# 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 = eÏƒâˆšh
• 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
• 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%
• Thus stock price takes the following two values
• Rs. 85 x 1.3333 = Rs. 113.33
• Rs. 85 x 0.75 = 63.75