import numpy as np
import pandas as pd
import matplotlib.pyplot as plt


# We loaded necessary packages.


# we use seaborn style for default plotting settings
plt.style.use('seaborn-v0_8')


pd.set_option('display.max_columns', 20)
pd.set_option('display.width', 120)

# the following is for making plots a little larger and consistent.
plt.rcParams['figure.figsize'] = (10, 6)
plt.rcParams['axes.titlesize'] = 13
plt.rcParams['axes.labelsize'] = 11
plt.rcParams['legend.fontsize'] = 10

# Loading the file to a pandas DataFrame named raw. the second line shows just the first 5 rows so we can check the structure. 

raw = pd.read_pickle('stk1999.pkl')
raw.head(10)

#check the type again for raw to make surte it is loaded as a DataFrame. 
print(type(raw))

#How many columns and rows are there in the data? 
print(raw.shape)
print(raw.columns)


#a detailed summary to see each columns information and types. 
raw.info()

<class 'pandas.core.frame.DataFrame'>
(526609, 6)
Index(['Symbol', 'Open', 'High', 'Low', 'Close', 'Volume'], dtype='object')
<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 526609 entries, 1999-01-01 to 1999-12-31
Data columns (total 6 columns):
 #   Column  Non-Null Count   Dtype  
---  ------  --------------   -----  
 0   Symbol  526609 non-null  object 
 1   Open    526609 non-null  float64
 2   High    526609 non-null  float64
 3   Low     526609 non-null  float64
 4   Close   526609 non-null  float64
 5   Volume  526609 non-null  int64  
dtypes: float64(4), int64(1), object(1)
memory usage: 28.1+ MB

#this is just to see the date format
print(raw.index[:5])
print(raw.index[-5:])


#What are the unique symbols in the data? 
print(raw['Symbol'].unique())

DatetimeIndex(['1999-01-01', '1999-01-01', '1999-01-01', '1999-01-01', '1999-01-01'], dtype='datetime64[ns]', name='Date', freq=None)
DatetimeIndex(['1999-12-31', '1999-12-31', '1999-12-31', '1999-12-31', '1999-12-31'], dtype='datetime64[ns]', name='Date', freq=None)
['ACU' 'ACY' 'AE' ... 'A' 'TDY' 'CCZ']

# Since we will be working with MSFT and SPY. I just wanted to confirm how many times they occur in the data. 

print((raw['Symbol'] == 'MSFT').sum())
print((raw['Symbol'] == 'SPY').sum())

261
261

#extract our target tickers and keep only the columns that we need which is the closing price column 
data_1999 = raw[raw['Symbol'].isin(['MSFT', 'SPY'])].copy()
data_1999 = data_1999[['Symbol', 'Close']]

data_1999.head()

#right now we only have MSFT and SPY after these lines

#we will reshape the data so that we have one column for MSFT and one column for SPY.
#I will then sort the data by date just to be sure that everything is ordrered correctly. 
prices = data_1999.pivot_table(index=data_1999.index, columns='Symbol', values='Close')
prices = prices.sort_index()
prices.head()

#removing any missing rows so that both tickers will line up on the same trading day
prices = prices.dropna().copy()

print(prices.shape)
prices.head()

(261, 2)

#This is to show you the final DataFrame that we will perform our calcualtions on. index start and end dates are shown and the table end is printed again for your reference. 

print(prices.index.min())
print(prices.index.max())
print(prices.columns)
prices.tail()

1999-01-01 00:00:00
1999-12-31 00:00:00
Index(['MSFT', 'SPY'], dtype='object', name='Symbol')

#create a new copy of prices as macd data. 

macd_data = prices.copy()


# this is the core of this strategy. My assumption is that MACD(5,10) = EMA(5) - EMA(10)
# the positions are +1 if MACD is higher than zero adn -1 otherwise 


#5 and 10 day EMAs are calcualted here on Microsoft. I used pandas ewm() object which calculates EMA. span =5 for 5 days, 10 for 10 days.
macd_data['EMA_5'] = macd_data['MSFT'].ewm(span=5, adjust=False).mean()
macd_data['EMA_10'] = macd_data['MSFT'].ewm(span=10, adjust=False).mean()



#MACD(5,10) is the difference between the two EMAs
macd_data['MACD'] = macd_data['EMA_5'] - macd_data['EMA_10']


macd_data.head(10)

# Let's see if these values make sense. 5 day EMA should be more responsive and MACD should be the difference.

macd_data[['MSFT', 'EMA_5', 'EMA_10', 'MACD']].head(15) 


#Everyhting looks good for now.

# For strategy one, we will go long (+1) when MACD > 0, short (-1) otherwise

#this creates the +1 and -1 positions in a new column. 
macd_data['pos_s1'] = np.where(macd_data['MACD'] > 0, 1, -1)


# Close all the positions at the end of 1999
macd_data.iloc[-1, macd_data.columns.get_loc('pos_s1')] = 0

macd_data[['MSFT', 'EMA_5', 'EMA_10', 'MACD', 'pos_s1']].head(15)

# check the tail and make sure that the positions are indeed closed at the end. 

macd_data[['MSFT', 'MACD', 'pos_s1']].tail(10)

# this counts how many times the position changes from long to short and vice versa.
# this will tell us how active our strategy is


macd_data['trade_s1'] = macd_data['pos_s1'].diff().fillna(0)
num_changes_s1 = (macd_data['trade_s1'] != 0).sum()

print("Number of position changes in Strategy 1:", num_changes_s1)

Number of position changes in Strategy 1: 22

#compute daily MSFT returns
macd_data['ret_msft'] = macd_data['MSFT'].pct_change()


#  if yesterday’s position was 1, strategy return will be MSFT return today
#if yesterdays position was -1, strategy return will be the negative of MSFT return today becasue we are using yesterday's signal to trade.
macd_data['strategy1_ret'] = macd_data['pos_s1'].shift(1) * macd_data['ret_msft']


#this replaces missing first row return with 0. 
macd_data['strategy1_ret'] = macd_data['strategy1_ret'].fillna(0)


#this creates the buy and hold return which we can compare later to our return.
macd_data['buyhold_ret'] = macd_data['ret_msft'].fillna(0)

macd_data[['MSFT', 'pos_s1', 'ret_msft', 'strategy1_ret', 'buyhold_ret']].head(10)



# so in the final table, ret_msft is the daily percentage return of MSFT
# strategy1_ret is our strategy’s daily return
# buyhold_ret is the benchmark return on MSFT

# this section will turn daily returns to cumultive returns. 
#so if it starts at 1 and ends at 1.20, it means that $1 grows to $1.20 which represents 20% total return. 
#we will create cumulative performaces of both to compare easily.

macd_data['cum_buyhold'] = (1 + macd_data['buyhold_ret']).cumprod()
macd_data['cum_strategy1'] = (1 + macd_data['strategy1_ret']).cumprod()


macd_data[['cum_buyhold', 'cum_strategy1']].head(10)

# Here are the ending values for both strategies. 


print("Final buy-and-hold value:", macd_data['cum_buyhold'].iloc[-1])
print("Final Strategy 1 value:", macd_data['cum_strategy1'].iloc[-1])

Final buy-and-hold value: 1.6835866524384984
Final Strategy 1 value: 1.333540699321843

#MSFT price with EMA(5) and EMA(10), raw inputs for the strategy 

plt.figure(figsize=(10, 6))
plt.plot(macd_data.index, macd_data['MSFT'], label='MSFT')
plt.plot(macd_data.index, macd_data['EMA_5'], label='EMA_5')
plt.plot(macd_data.index, macd_data['EMA_10'], label='EMA_10')

plt.title('MSFT Price with EMA(5) and EMA(10) in 1999')
plt.xlabel('Date')
plt.ylabel('Price')
plt.legend()
plt.show()

#this shows how the strategy flips over the position over time. We can easily see when we are long and short and for how long. 

fig, ax1 = plt.subplots(figsize=(10, 6))

# Left axis shows the price and EMAs
ax1.plot(macd_data.index, macd_data['MSFT'], label='MSFT')
ax1.plot(macd_data.index, macd_data['EMA_5'], label='EMA_5')
ax1.plot(macd_data.index, macd_data['EMA_10'], label='EMA_10')
ax1.set_xlabel('Date')
ax1.set_ylabel('Price')

# Right axis shows the postition, which oscillates between -1 and 1 as seen below.
ax2 = ax1.twinx()
ax2.plot(macd_data.index, macd_data['pos_s1'], label='Position', linestyle='--')
ax2.set_ylabel('Position')
ax2.set_ylim(-1.1, 1.1)

#combining the legends 
lines1, labels1 = ax1.get_legend_handles_labels()
lines2, labels2 = ax2.get_legend_handles_labels()
ax1.legend(lines1 + lines2, labels1 + labels2, loc='upper left')

plt.title('MSFT, EMA(5), EMA(10), and Strategy 1 Position')
plt.show()

# we just translate what we have found in cumulative performance part into a graph. 

plt.figure(figsize=(10, 6))
plt.plot(macd_data.index, macd_data['cum_buyhold'], label='Buy-and-Hold MSFT')
plt.plot(macd_data.index, macd_data['cum_strategy1'], label='Strategy 1: MACD(5,10)')

plt.title('Performance of MSFT and Strategy 1 Over Time')
plt.xlabel('Date')
plt.ylabel('Cumulative Value')
plt.legend()
plt.show()

# This highlights the short periods, which may help visually explain where the strategy differs from buy and hold.


plt.figure(figsize=(10, 6))
plt.plot(macd_data.index, macd_data['cum_buyhold'], label='Buy-and-Hold MSFT')
plt.plot(macd_data.index, macd_data['cum_strategy1'], label='Strategy 1: MACD(5,10)')



# Shade periods where the strategy is short 
short_mask = macd_data['pos_s1'] == -1
plt.fill_between(
    macd_data.index,
    macd_data['cum_buyhold'].min(),
    macd_data[['cum_buyhold', 'cum_strategy1']].max().max(),
    where=short_mask,
    alpha=0.15
)






plt.title('Performance of MSFT and Strategy 1 Over Time')
plt.xlabel('Date')
plt.ylabel('Cumulative Value')
plt.legend()
plt.show()

# Computing Strategy 1 running maximum in this line 
macd_data['cummax_strategy1'] = macd_data['cum_strategy1'].cummax()

# drawdown for Strategy 1
macd_data['drawdown_strategy1'] = (
    macd_data['cum_strategy1'] / macd_data['cummax_strategy1'] - 1
)



# maximum drawdown date for Strategy 1
max_dd_date_s1 = macd_data['drawdown_strategy1'].idxmin()
max_dd_value_s1 = macd_data['drawdown_strategy1'].min()

# this will give us the graph that is similar to 16-7 in the textbook. 
# equity is the cumualtive value of strategy 1 
# cummax is the running maximum of that equity curve 
#we will pinpoint the max drawdown date with a vertical line


plt.figure(figsize=(10, 6))
plt.plot(macd_data.index, macd_data['cum_strategy1'], label='equity')
plt.plot(macd_data.index, macd_data['cummax_strategy1'], label='cummax')
plt.axvline(max_dd_date_s1, linestyle='--', label='max drawdown date')



plt.title('Strategy 1 Equity Curve and Running Maximum')
plt.xlabel('Date')
plt.ylabel('Cumulative Value')
plt.legend()
plt.show()



print("Strategy 1 max drawdown date:", max_dd_date_s1)
print("Strategy 1 max drawdown:", max_dd_value_s1)

Strategy 1 max drawdown date: 1999-06-16 00:00:00
Strategy 1 max drawdown: -0.21656153771907927

# MSFT will be taking the same signal as Strategy 1

# SPY takes the opposite signal
macd_data['pos_s2_msft'] = macd_data['pos_s1']
macd_data['pos_s2_spy'] = -macd_data['pos_s1']

macd_data[['MSFT', 'SPY', 'MACD', 'pos_s1', 'pos_s2_msft', 'pos_s2_spy']].head(15)

#check tail to see if the positions are closed at the year end. 
macd_data[['MACD', 'pos_s2_msft', 'pos_s2_spy']].tail(10)

# This counts signal changes for the paired strategy as we did in strategy 1.

# Since Strategy 2 is driven by the same MACD signal as Strategy 1, this number should match Strategy 1.


macd_data['trade_s2'] = macd_data['pos_s2_msft'].diff().fillna(0)

num_changes_s2 = (macd_data['trade_s2'] != 0).sum()

print("Number of position changes in Strategy 2:", num_changes_s2)

Number of position changes in Strategy 2: 22

#   daily SPY returns
macd_data['ret_spy'] = macd_data['SPY'].pct_change()


# Strategy 2 daily return

# we are using yesterday's paired positions same as strategy 1. 

# we are assigning +0.5 weight on one asset, -0.5 weight on the other asset and same dollar size on both legs
# So the whole strategy is scaled to a net starting capital of 1.0.


macd_data['strategy2_ret'] = (
    0.5 * macd_data['pos_s2_msft'].shift(1) * macd_data['ret_msft']
    + 0.5 * macd_data['pos_s2_spy'].shift(1) * macd_data['ret_spy']
)

# this replaces missing first row return with 0
macd_data['strategy2_ret'] = macd_data['strategy2_ret'].fillna(0)



macd_data[['ret_msft', 'ret_spy', 'pos_s2_msft', 'pos_s2_spy', 'strategy2_ret']].head(10)

#This turns Strategy 2 daily returns into a cumulative equity curve, same as we did for Strategy 1.
macd_data['cum_strategy2'] = (1 + macd_data['strategy2_ret']).cumprod()


macd_data[['cum_strategy2']].head(10)

# Final cumulative value of Strategy 2
print("Final Strategy 2 value:", macd_data['cum_strategy2'].iloc[-1])

Final Strategy 2 value: 1.286125708646444

#ending values for :
#buy and hold MSFT
# MACD on MSFT alone
# paired MACD strategy with SPY 

print("Final buy and hold value:", macd_data['cum_buyhold'].iloc[-1])
print("Final Strategy 1 value:", macd_data['cum_strategy1'].iloc[-1])
print("Final Strategy 2 value:", macd_data['cum_strategy2'].iloc[-1])

Final buy and hold value: 1.6835866524384984
Final Strategy 1 value: 1.333540699321843
Final Strategy 2 value: 1.286125708646444

#diagrams similar to, 15-3, 16-7, 16-5

# So in this block we will makem thses charts:
#Performance comparison chart
#Strategy 2 equity curve with cumulative maximum
#Drawdown chart

plt.figure(figsize=(10, 6))
plt.plot(macd_data.index, macd_data['cum_buyhold'], label='Buy-and-Hold MSFT')
plt.plot(macd_data.index, macd_data['cum_strategy2'], label='Strategy 2: MSFT-SPY Pair')

plt.title('Performance of MSFT and Strategy 2 Over Time')
plt.xlabel('Date')
plt.ylabel('Cumulative Value')
plt.legend()
plt.show()

# cumulative strategy2 is the actual equity curve, while the cummax strategy2 is the running peak so far.
#When the equity curve falls below the cumulative max, the strategy is in drawdown.



macd_data['cummax_strategy2'] = macd_data['cum_strategy2'].cummax()

plt.figure(figsize=(10, 6))
plt.plot(macd_data.index, macd_data['cum_strategy2'], label='equity')
plt.plot(macd_data.index, macd_data['cummax_strategy2'], label='cummax')

plt.title('Strategy 2 Equity Curve and Running Maximum')
plt.xlabel('Date')
plt.ylabel('Cumulative Value')
plt.legend()
plt.show()

# we will compute drawdown as a percentage below the running maximum

# Here 0 means the strategy is at a new peak.Negative values mean the strategy is below its previous peak and the most negative point is the maximum drawdown.

macd_data['drawdown_strategy2'] = (
    macd_data['cum_strategy2'] / macd_data['cummax_strategy2'] - 1
)

plt.figure(figsize=(10, 6))
plt.plot(macd_data.index, macd_data['drawdown_strategy2'], label='Drawdown')

plt.title('Strategy 2 Drawdown Over Time')
plt.xlabel('Date')
plt.ylabel('Drawdown')
plt.legend()
plt.show()

# here we find the date of maximum drawdown
max_dd_date = macd_data['drawdown_strategy2'].idxmin()
max_dd_value = macd_data['drawdown_strategy2'].min()

plt.figure(figsize=(10, 6))
plt.plot(macd_data.index, macd_data['cum_strategy2'], label='equity')
plt.plot(macd_data.index, macd_data['cummax_strategy2'], label='cummax')
plt.axvline(max_dd_date, linestyle='--', label='max drawdown date')

plt.title('Strategy 2 Equity Curve with Maximum Drawdown Date')
plt.xlabel('Date')
plt.ylabel('Cumulative Value')
plt.legend()
plt.show()

print("Max drawdown date:", max_dd_date)
print("Max drawdown:", max_dd_value)

Max drawdown date: 1999-06-16 00:00:00
Max drawdown: -0.08934745065196747

# with min(), we find the most negative drawdown, idxmin() finds the date where that worst drawdown happens
#So overall this gives us the deepest loss from a previous peak.


max_drawdown = macd_data['drawdown_strategy2'].min()
max_drawdown_date = macd_data['drawdown_strategy2'].idxmin()

print("Maximum drawdown:", max_drawdown)
print("Maximum drawdown date:", max_drawdown_date)

Maximum drawdown: -0.08934745065196747
Maximum drawdown date: 1999-06-16 00:00:00

# wjat is the peak level just before the max drawdown? 

peak_value_before_dd = macd_data.loc[:max_drawdown_date, 'cummax_strategy2'].iloc[-1]

# Find the first date where the strategy reached that peak\
# That date is the start of the max drawdown period

drawdown_start_date = macd_data.loc[:max_drawdown_date, 'cum_strategy2'][
    macd_data.loc[:max_drawdown_date, 'cum_strategy2'] == peak_value_before_dd
].index[0]

print("Drawdown start date:", drawdown_start_date)

Drawdown start date: 1999-05-14 00:00:00

# This is where we check whether the equity curve ever climbs back to the old peak after the worst drawdown if yes, we record the first recovery date, if not, recovery is None



recovery_candidates = macd_data.loc[max_drawdown_date:, 'cum_strategy2']
recovery_candidates = recovery_candidates[recovery_candidates >= peak_value_before_dd]

if len(recovery_candidates) > 0:
    recovery_date = recovery_candidates.index[0]
else:
    recovery_date = None

print("Recovery date:", recovery_date)

Recovery date: 1999-08-24 00:00:00

# Drawdown duration in trading days. 
# we wwant to see how many days the drawdown lasted, from the peak date to the recovery date. 

if recovery_date is not None:
    drawdown_duration = macd_data.loc[drawdown_start_date:recovery_date].shape[0] - 1
else:
    drawdown_duration = macd_data.loc[drawdown_start_date:].shape[0] - 1

print("Drawdown duration (trading days):", drawdown_duration)

Drawdown duration (trading days): 72

# we put everything that we calculated in a table. 

drawdown_summary = pd.DataFrame({
    'Metric': [
        'Maximum Drawdown',
        'Max Drawdown Date',
        'Drawdown Start Date',
        'Recovery Date',
        'Drawdown Duration (days)'
    ],
    'Value': [
        max_drawdown,
        max_drawdown_date,
        drawdown_start_date,
        recovery_date,
        drawdown_duration
    ]
})



drawdown_summary

#How many trading days do we have in this sample? 


n_days = len(macd_data)


# Annualization factor for daily data
annual_factor = 252


# Maximum drawdown for buy and hold and Strategy 1, we have already computed it for Strategy 2 so we don;t need to do it again. 


macd_data['cummax_buyhold'] = macd_data['cum_buyhold'].cummax()
macd_data['drawdown_buyhold'] = macd_data['cum_buyhold'] / macd_data['cummax_buyhold'] - 1

macd_data['cummax_strategy1'] = macd_data['cum_strategy1'].cummax()
macd_data['drawdown_strategy1'] = macd_data['cum_strategy1'] / macd_data['cummax_strategy1'] - 1

summary_table = pd.DataFrame({
    'Final Value': [
        macd_data['cum_buyhold'].iloc[-1],
        macd_data['cum_strategy1'].iloc[-1],
        macd_data['cum_strategy2'].iloc[-1]
    ],
    'Total Return': [
        macd_data['cum_buyhold'].iloc[-1] - 1,
        
        macd_data['cum_strategy1'].iloc[-1] - 1,
        macd_data['cum_strategy2'].iloc[-1] - 1
    ],

    
    'Annualized Return': [
        macd_data['cum_buyhold'].iloc[-1] ** (annual_factor / n_days) - 1,
        
        macd_data['cum_strategy1'].iloc[-1] ** (annual_factor / n_days) - 1,
        macd_data['cum_strategy2'].iloc[-1] ** (annual_factor / n_days) - 1
    ],



    
    'Annualized Volatility': [
        macd_data['buyhold_ret'].std() * np.sqrt(annual_factor),
        macd_data['strategy1_ret'].std() * np.sqrt(annual_factor),
        macd_data['strategy2_ret'].std() * np.sqrt(annual_factor)
        
    ],

    
    'Sharpe-like Ratio': [
        macd_data['buyhold_ret'].mean() / macd_data['buyhold_ret'].std() * np.sqrt(annual_factor),
        macd_data['strategy1_ret'].mean() / macd_data['strategy1_ret'].std() * np.sqrt(annual_factor),
        macd_data['strategy2_ret'].mean() / macd_data['strategy2_ret'].std() * np.sqrt(annual_factor)
    ],

    
    'Maximum Drawdown': [
        macd_data['drawdown_buyhold'].min(),
        macd_data['drawdown_strategy1'].min(),
        macd_data['drawdown_strategy2'].min()
    ]
}, index=[
    'Buy-and-Hold MSFT',
    'Strategy 1',
    'Strategy 2'
])

summary_table



summary_table_rounded = summary_table.copy()
summary_table_rounded = summary_table_rounded.round(4)

summary_table_rounded

	Symbol	Open	High	Low	Close	Volume
Date
1999-01-01	ACU	2.2500	2.2500	2.2500	2.2500	0
1999-01-01	ACY	8.4400	8.4400	8.4400	8.4400	0
1999-01-01	AE	5.7500	5.7500	5.7500	5.7500	0
1999-01-01	AMS	1.1900	1.1900	1.1900	1.1900	0
1999-01-01	APT	0.5000	0.5000	0.5000	0.5000	0
1999-01-01	AWX	7.0600	7.0600	7.0600	7.0600	0
1999-01-01	BCV	22.7500	22.7500	22.7500	22.7500	0
1999-01-01	BDL	5.0600	5.0600	5.0600	5.0600	0
1999-01-01	BDR	6.6200	6.6200	6.6200	6.6200	0
1999-01-01	BHB	15.8333	15.8333	15.8333	15.8333	0

Symbol	MSFT	SPY
Date
1999-01-01	34.673	123.31
1999-01-04	35.250	123.03
1999-01-05	36.625	124.44
1999-01-06	37.813	127.44
1999-01-07	37.625	126.81

Symbol	MSFT	SPY
Date
1999-01-01	34.673	123.31
1999-01-04	35.250	123.03
1999-01-05	36.625	124.44
1999-01-06	37.813	127.44
1999-01-07	37.625	126.81

Symbol	MSFT	SPY
Date
1999-12-27	59.560	146.28
1999-12-28	58.750	146.19
1999-12-29	58.970	146.81
1999-12-30	58.810	146.63
1999-12-31	58.375	146.88

Symbol	MSFT	SPY	EMA_5	EMA_10	MACD
Date
1999-01-01	34.673	123.31	34.673000	34.673000	0.000000
1999-01-04	35.250	123.03	34.865333	34.777909	0.087424
1999-01-05	36.625	124.44	35.451889	35.113744	0.338145
1999-01-06	37.813	127.44	36.238926	35.604518	0.634408
1999-01-07	37.625	126.81	36.700951	35.971878	0.729073
1999-01-08	37.470	127.75	36.957300	36.244264	0.713037
1999-01-11	36.875	126.53	36.929867	36.358943	0.570924
1999-01-12	35.548	124.25	36.469245	36.211499	0.257746
1999-01-13	35.953	123.38	36.297163	36.164499	0.132664
1999-01-14	35.438	121.22	36.010775	36.032408	-0.021633

1. Import libraries and set plotting style¶

2. Load stk1999.pkl and inspect the data¶

3. Create a clean 1999 closing price table for MSFT and SPY¶

4. Build the MACD(5,10) indicator for MSFT¶

5. Strategy 1¶

6. Backtesting Strategy 1¶

7. Plots - Strategy 1¶

7.1 MSFT with EMA(5) and EMA(10)¶

7.2 MSFT + EMAs + Strategy 1 position¶

7.3 Cumulative performance of Strategy 1 vs buy and hold¶

7.4 Shaded long/short regions to performance chart¶

7.5 Strategy 1 equity and cumulative maximum¶

8. Strategy 2¶

9. Backtesting Strategy 2¶

10. Plots - Strategy 2¶

10.1 Performance comparison chart for Strategy 2¶

10.2 Equity curve and cumulative maximum¶

10.3 Drawdown for Strategy 2¶

10.4 Vertical line at the max drawdown date¶

11. Drawdown statistics¶

11.1 Maximum drawdown value and date¶

11.2 Start date of the max drawdown period¶

11.3 Find the recovery date, if it exists¶

11.4 Drawdown duration in trading days¶

11.5 Put drawdown statistics into a small table¶

12. Summary table of results¶

12.1 Calculate the performance statistics¶

12.2 Summary table¶

Symbol	MSFT	MACD	pos_s1
Date
1999-12-20	56.375	2.526925	1
1999-12-21	57.935	2.536527	1
1999-12-22	58.780	2.516065	1
1999-12-23	58.720	2.343325	1
1999-12-24	58.720	2.107083	1
1999-12-27	59.560	1.977794	1
1999-12-28	58.750	1.664680	1
1999-12-29	58.970	1.426334	1
1999-12-30	58.810	1.185640	1
1999-12-31	58.375	0.916586	0

Symbol	cum_buyhold	cum_strategy1
Date
1999-01-01	1.000000	1.000000
1999-01-04	1.016641	0.983359
1999-01-05	1.056297	1.021717
1999-01-06	1.090560	1.054858
1999-01-07	1.085138	1.049613
1999-01-08	1.080668	1.045289
1999-01-11	1.063508	1.028691
1999-01-12	1.025236	0.991672
1999-01-13	1.036916	1.002970
1999-01-14	1.022063	0.988603

	Metric	Value
0	Maximum Drawdown	-0.089347
1	Max Drawdown Date	1999-06-16 00:00:00
2	Drawdown Start Date	1999-05-14 00:00:00
3	Recovery Date	1999-08-24 00:00:00
4	Drawdown Duration (days)	72

	Final Value	Total Return	Annualized Return	Annualized Volatility	Sharpe-like Ratio	Maximum Drawdown
Buy-and-Hold MSFT	1.6836	0.6836	0.6536	0.3741	1.5308	-0.1969
Strategy 1	1.3335	0.3335	0.3204	0.3752	0.9272	-0.2166
Strategy 2	1.2861	0.2861	0.2750	0.1522	1.6730	-0.0893

Symbol	ret_msft	ret_spy	pos_s2_msft	pos_s2_spy	strategy2_ret
Date
1999-01-01	NaN	NaN	-1	1	0.000000
1999-01-04	0.016641	-0.002271	1	-1	-0.009456
1999-01-05	0.039007	0.011461	1	-1	0.013773
1999-01-06	0.032437	0.024108	1	-1	0.004164
1999-01-07	-0.004972	-0.004944	1	-1	-0.000014
1999-01-08	-0.004120	0.007413	1	-1	-0.005766
1999-01-11	-0.015879	-0.009550	1	-1	-0.003165
1999-01-12	-0.035986	-0.018019	1	-1	-0.008983
1999-01-13	0.011393	-0.007002	1	-1	0.009198
1999-01-14	-0.014324	-0.017507	-1	1	0.001591