# Lesson 13

## for Loops¶

This lesson covers:

• for loops
• Nested loops

### Problem: Basic For Loops¶

Construct a for loop to sum the numbers between 1 and N for any N. A for loop that does nothing can be written:

n = 10
for i in range(n):
pass

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### Problem: Compute a compound return¶

The compound return on a bond that pays interest annually at rate r is given by $cr_{t}=\prod_{i=1}^{T}(1+r)=(1+r)^{T}$. Use a for loop compute the total return for £100 invested today for $1,2,\ldots,10$ years. Store this variable in a 10 by 1 vector cr.

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### Problem: Simulate a random walk¶

(Pseudo) Normal random variables can be simulated using the command np.random.standard_normal(shape) where shape is a tuple (or a scalar) containing the dimensions of the desired random numbers. Simulate 100 normals in a 100 by 1 vector and name the result e. Initialize a vector p containing zeros using the function zeros. Add the 1st element of e to the first element of p. Use a for loop to simulate a process $y_{i}=y_{i-1}+e_{i}$. When finished plot the results using

%matplotlib inline

import matplotlib.pyplot as plt
plt.rc('figure', figsize=(16,6))

plt.plot(y)

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### Problem: Nested Loops¶

Begin by loading momentum data used in an earlier lesson. Compute a 22-day moving-window standard deviation for each of the columns. Store the value at the end of the window.

When finished, make sure that std_dev is a DataFrame and plot the annualized percentage standard deviations using:

ann_std_dev = 100 * np.sqrt(252) * std_dev
ann_std_dev.plot()

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# Setup: Load the momentum data

import pandas as pd
momentum = pd.read_csv("data/momentum.csv", index_col="date", parse_dates=True)
momentum = momentum / 100  # Convert to numeric values from percentages

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### Exercises¶

#### Exercise¶

1. Simulate a 1000 by 10 matrix consisting of 10 standard random walks using both nested loops and np.cumsum.
2. Plot the results.

Question to think about

If you rerun the code in this Exercise, do the results change? Why?

#### Exercise: Compute Drawdowns¶

Using the momentum data, compute the maximum drawdown over all 22-day consecutive periods defined as the smallest cumulative produce of the gross return (1+r) for 1, 2, .., 22 days.

Finally, compute the mean drawdown for each of the portfolios.

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