = 63.75