## What will we cover?

In this tutorial we will cover.

- What is a
**backtesting strategy**? - How to measure the
**performance**of a backtesting strategy? - How to implement a backtesting strategy with
**Pandas**?

## What is a backtesting strategy?

In a trading strategy backtesting seeks to estimate the performance of a strategy or model if it had been employed during a past period (source).

The way to analyze the performance of a strategy is to compare it with **return**, **volatility**, and **max drawdown**. Other metrics can also be used, but for this tutorial we will use these.

## Step 1: Read data from Yahoo! Finance API with Pandas Datareader

Let’s get started by importing a few libraries and retrieve some data from **Yahoo! Finance API** with **Pandas Datareader**.

```
import pandas as pd
import pandas_datareader as pdr
import datetime as dt
import numpy as np
start = dt.datetime(2010, 1, 1)
data = pdr.get_data_yahoo("AAPL", start)
```

Which will read data for the Apple ticker (AAPL) since 2010.

Below is shown the head of data.

```
High Low Open Close Volume Adj Close
Date
2010-01-04 7.660714 7.585000 7.622500 7.643214 493729600.0 6.583586
2010-01-05 7.699643 7.616071 7.664286 7.656429 601904800.0 6.594968
2010-01-06 7.686786 7.526786 7.656429 7.534643 552160000.0 6.490066
2010-01-07 7.571429 7.466071 7.562500 7.520714 477131200.0 6.478067
2010-01-08 7.571429 7.466429 7.510714 7.570714 447610800.0 6.521136
```

## Step 2: Calculate signals for a simple strategy

The simple strategy we will use is moving average of period 5 and 20.

When the moving average of the Adj Close price of 5 days is above the moving average of 20 days, we go long (buy and hold) otherwise short (sell).

This can be calculated as follows.

```
data['Signal'] = data['Adj Close'].rolling(5).mean() - data['Adj Close'].rolling(20).mean()
data['Position'] = (data['Signal'].apply(np.sign) + 1)/2
```

This results in a Signal line, which is the differences of the two moving averages. When the signal line is positive our position is 1 (buy and hold) otherwise 0 (sell).

```
High Low Open ... Adj Close Signal Position
Date ...
2021-02-26 124.849998 121.199997 122.589996 ... 121.260002 -7.610835 0.0
2021-03-01 127.930000 122.790001 123.750000 ... 127.790001 -7.054179 0.0
2021-03-02 128.720001 125.010002 128.410004 ... 125.120003 -6.761187 0.0
2021-03-03 125.709999 121.839996 124.809998 ... 122.059998 -6.782757 0.0
2021-03-04 123.599998 118.620003 121.750000 ... 120.129997 -6.274249 0.0
```

The reason why we want long to 1 and short to be 0 is for computational reasons, which will be clear soon.

## Step 3: Remove unnecessary data columns and rows

To have a cleaner dataset we will clean it up.

```
data.drop(['High', 'Low', 'Open', 'Volume', 'Close'], axis=1, inplace=True)
data.dropna(inplace=True)
```

Where **drop** removes columns not needed and **dropna** removes rows with **NaN**.

The **inplace=True** is simply to apply it on the DataFrame.

```
Adj Close Signal Position
Date
2010-02-01 5.990476 -0.217986 0.0
2010-02-02 6.025239 -0.252087 0.0
2010-02-03 6.128909 -0.282004 0.0
2010-02-04 5.908031 -0.297447 0.0
2010-02-05 6.012933 -0.253271 0.0
```

## Step 4: Calculate the return of the strategy

To calculate the return we will use log returns as we will see is an advantage.

Then we use the Position, but we shift it by 1, as we assume we first react on a position the day after the signal.

```
data['Log return'] = np.log(data['Adj Close']/data['Adj Close'].shift())
data['Return'] = data['Position'].shift(1)*data['Log return']
```

This result in the following.

```
Adj Close Signal Position Log return Return
Date
2021-02-26 121.260002 -7.610835 0.0 0.002229 0.0
2021-03-01 127.790001 -7.054179 0.0 0.052451 0.0
2021-03-02 125.120003 -6.761187 0.0 -0.021115 -0.0
2021-03-03 122.059998 -6.782757 0.0 -0.024761 -0.0
2021-03-04 120.129997 -6.274249 0.0 -0.015938 -0.0
```

Now the additive advance of log returns comes in handy.

Remember that that we can add up log returns to calculate the final return. For details I refer to this.

Hence, we get that the return can be calculated as follows.

```
data[['Log return', 'Return']].cumsum().apply(np.exp)
```

Resulting in the following.

```
Log return Return
Date
2021-02-26 20.242133 7.29214
2021-03-01 21.332196 7.29214
2021-03-02 20.886489 7.29214
2021-03-03 20.375677 7.29214
2021-03-04 20.053499 7.29214
```

Using a bit calculations.

```
np.exp(data[['Log return', 'Return']].mean()*252)
```

We get.

```
Log return 1.310917
Return 1.196485
dtype: float64
```

Which tells us that the annualized return of our strategy giver 19.6485% return. A buy and hold strategy would give 31.0917%

The natural question is: What did we gain with our strategy?

## Step 5: Evaluating our strategy

If we compute the volatility comparing the buy-and-hold strategy with ours. The volatility of a stock can be calculated in many ways. Here we will use the standard deviation. For other measures refer to **Investpedia**.

```
data[['Log return', 'Return']].std()*252**.5
```

Which gives the annualized standard deviation.

```
Log return 0.283467
Return 0.188044
dtype: float64
```

Hence, the gain from our strategy is a less volatile strategy.

## 12% Investment Solution

Would you like to get 12% in return of your investments?

D. A. Carter promises and shows how his simple investment strategy will deliver that in the book **The 12% Solution**. The book shows how to test this statement by using backtesting.

**Did Carter find a strategy that will consistently beat the market?**

Actually, it is not that hard to use Python to validate his calculations. But we can do better than that. If you want to work smarter than traditional investors then continue to read here.

Hey Rune, thanks for your great work! Have a question about log returns and the „additive advantage“. I don‘t quite get it: Couldn‘t I use returns and cumprod() instead of log returns and cumsum(), and get the same effect? Thx!

Hey Volker.

Sure it is the same. The difference is that sum is faster than product.

If the difference in these problems is big I didn’t try. But it is custom to use sum for the above reason.

Dear Rune. Thanks you for this excelent work. I have a doubt with this sentence

data[‘Position’] = (data[‘Signal’].apply(np.sign) + 1)/2

I undestand that the fucntion np.sign(), return the next:

np.sign(x) -1 if signal >= 0, for so much “data[‘Position’]” will be (-1+1)/2 = 0

np.sign(x) 0 if signal == 0 , for so much “data[‘Position’]” will be (0+1)/2 = 0.5 ¿?

np.sign(x) 1 if signal <= 0, for so much "data['Position']"will be (1+1)/2 = 1

If we are looking for data['Position'] 0 y 1, please explain this sentence to us. Cordial greetings

Let’s try to break it down.

data['Signal'] = data['Adj Close'].rolling(5).mean() - data['Adj Close'].rolling(20).mean()

In signal we have the rolling average of 5 days minus rolling average of 20 days.

We want to use that as a signal.

`data['Position'] = (data['Signal'].apply(np.sign) + 1)/2`

Let’s break that down too.

`data['Signal'].apply(np.sign)`

This gives the sign of the signal: -1 if negative, 1 if positive (0 if 0).

`+ 1`

Says, if -1 we get 0 and 2 if 1.

Then

`/2`

Ensure we have 0 if short and 1 if long.

That is what we try to do in step 2.

Dear Rune

I keep trying to understand these sentences. In this case, I do not understand :

data[[‘Log return’, ‘Return’]].cumsum().apply(np.exp)

np.exp(data[[‘Log return’, ‘Return’]].mean()*252)

¿The last row of the DataFrame data[[‘Log return’, ‘Return’]].cumsum()

Isn’t the final result of the purchase/sales strategy and the strategy of maintaining the position?. ¿For what is necessary to apply the np.exp() function.

I need to understand it to be able to trust the result. Thanks in advance. cordial greetings

Let’s try to break it down.

`data['Return'] = data['Position'].shift(1)*data['Log return']`

Keeps the return of our investment. It keeps the log-return for each day we have invested. The shift is because we need one day to react. We decide after closing hours to hold, buy, or sell. If we hold – we have a 1 in our position. Then we get the log return. otherwise, we have 0 and get nothing (0).

`data[[‘Log return’, ‘Return’]].cumsum().apply(np.exp)`

This then shows what we get if we had the investment all the time (log return) vs our investment strategy (return).

The cumsum() is summing up all log-returns (in both log-return and return) and the we apply np.exp to get the actual return. This is the beauty of calculating with log returns.

The mean()*252 is just used to get an annualized return.

Please feel free to ask any clarifying questions.

/Rune

Thanks Rune

In yours book “Python for Financial Analisys”, this question is is perfectly explained.

In the chapter “Log returns ” we can see 𝑎×𝑏=exp(𝑙𝑜𝑔(𝑎×𝑏))=exp(log(𝑎)+log(𝑏))

Awesome – thanks for sharing

Dear Rune

I keep learning with your script. I have another question that I will thank you for clarifying.

In the statement “data [[‘Log return’, ‘Return’]]. Cumsum (). Apply (np.exp)”, you apply the function np.exp () to the two columns.

I understand that we may use: “cumsum” with “return” and “cumprod” with “log return”, and that “np.exp()”, It is only applicable to logarithms .

Can you confirm that your sentence is correct and what is my mistake? I appreciate your help in advance.

I think you are right.

Let us see.

The log returns are used to make it possible to add returns together.

The np.exp is to transform log-returns to %-returns.

Hence the cumsum().apply(np.exp) is adding log-returns and transforms them to %-return.

If you had %-returns it would be:

cumprod() directly. But this is slower and the standard in finance is to use log-returns in these cases.

Hope it helps,

Rune

Dear Rune:

Computers, Artificial Intelligence, Machine Learning with its algorithms, geopolitics, etc., have so complicated the financial system, which sometimes can’t understand today.

For this reason, to the people who cannot trust in a long way for their investments, the classic strategies do not serve. In my opinion, it is necessary to look for stock portfolio management strategies that allow us to preserve it in the worst circumstance that exists and achieve a benefit that even surpasses the cost of life index.

As I learn this illusive language, I am committed to searching for some strategy with this objective. I would like to count with your authorization to use, adapting them, some sentences of this script.

cordial greetings

I believe you are right. It is very difficult to make a bullet proof strategy. In this tutorial we only focus on backtesting in a classical way.

I am interested to add ML to the strategy in new ways and test it.

Rune, I’ve been stubborn, delete the last query, please. Thanks

It is done. Sorry I was a bit slow to reply.

Dear Rune.

In the statement ‘data[‘Position’] = (data[‘Signal’].apply(np.sign) + 1)/2′, I see the following problem. When ‘signal’ is equal to 0, this statement will return 0.5 in ‘position’.

To make these 0.5 values 0, I have done the following.

# Order number of records with 0.5 in position

data.reset_index(inplace=True)

lista = np.where(data[‘position’] == 0.5)

# Change 0.5 to 0

for each_value in lista:

data.loc[each_value, ‘position’] = 0

What do you think about this? Am I wrong?

Hi Efueyo,

You might be right in the special case of signal == 0.

Thank you for pointing it out.