BSAR Trading System - The EMA of Lows

1. How is BSAR value calculated?
• Biased Stop And Reverse is a value derived by calculating the Exponential Moving Average (EMA) of Lows of the period.
• First take up the Simple Average of the Lows of the period, e.g., if you want to calculate the Exponential Moving Average of Lows for 9 periods, first calculate the Simple Average of the first 9 periods Low
• Then Calculate the Smoothing Percentage by the following formula:
  α = 2 / (N + 1);
  Since N in our case is 9;
  => N = 9;
  => N + 1 = 9 + 1 = 10;
  => α = 2 / (10);
  => α = 0.2;
  
• Then to calculate the EMA of Lows, the formula is:;
  
  EMA (today) = EMA (Yesterday) + α * {Low (today)- EMA (Yesterday)}
  
  Where EMA (yesterday) is the yesterday's value of Exponential Moving Average, but the very first day we had calculated the Simple Average of Lows, hence just for the second day, the EMA (yesterday) would be Simple Average of Lows calculated Yesterday;
  
  So,
  1st Value of BSAR is Simple Average of Lows for the Period;
  
  2nd Value is the EMA of the Lows for the Period;
  where the EMA(Yesterday) = Simple Average of Lows calculated Yesterday or 1st Value ;
  
  3rd Value of BSAR is the EMA of Lows for the Period;
  where the EMA(Yesterday) = EMA of Lows calculated on 2nd Day.
2. What is the α in above equation
• α is the Greek alphabet "Alpha".
• It is the smoothing factor in EMA formula which defines the weight that is assigned to the current value
• It's value range is between 0 and 1
• For Example a 18% weight-age for the current value means α = (18/100) = 0.18 and a 47% weightage for the current value means α = (47/100) = 0.47
• For calculating α for time periods the formula is:
  α = 2 / (N + 1)
• For Example, for calculating 5 day EMA the α would be 2 / (5 + 1) = 2/6 = 0.33 which is equivalent to 33% weight-age to the Current Value. Similarly, for calculating 21 days EMA, the α would be 2 / (21 + 1) = 2 / (22) = 0.09 Which is equivalent to 9% Weightage to the current value
• The EMA formula could be expressed in two ways:
  EMA (today) = EMA (Yesterday) + α * {Raw Value for Today - EMA (Yesterday)}
  EMA (today) = (α * Raw Value for today) + {(1 - α) * EMA (Yesterday)}
  both would give the same value.
3. What is the Optimum Value for α?
• α for different assets would be different, and it should be chosen on the basis of the mean price volatility of the asset
• For most of the assets a 20% to 25% weightage or α = 0.20 to α = 0.25 would work; but personally I prefer α = 0.236 or 23.6% which is {Phi * ( 1 - Phi)}
• To put it even more simply, EMA of 7, 8 or 9 period Lows should work fine.