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​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 = eσ√h
    • 1 + downside change = d = 1/ u
      •  Where, e = base of natural logarithms = 2.718
      • σ = standard deviation of (continuously compounded) stock returns
      • h = time interval as fraction of year
  • In our example, standard deviation of stock returns, σ = 40.69%, h = 0.5
    • u= e 0.4069√0.5 = 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





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