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+ "# Python for Finance, Part 3: Moving Average Trading Strategy\n",
+ "\n",
+ "In the previous article of this series, we continued to discuss general concepts whicch are fundamental to the design and backtesting of any [quantitative trading strategy](http://www.learndatasci.com/python-finance-part-2-intro-quantitative-trading-strategies/). In detail, we have discussed about \n",
+ "\n",
+ "1. relative and log-returns, their properties, differences and how to use each one,\n",
+ "2. a generic representation of a trading strategy using the normalised asset weights $w_i\\left(t\\right)$ for a set of $N$ \n",
+ " tradable assets and \n",
+ "3. a very simple, yet profitable strategy, the way to represent it and how to calculate its total return.\n",
+ "\n",
+ "If you just found this article, see [Part 1](http://www.learndatasci.com/python-finance-part-yahoo-finance-api-pandas-matplotlib/) and [Part 2](http://www.learndatasci.com/python-finance-part-2-intro-quantitative-trading-strategies/).\n",
+ "\n",
+ "In this article, we will start designing a more complex trading strategy, which will have non-constant weights $w_i\\left(t\\right)$, and thus adapt in some way to the recent behaviour of the price of our assets. \n",
+ "\n",
+ "We will again assume we have a universe of just 3 tradable assets, the Apple and Microsoft stocks (with tickers **AAPL** and **MSFT** respectively) and the S&P 500 Index (ticker **^GSPC**).\n",
+ "\n",
+ "As a reminder, the dataframe containing the three \"cleaned\" price timeseries has the following format:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
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+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " AAPL | \n",
+ " MSFT | \n",
+ " ^GSPC | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 2000-01-03 | \n",
+ " 3.625643 | \n",
+ " 39.334630 | \n",
+ " 1455.219971 | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-04 | \n",
+ " 3.319964 | \n",
+ " 38.005900 | \n",
+ " 1399.420044 | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-05 | \n",
+ " 3.368548 | \n",
+ " 38.406628 | \n",
+ " 1402.109985 | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-06 | \n",
+ " 3.077039 | \n",
+ " 37.120080 | \n",
+ " 1403.449951 | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-07 | \n",
+ " 3.222794 | \n",
+ " 37.605172 | \n",
+ " 1441.469971 | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-10 | \n",
+ " 3.166112 | \n",
+ " 37.879354 | \n",
+ " 1457.599976 | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-11 | \n",
+ " 3.004162 | \n",
+ " 36.909170 | \n",
+ " 1438.560059 | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-12 | \n",
+ " 2.823993 | \n",
+ " 35.706986 | \n",
+ " 1432.250000 | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-13 | \n",
+ " 3.133722 | \n",
+ " 36.381897 | \n",
+ " 1449.680054 | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-14 | \n",
+ " 3.253159 | \n",
+ " 37.879354 | \n",
+ " 1465.150024 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " AAPL | \n",
+ " MSFT | \n",
+ " ^GSPC | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 2000-01-03 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-04 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ "
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+ " \n",
+ " | 2000-01-05 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-06 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-07 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-10 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-11 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-12 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-13 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-14 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-17 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-18 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-19 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-20 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ "
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+ " \n",
+ " | 2000-01-21 | \n",
+ " NaN | \n",
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+ " NaN | \n",
+ "
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+ " \n",
+ " | 2000-01-24 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ "
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+ " \n",
+ " | 2000-01-25 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-26 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-27 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ "
\n",
+ " \n",
+ " | 2000-01-28 | \n",
+ " 3.342434 | \n",
+ " 36.389278 | \n",
+ " 1429.120007 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " AAPL | \n",
+ " MSFT | \n",
+ " ^GSPC | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 2016-12-26 | \n",
+ " 110.958205 | \n",
+ " 58.418182 | \n",
+ " 2176.628791 | \n",
+ "
\n",
+ " \n",
+ " | 2016-12-27 | \n",
+ " 111.047874 | \n",
+ " 58.476117 | \n",
+ " 2177.500190 | \n",
+ "
\n",
+ " \n",
+ " | 2016-12-28 | \n",
+ " 111.140589 | \n",
+ " 58.532936 | \n",
+ " 2178.244490 | \n",
+ "
\n",
+ " \n",
+ " | 2016-12-29 | \n",
+ " 111.233698 | \n",
+ " 58.586112 | \n",
+ " 2178.879189 | \n",
+ "
\n",
+ " \n",
+ " | 2016-12-30 | \n",
+ " 111.315270 | \n",
+ " 58.635267 | \n",
+ " 2179.426990 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
![](\"http://www.learndatasci.com/wp-content/uploads/2017/07/Moving-Average-Price-Crossover-Illustration.png\")
"
+ ]
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+ "How is this translated to the framework described in our previous article about the weights $w\\left(t\\right)$? \n",
+ "\n",
+ "Well for this strategy it is pretty straghtforward. All we need is to have a long position, i.e. $w_i\\left(t\\right)$ >0, as long as the price timeseries is above the EMA timeseries and a short position, i.e. $w_i\\left(t\\right)$ < 0, as long as the price timeseries is below the EMA timeseries. \n",
+ "\n",
+ "Since, at this point, we are not interested yet in position sizing, we will assume that we use all our funds available to trade asset $i$. We will also assume that our funds are split equally across all $3$ assets (MSFT, AAPL and ^GSPC).\n",
+ "\n",
+ "Based on these assumptions, our strategy for each of the assets $i, i = 1, \\ldots, 3$ can be translated as follows:\n",
+ "\n",
+ "+ Go long condition: If $p_i\\left(t\\right) > e_i\\left(t\\right)$, then $w_i\\left(t\\right) = \\frac{1}{3}$\n",
+ "+ Go short condition: If $p_i\\left(t\\right) < e_i\\left(t\\right)$, then $w_i\\left(t\\right) = -\\frac{1}{3}$\n",
+ "\n",
+ "Whenever, the trade conditions are satisfied, the weights are $\\frac{1}{3}$ because $\\frac{1}{3}$ of the total funds are assigned to each asset and whenever we are long or short, all of the available funds are invested.\n",
+ "\n",
+ "How is this implemented in Python? The trick is to take the sign of the difference between then price $p_i\\left(t\\right)$ and the EMA $e_i\\left(t\\right)$."
+ ]
+ },
+ {
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