Running Simple Moving Average (SMA)

When building a platform to test trading ideas...one of the big issues to deal with is all the indicators that require a spin through the price series in order to calculate. For example, in order to calculate the 200 day simple moving average (SMA) of closing prices for Google today you would have to loop back 200 - 1 days ago and sum the closing prices and divide by 200.

When you are backtesting an idea you often need to start from day 1 of a stock's trading history and loop forward to the most current day. In essence, pretending each day is the current day at that point in time. Thus, you are looping back 200 - 1 data points for each day in the series. This isn't such a big deal with a stock such as Google whose trading history is rather limited (2004). But, take a stock like IBM with a more extensive trading history and your code is going to bog down with each call to the SMA indicator. Throw 20,000 securities into your backtest and the looping adds up.

Therefore, running calculations are the preferred method in order to spin just once through the data points. So, in order to calculate the running simple moving average for closing prices you apply the following formula:
\(SMA_{today} = SMA_{yesterday} + ((Price_{today} - Price_{today - n}) /n)\)
Where

• \(n\) = number of values included in your rolling computational window.

Straight-forward and avoids the loop. Here's the sample Python code for the Running SMA:

def cumulative_sma(bar, series, prevma):
    """
    Returns the cumulative or unweighted simple moving average.
    Avoids sum of series per call.

    Keyword arguments:
    bar     --  current index or location of the value in the series
    series  --  list or tuple of data to average
    prevma  --  previous average (n - 1) of the series.
    """
   
    if bar <= 0:
        return series[0]

    return prevma + ((series[bar] - prevma) / (bar + 1.0))

def running_sma(bar, series, period, prevma):
    """
    Returns the running simple moving average - avoids sum of series per call.

    Keyword arguments:
    bar     --  current index or location of the value in the series
    series  --  list or tuple of data to average
    period  --  number of values to include in average
    prevma  --  previous simple moving average (n - 1) of the series
    """

    if period < 1:
        raise ValueError("period must be 1 or greater")

    if bar <= 0:
        return series[0]

    elif bar < period:
        return cumulative_sma(bar, series, prevma)

    return prevma + ((series[bar] - series[bar - period]) / float(period))

And the example call and results:

prices = [10, 15, 25, 18, 13, 16]
prevsma = prices[0]   #1st day nothing to average so return itself.
for bar, close in enumerate(prices):
    currentsma = running_sma(bar, prices, 3, prevsma)
    print "Today's 3-day SMA = %.4f" % currentsma
    prevsma = currentsma

------- Results ----------------
Today's 3-day SMA = 10.0000
Today's 3-day SMA = 12.5000
Today's 3-day SMA = 16.6667
Today's 3-day SMA = 19.3333
Today's 3-day SMA = 18.6667
Today's 3-day SMA = 15.6667