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Abstract

-comment"># defining a data frame to store portfolio returns portfolio_strategy_returns = pd.DataFrame() portfolio_bnh_returns = pd.DataFrame()

# buy and hold returns for individual stocs bnh_stock_returns = [] bnh_stock_sharpe = []

# iterating over stocks in the portfolio for stock in portfolio_stocks: data = get_daily_data(stock, start, end)

<span class="hljs-comment"># Calculating daily returns</span>
data[<span class="hljs-string">"bnh_returns"</span>] = np.log(data[<span class="hljs-string">"Close"</span>]/data[<span class="hljs-string">"Close"</span>].shift())

portfolio_strategy_returns[stock] = ma(data,ma1 = <span class="hljs-number">10</span>, ma2 = <span class="hljs-number">25</span>)

bnh_stock_returns.append(get_cumulative_return(data[<span class="hljs-string">"strategy_returns"</span>]))
bnh_stock_sharpe.append(get_annualized_sharpe_ratio(data[<span class="hljs-string">"strategy_returns"</span>]))</pre></div><ul><li>Printing the SMA strategy returns</li></ul><div id="c7fc"><pre><span class="hljs-built_in">print</span>(<span class="hljs-string">"\nSTRATEGY RETURNS ON PORTFOLIO"</span>)

portfolio_strategy_returns["Portfolio_rets"] = portfolio_strategy_returns.mean(axis=1) portfolio_strategy_returns.round(decimals = 4).tail(10)</pre></div><figure id="9d01"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*uI6K6ZXoWxLSwkoaooTerQ.png"><figcaption>STRATEGY RETURNS ON PORTFOLIO</figcaption></figure><ul><li>Calculating cumulative returns and the annualized Sharpe ratio</li></ul><div id="b235"><pre>perf = pd.DataFrame(index=portfolio_stocks,columns=["Cumulative returns","Annualized Sharpe Ratio"])

for i,stock in enumerate(portfolio_stocks): cum_ret = bnh_stock_returns[i] anu_shp = bnh_stock_sharpe[i] perf.loc[stock] = [cum_ret,anu_shp]

perf

Cumulative returns Annualized Sharpe Ratio NVDA 2.375256 1.071783 AAPL 1.176463 1.020626 SNOW -0.110298 -0.068875 KBH 0.839733 0.482885 ENPH 2.455573 0.784543 PDD 2.237751 0.900318 SPY 0.592832 0.886599 QQQ 0.637886 0.746084 IWM 0.213217 0.233466 KWEB 0.549323 0.404803</pre></div><ul><li>Comparing the Stock Cumulative Returns</li></ul><div id="96d8"><pre>perf['Cumulative returns'].plot.bar(title='Cumulative returns')</pre></div><figure id="d303"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*TnGcb1YxZ5ChXCLbcLYqzw.png"><figcaption>Stock Cumulative Returns</figcaption></figure><ul><li>Comparing the Stock Annualized Sharpe Ratio</li></ul><div id="cbb3"><pre>perf['Annualized Sharpe Ratio'].plot.bar(title='Annualized Sharpe Ratio')</pre></div><figure id="9680"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*O8SRFclHvcr36uPp7YuYmw.png"><figcaption>Stock Annualized Sharpe Ratio</figcaption></figure><ul><li>Calculating the stock performance mean value</li></ul><div id="935a"><pre>perf.mean() Cumulative returns 1.096774 Annualized Sharpe Ratio 0.646223 dtype: object</pre></div><ul><li>Calculating the SMA strategy cumulative return and the annualized Sharpe ratio</li></ul><div id="879d"><pre>print("Cumulative returns SMA Strategy :",get_cumulative_return(portfolio_strategy_returns["Portfolio_rets"])) print("Annualized sharpe ratio SMA Strategy :",get_annualized_sharpe_ratio(portfolio_strategy_returns["Portfolio_rets"]))

Cumulative returns SMA Strategy : 1.17530067503038 Annualized sharpe ratio SMA Strategy : 1.2276872946556154</pre></div><ul><li>We can see that the SMA strategy results in ROI ~ 17.5%, and the annualized Sharpe ratio from 1 to 1.99 is considered adequate/good.</li><li>Plotting and comparing the SMA strategy cumulative returns</li></ul><div id="53e3"><pre>import matplotlib.pyplot as plt colors = ['tab:cyan','tab:purple','tab:pink','tab:orange','tab:blue','tab:green','tab:gray','tab:olive','tab:brown','tab:red',"k"] portfolio_strategy_returns.cumsum().plot(figsize=(12,7), title="MOVING AVERAGES STRATEGY CUMULATIVE RETURNS", color=colors) plt.grid()</pre></div><figure id="a158"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*NdXscvvjAMCM_4gaBkdRrA.png"><figcaption>SMA strategy cumulative returns (step 1).</figcaption></figure><ul><li>Let’s move to step 2 by excluding the worst performer SNOW with the lowest cumulative return and the negative annualized Sharpe ratio (a Sharpe ratio less than 1 is considered bad).</li></ul><h2 id="6707">Step 2: Excluding Worst Performers with Lowest Returns</h2><ul><li>Applying the above sequence to the updated portfolio of 9 assets without SNOW</li></ul><div id="e972"><pre># portfolio of stocks portfolio_stocks = ["NVDA","AAPL","KBH","ENPH","PDD","SPY","QQQ","IWM","KWEB"]</pre></div><ul><li>Calculating the stock performance mean value</li></ul><div id="af02"><pre>perf.mean() Cumulative returns 1.300106 Annualized Sharpe Ratio 0.767578 dtype: object</pre></div><ul><li>Calculating the SMA strategy cumulative return and the annualized Sharpe ratio</li></ul><div id="5e92"><pre>print("Cumulative returns SMA Strategy :",get_cumulative_return(portfolio_strategy_returns["Portfolio_rets"])) print("Annualized sharpe ratio SMA Strategy :",get_annualized_sharpe_ratio(portfolio_strategy_returns["Portfolio_rets"]))

Cumula

Options

tive returns SMA Strategy : 1.3001058358012645 Annualized sharpe ratio SMA Strategy : 1.3648948755238106</pre></div><ul><li>We can see that the updated SMA strategy yields ROI ~ 30% and the improved annualized Sharpe ratio of 1.365.</li><li>Plotting and comparing the SMA strategy cumulative returns</li></ul><figure id="ea61"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*dv9mtGZT0-ejzNz-S1X-TA.png"><figcaption>SMA strategy cumulative returns (step 2).</figcaption></figure><ul><li>Let’s move to step 3 by thresholding the poor performers KWEB, IWM and SPY with the cumulative returns <0.6.</li></ul><h2 id="e5df">Step 3: Excluding Poor Performers with Lowest Sharpe Ratio</h2><ul><li>Applying the above sequence to the updated portfolio of 6 assets without SNOW, KWEB, IWM and SPY, viz.</li></ul><div id="e754"><pre># portfolio of stocks portfolio_stocks = ["NVDA","AAPL","KBH","ENPH","PDD","QQQ"]</pre></div><ul><li>Calculating the stock performance mean value</li></ul><div id="cbbb"><pre>perf.mean()

Cumulative returns 1.776673 Annualized Sharpe Ratio 0.936473 dtype: object</pre></div><ul><li>Calculating the SMA strategy cumulative return and the annualized Sharpe ratio</li></ul><div id="8b7d"><pre>print("Cumulative returns SMA Strategy :",get_cumulative_return(portfolio_strategy_returns["Portfolio_rets"])) print("Annualized sharpe ratio SMA Strategy :",get_annualized_sharpe_ratio(portfolio_strategy_returns["Portfolio_rets"]))

Cumulative returns SMA Strategy : 1.7766732115541535 Annualized sharpe ratio SMA Strategy : 1.5475252825461494</pre></div><ul><li>We can see that the updated SMA strategy yields ROI ~ 77.6% and the improved annualized Sharpe ratio of ~1.55 (significantly closer to the very good value of 2 than other two portfolios).</li><li>Plotting and comparing the SMA strategy cumulative returns</li></ul><figure id="6d1f"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*5hH04HJMoUMDBiPchyIV2A.png"><figcaption>SMA strategy cumulative returns (step 3).</figcaption></figure><h2 id="ecc5">Conclusions</h2><ul><li>Here is the visual summary of our three updates towards the optimal portfolio:</li></ul><div id="0b0e"><pre># creating the dataset data = {'Step 1':1.227, 'Step 2':1.365, 'Step 3': 1.547} courses = list(data.keys()) values = list(data.values())

fig = plt.figure(figsize = (10, 5))

# creating the bar plot plt.bar(courses, values, color ='red', width = 0.4)

plt.xlabel("Portfolio Update") plt.ylabel("Annualized Sharpe Ratio") plt.title("Annualized Sharpe Ratio SMA Strategy") plt.show()</pre></div><figure id="296b"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*Fs_UIEwSLNO-u3_Wki1bnw.png"><figcaption>Annualized Sharpe Ratio SMA Strategy</figcaption></figure><div id="fef2"><pre># creating the dataset data = {'Step 1':1.175, 'Step 2':1.300, 'Step 3': 1.776} courses = list(data.keys()) values = list(data.values())

fig = plt.figure(figsize = (10, 5))

# creating the bar plot plt.bar(courses, values, color ='green', width = 0.4)

plt.xlabel("Portfolio Update") plt.ylabel("Cumulative Returns") plt.title("Cumulative Returns SMA Strategy") plt.show()</pre></div><figure id="e5e0"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*jAogfMJTZdnmZaDTNAliyQ.png"><figcaption>Cumulative Returns SMA Strategy</figcaption></figure><ul><li>In summary, this IPO project intended to investigate the ability of proposed SMA portfolio updates to assist investors to make profitable trading decisions.</li><li>Our backtesting experiments show that the proposed workflow can maximize risk-adjusted returns of portfolios while minimizing the number of assets involved in the optimization process.</li><li>Our Road Ahead in Portfolio Management is to combine advanced trading strategies, financial health/risk metrics and stochastic portfolio optimization algorithms into a single framework to optimize the advantages of each.</li></ul><h2 id="cbbc">Explore More</h2><ul><li><a href="https://wp.me/pdMwZd-4Je">Portfolio Optimization of 20 Dividend Growth Stocks</a></li><li><a href="https://wp.me/pdMwZd-4IB">Towards Max(ROI/Risk) Trading</a></li><li><a href="https://wp.me/pdMwZd-371">XOM SMA-EMA-RSI Golden Crosses ‘22</a></li><li><a href="https://wp.me/pdMwZd-7A3">Plotly Dash TA Stock Market App</a></li><li><a href="https://wp.me/pdMwZd-2f2">Bear vs. Bull Portfolio Risk/Return Optimization QC Analysis</a></li><li><a href="https://wp.me/pdMwZd-1D2">Towards min(Risk/Reward) — SeekingAlpha August Bear Market Update</a></li></ul><h2 id="11a3">References</h2><ul><li><a href="https://blog.devgenius.io/algorithmic-trading-backtesting-portfolio-of-stocks-in-python-9be75ce9f232">Algorithmic Trading — Backtesting Portfolio of Stocks in Python</a></li><li><a href="https://readmedium.com/maximizing-profitability-of-moving-average-crossover-trading-strategy-what-moving-averages-to-use-e5cd70085690">Maximizing Profitability of Moving Average Crossover Trading Strategy: What moving averages to use?</a></li><li><a href="https://www.pythonforfinance.net/2017/01/28/optimisation-of-moving-average-crossover-trading-strategy-in-python/">OPTIMIZATION OF MOVING AVERAGE CROSSOVER TRADING STRATEGY IN PYTHON</a></li><li><a href="https://www.investopedia.com/articles/active-trading/052014/how-use-moving-average-buy-stocks.asp">How to Use a Moving Average to Buy Stocks</a></li><li><a href="https://www.investopedia.com/investing/how-renew-and-adjust-your-portfolio/">How To Adjust and Renew Your Portfolio</a></li><li><a href="https://www.youtube.com/watch?v=wJmXMboLE64">How to beat the Market. Momentum and Portfolio Optimization</a></li><li><a href="https://www.fmz.com/lang/en/strategy/439870">Moving Average Crossover Trading Strategy</a></li><li><a href="https://www.quantstart.com/static/ebooks/sat/sample.pdf">Strategy Optimization</a></li></ul><h2 id="9308">Contacts</h2><ul><li><a href="https://newdigitals.org/">Website</a></li><li><a href="https://github.com/alva922">GitHub</a></li><li><a href="https://twitter.com/alzapress">X/Twitter</a></li><li><a href="https://nl.pinterest.com/alexzap922/">Pinterest</a></li><li><a href="https://mastodon.social/@alexzap">Mastodon</a></li><li><a href="https://alva922.tumblr.com/">Tumblr</a></li></ul></article></body>

Striking a Balance between Portfolio Returns & Sharpe Ratio with Three-Step SMA Scenario Testing

This is an investment portfolio optimization (IPO) project aimed at maximizing the risk-adjusted returns of an initial portfolio by resolving a trade-off between expected returns (backtesting) and annualized Sharpe ratio of ad-hoc assets.
Motivation: Why updating your portfolio may be important in helping you achieve your goals.
The simple moving average (SMA) is a widely used technical indicator that plays an important role in fintech since it directly reflects stock fluctuations. However, most studies ignore the parameter settings of the SMA, which leads to underestimation of the potential of the SMA.
That’s why our first step will be to extend the limits of the SMA by scanning over possible combinations of short/long window lengths.
The underlying methodology is based on the implemented SMA trading strategy algorithm in Python (cf. notebook) without portfolio weights involved in the optimization process.
The proposed user-interactive SMA scenario testing workflow consists of the following three steps (see the flowchart below):

Optimizing SMA Window Lengths 5
Identify and exclude worst performers with the lowest cumulative returns while maximizing Returns
Identify and exclude poor performers with the lowest Sharpe ratio (highest risk) and low cumulative returns while examining the condition Max (Return>0 & Sharpe Ratio > 1.0).

If the above condition is not met then we need to change the initial portfolio by using one of popular 3rd party IPO products such as the AI-powered Macroaxis Wealth Optimization Platform.
Conversely, we can consider more advanced trading strategies beyond SMA.

A Thee-Step SMA Scenario Testing Flowchart

Let’s get into the details of the proposed IPO project and figure out how we can make it successful.

Basic Imports, Installations & Settings

Setting the working directory YOURPATH

import os
os.chdir('YOURPATH')    # Set working directory
os. getcwd()

Basic imports & installations

!pip install nsepy, yfinance, statistics

import warnings
warnings.filterwarnings('ignore')

import numpy as np
import pandas as pd
from datetime import datetime as dt
import yfinance as yf
import nsepy
from statistics import mean

Key IPO Functions

Invoking the SMA Backtesting, Cumulative Returns & Sharpe Ratio functions

# get daily data from yfinance
def get_daily_data(symbol, start, end):
    data = yf.download(tickers=symbol, start=start, end=end)
    # data = nsepy.get_history(symbol=symbol, start=start, end=end)
    return data

# moving averages strategy on close price data
def ma(data,ma1,ma2):
    # calculating moving averages
    data['ma_short'] = data['Close'].ewm(span=ma1).mean().shift()
    data['ma_long'] = data['Close'].ewm(span=ma2).mean().shift()

    # creating positions
    # data["position"] = [0]*len(data)
    data['position'] = np.where(data["ma_short"] > data["ma_long"], 1, 0)    
    data["strategy_returns"] = data["bnh_returns"] * data["position"]
    
    # returning strategy returns
    return data["strategy_returns"]

# Cumulative returns function
def get_cumulative_return(df):
    return list(df.cumsum())[-1]

#  Annualized sharpe ratio function
def get_annualized_sharpe_ratio(df):
    return 252**(1/2) * (df.mean() / df.std())

Step 1: Optimizing SMA Window Lengths for the Initial Portfolio

Defining the time period

# backtesting parameters
days = 2000
end = dt.today()
start = end - pd.Timedelta(days=days)

Introducing the initial portfolio of 10 ad-hoc assets

# portfolio of stocks
portfolio_stocks = ["NVDA","AAPL","SNOW","KBH","ENPH","PDD","SPY","QQQ","IWM","KWEB"]

Calculating the portfolio/stock cumulative returns and the annualized Sharpe ratio by finding the optimal values ma1 = 10, ma2 = 25 after scanning over a range of widow lengths 5

# defining a data frame to store portfolio returns
portfolio_strategy_returns = pd.DataFrame()
portfolio_bnh_returns = pd.DataFrame()

# buy and hold returns for individual stocs
bnh_stock_returns = []
bnh_stock_sharpe = []

# iterating over stocks in the portfolio
for stock in portfolio_stocks:
    data = get_daily_data(stock, start, end)
    
    # Calculating daily returns
    data["bnh_returns"] = np.log(data["Close"]/data["Close"].shift())

    portfolio_strategy_returns[stock] = ma(data,ma1 = 10, ma2 = 25)
    
    bnh_stock_returns.append(get_cumulative_return(data["strategy_returns"]))
    bnh_stock_sharpe.append(get_annualized_sharpe_ratio(data["strategy_returns"]))

Printing the SMA strategy returns

print("\nSTRATEGY RETURNS ON PORTFOLIO")
portfolio_strategy_returns["Portfolio_rets"] = portfolio_strategy_returns.mean(axis=1)
portfolio_strategy_returns.round(decimals = 4).tail(10)

Calculating cumulative returns and the annualized Sharpe ratio

perf = pd.DataFrame(index=portfolio_stocks,columns=["Cumulative returns","Annualized Sharpe Ratio"])

for i,stock in enumerate(portfolio_stocks):
    cum_ret = bnh_stock_returns[i]
    anu_shp = bnh_stock_sharpe[i]
    perf.loc[stock] = [cum_ret,anu_shp]
    
perf

Cumulative returns Annualized Sharpe Ratio
NVDA    2.375256      1.071783
AAPL    1.176463      1.020626
SNOW   -0.110298     -0.068875
KBH     0.839733      0.482885
ENPH    2.455573      0.784543
PDD     2.237751      0.900318
SPY     0.592832      0.886599
QQQ     0.637886      0.746084
IWM     0.213217      0.233466
KWEB    0.549323      0.404803

Comparing the Stock Cumulative Returns

perf['Cumulative returns'].plot.bar(title='Cumulative returns')

Comparing the Stock Annualized Sharpe Ratio

perf['Annualized Sharpe Ratio'].plot.bar(title='Annualized Sharpe Ratio')

Calculating the stock performance mean value

perf.mean()
Cumulative returns         1.096774
Annualized Sharpe Ratio    0.646223
dtype: object

Calculating the SMA strategy cumulative return and the annualized Sharpe ratio

print("Cumulative returns SMA Strategy                  :",get_cumulative_return(portfolio_strategy_returns["Portfolio_rets"]))
print("Annualized sharpe ratio SMA Strategy             :",get_annualized_sharpe_ratio(portfolio_strategy_returns["Portfolio_rets"]))

Cumulative returns SMA Strategy                  : 1.17530067503038
Annualized sharpe ratio SMA Strategy             : 1.2276872946556154

We can see that the SMA strategy results in ROI ~ 17.5%, and the annualized Sharpe ratio from 1 to 1.99 is considered adequate/good.
Plotting and comparing the SMA strategy cumulative returns

import matplotlib.pyplot as plt
colors = ['tab:cyan','tab:purple','tab:pink','tab:orange','tab:blue','tab:green','tab:gray','tab:olive','tab:brown','tab:red',"k"]
portfolio_strategy_returns.cumsum().plot(figsize=(12,7), title="MOVING AVERAGES STRATEGY CUMULATIVE RETURNS", color=colors)
plt.grid()

SMA strategy cumulative returns (step 1).

Let’s move to step 2 by excluding the worst performer SNOW with the lowest cumulative return and the negative annualized Sharpe ratio (a Sharpe ratio less than 1 is considered bad).

Step 2: Excluding Worst Performers with Lowest Returns

Applying the above sequence to the updated portfolio of 9 assets without SNOW

# portfolio of stocks
portfolio_stocks = ["NVDA","AAPL","KBH","ENPH","PDD","SPY","QQQ","IWM","KWEB"]

Calculating the stock performance mean value

perf.mean()
Cumulative returns         1.300106
Annualized Sharpe Ratio    0.767578
dtype: object

Calculating the SMA strategy cumulative return and the annualized Sharpe ratio

print("Cumulative returns SMA Strategy                  :",get_cumulative_return(portfolio_strategy_returns["Portfolio_rets"]))
print("Annualized sharpe ratio SMA Strategy             :",get_annualized_sharpe_ratio(portfolio_strategy_returns["Portfolio_rets"]))

Cumulative returns SMA Strategy                  : 1.3001058358012645
Annualized sharpe ratio SMA Strategy             : 1.3648948755238106

We can see that the updated SMA strategy yields ROI ~ 30% and the improved annualized Sharpe ratio of 1.365.
Plotting and comparing the SMA strategy cumulative returns

SMA strategy cumulative returns (step 2).

Let’s move to step 3 by thresholding the poor performers KWEB, IWM and SPY with the cumulative returns <0.6.

Step 3: Excluding Poor Performers with Lowest Sharpe Ratio

Applying the above sequence to the updated portfolio of 6 assets without SNOW, KWEB, IWM and SPY, viz.

# portfolio of stocks
portfolio_stocks = ["NVDA","AAPL","KBH","ENPH","PDD","QQQ"]

Calculating the stock performance mean value

perf.mean()

Cumulative returns         1.776673
Annualized Sharpe Ratio    0.936473
dtype: object

Calculating the SMA strategy cumulative return and the annualized Sharpe ratio

print("Cumulative returns SMA Strategy                  :",get_cumulative_return(portfolio_strategy_returns["Portfolio_rets"]))
print("Annualized sharpe ratio SMA Strategy             :",get_annualized_sharpe_ratio(portfolio_strategy_returns["Portfolio_rets"]))

Cumulative returns SMA Strategy                  : 1.7766732115541535
Annualized sharpe ratio SMA Strategy             : 1.5475252825461494

We can see that the updated SMA strategy yields ROI ~ 77.6% and the improved annualized Sharpe ratio of ~1.55 (significantly closer to the very good value of 2 than other two portfolios).
Plotting and comparing the SMA strategy cumulative returns

SMA strategy cumulative returns (step 3).

Conclusions

Here is the visual summary of our three updates towards the optimal portfolio:

# creating the dataset
data = {'Step 1':1.227, 'Step 2':1.365, 'Step 3': 1.547}
courses = list(data.keys())
values = list(data.values())
  
fig = plt.figure(figsize = (10, 5))
 
# creating the bar plot
plt.bar(courses, values, color ='red', 
        width = 0.4)
 
plt.xlabel("Portfolio Update")
plt.ylabel("Annualized Sharpe Ratio")
plt.title("Annualized Sharpe Ratio SMA Strategy")
plt.show()

# creating the dataset
data = {'Step 1':1.175, 'Step 2':1.300, 'Step 3': 1.776}
courses = list(data.keys())
values = list(data.values())
  
fig = plt.figure(figsize = (10, 5))
 
# creating the bar plot
plt.bar(courses, values, color ='green', 
        width = 0.4)
 
plt.xlabel("Portfolio Update")
plt.ylabel("Cumulative Returns")
plt.title("Cumulative Returns SMA Strategy")
plt.show()

In summary, this IPO project intended to investigate the ability of proposed SMA portfolio updates to assist investors to make profitable trading decisions.
Our backtesting experiments show that the proposed workflow can maximize risk-adjusted returns of portfolios while minimizing the number of assets involved in the optimization process.
Our Road Ahead in Portfolio Management is to combine advanced trading strategies, financial health/risk metrics and stochastic portfolio optimization algorithms into a single framework to optimize the advantages of each.