Sunday, August 08, 2010

Portfolio Performance for July 2010

One thing I've noticed in trading systems over the years is the observer effect. Typically, when a thoroughly backtested system fails...the trader will dismiss the system as being too optimized.

You never hear about the observer effect with real-time trading of the system. That is probably the most difficult aspect of developing systems. Just the mere fact of participating in the price pattern you've discovered changes the price pattern. Despite how small a fish you may be in the market.

All we can hope for as system traders is finding an edge that is large enough to accommodate the increased order flow. So, when we jump in and reduce the edge...there is still enough leftover for us to be profitable. I guess, that is why I've always traded very long-term systems. And probably why I still lack confidence in this new short-term mean-reversion system.

Moving on...

July was an excellent month for the market. The portfolio was trounced. But, still finished the month with another positive number. This marks the second month trading the new system.

Adding a new chart to the reporting: Investment Levels. This reflects the amount of capital that TaylorTree is invested at the end of the month. As you can see, when the portfolio is less than 100% invested in the market and the market has a month like this is extremely difficult to beat it. Cash drag kills you when the market turns around.
TaylorTree Investment Levels as of 07/2010

The picture above of the alligator is from our stay at The Retreat at Artesian Lakes located just outside Cleveland, TX. They had several cabins overlooking the lakes. Step out on your front porch and this 6ft alligator would come swimming up - day or night.

Later Trades,


Saturday, August 07, 2010

New Books

Received 2 books today:

I first heard about John Allspaw from his excellent slides, Ops Meta-Metrics. When I found out he had a book covering capacity planning...well, had to buy it.

Jeffrey MA was the the basis for the main character in the fun book, Bringing Down the House. I'm a stats any book covering stats and business is a must-read for yours truly.


Sunday, August 01, 2010

Exponential Moving Average (EMA)

Now that we've tackled Running Simple Moving Averages (SMA)...let's move on to Exponential Moving Averages (EMA). You may wonder why we're not covering Running Exponential Moving Averages? The default formula for EMA is the running method - so we're already covered.

Check out the posts below to understand the background on Exponential Moving Averages (EMA) and their calculation. Be careful with using EMAs in your backtesting. Or any of these running type of indicators. Since all of them require a starting value. If that starting value changes - your signals change. Which can happen if you switch price quote providers that have different history requirements. Should not be a big deal but something to be aware of.

Let's begin. We need to calculate our smoothing factor for the time series. Typical use in technical analysis is:
\( \alpha = 2.0 / (periods + 1.0) \)

We can use any value between 0 & 1 for the smoothing factor. Closer to one is less smooth and places greater weight on the more recent values. Use a value of 1 and you get the most recent value back. Closer to zero is more smooth and places greater weight on the older values.

Now, the formula for an EMA given our smoothing factor:
\( EMA_{today} = EMA_{yesterday} + \alpha(price_{today} - EMA_{yesterday}) \)

Coding in Python we get:
def ema(bar, series, period, prevma, smoothing=None):
    '''Returns the Exponential Moving Average of a series.

    Keyword arguments:
    bar         -- currrent index or location of the series
    series      -- series of values to be averaged
    period      -- number of values in the series to average
    prevma      -- previous exponential moving average
    smoothing   -- smoothing factor to use in the series.
        valid values: between 0 & 1.
        default: None - which then uses formula = 2.0 / (period + 1.0)
        closer to 1 to gives greater weight to recent values - less smooth
        closer to 0 gives greater weight to older values -- more smooth
    if period < 1:
        raise ValueError("period must be 1 or greater")

    if smoothing:
        if (smoothing < 0) or (smoothing > 1.0):
            raise ValueError("smoothing must be between 0 and 1")

        smoothing = 2.0 / (period + 1.0)

    if bar <= 0:
        return series[0]

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

    return prevma + smoothing * (series[bar] - prevma)

def cumulative_sma(bar, series, prevma):
    Returns the cumulative or unweighted simple moving average.
    Avoids averaging the entire series on each 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))

Example call and results using the typical smoothing factor of 2 / (period + 1):
prices = [32.47, 32.70, 32.77, 33.11, 33.25, 33.23, 33.23, 33.0, 33.04, 33.21]
period = 5   #number of bars to average
prevsma = prevema = prices[0]   #1st day nothing to average

for bar, close in enumerate(prices):
    currentema = ema(bar, prices, period, prevema, smoothing=None)

    #running_sma defined in simple moving average blog post
    currentsma = running_sma(bar, prices, period, prevsma)

    print "Day %02d Value=%.2f %i-bar SMA=%f and EMA=%f" % (bar + 1, close, period, currentsma, currentema)
    prevema = currentema
    prevsma = currentsma

Results of call:

Day 01 Value=32.47 5-day SMA=32.470000 and EMA=32.470000
Day 02 Value=32.70 5-day SMA=32.585000 and EMA=32.585000
Day 03 Value=32.77 5-day SMA=32.646667 and EMA=32.646667
Day 04 Value=33.11 5-day SMA=32.762500 and EMA=32.762500
Day 05 Value=33.25 5-day SMA=32.860000 and EMA=32.860000
Day 06 Value=33.23 5-day SMA=33.012000 and EMA=32.983333
Day 07 Value=33.23 5-day SMA=33.118000 and EMA=33.065556
Day 08 Value=33.00 5-day SMA=33.164000 and EMA=33.043704
Day 09 Value=33.04 5-day SMA=33.150000 and EMA=33.042469
Day 10 Value=33.21 5-day SMA=33.142000 and EMA=33.098313