max_sharpe_port.to_csv(‘C:/Users/Sam/PycharmProjects/Test/.ipynb_checkpoints/PORTFOLIO OPTIMIZATION/Max Sharpe Portfolio.csv’). Now, given there is such a stretch in extreme long to shorts (i.e a range of +150% long to -80% short), how do I determine based on the above results how to actually translate these results to a portfolio of $100,000 today assuming I wanted to believe in these result allocations? The rule regarding diversification is that it’s marginal benefit reduces as the number of stocks increases…in other words, the diversification benefit you get when moving from 1 stock to 2 stocks, is larger than when moving from 2 stocks to 3 stocks and so on (this is obviously just a general rule and the actual diversification benefits of any given stock depends on its correlation with the existing portfolio). And again, thank you so much for the guidance and help. Truly appreciated! Thanks for the code help. sI’ve noticed you use np.sum. I assume its because the data set is so big. 300 and -300 would obviously get you 30% and -30% restriction. For example “marker=(3,1,0)” gives you a non-rotated solid 3 pointed triangle, whereas “marker=(4,2,0)” gives you what looks like a “+” sign and “marker=(4,2,45)” gives you a “+” rotated at 45 degrees to look like an “x”. do nothing. Por: Coursera. The ORDER of the weights seems to be wrong. This book covers topics in portfolio management and multicriteria decision analysis (MCDA), presenting a transparent and unified methodology for the portfolio construction process. Having exactly same issue. Hi Mario – that’s a perfectly reasonable questions, and well noticed. Now, the code works just fine and spits out the optimization in the console of all 100 stocks. The 1.0 at the end is calculated as being the percentage of your portfolio that you hold in cash – in this instance it is actually 100% as you have financed the 0.2, 0.2 and 0.1 holdings by selling 0.5 of Apple – leaving you flat and holding 100% of your portfolio value in cash. Yes this is correct, you need to enter your “stocks = [ stock1 , stock 2, etc. Essentially, I want to see the entire frame. Or would I need to adjust the long/short code to adhere to my objectives stated? As always, really appreciate your guidance and assistance. Shouldn’t the return be the percentage change from day-to-day, with the most recent day’s price as the last row of the dataframe? Strictly if I wanted to just mutliply the daily mean as I have done, I should have used daily log returns as the input, not arethmetic returns as I have. Hi Zack, is there a particular reason for using a Monte Carlo approach or would you be open to using an optimisation function with relevant constraints supplied as arguments? Hi JUYPter and Kamil, with regards to the error you are receiving, are you sure you have correctly set up thr results matrix? You can view the Python implementation of this model in GitHub. This method takes the algorithm object and a list of Insight objects. Awesome makes sense. Check this post out https://marketxls.com/calculate-sharpe-ratio-of-portfolio-in-excel/. This will spit out a csv file called “Max Sharpe Portfolio.csv” to your working directory which gives you access to the full DataFrame data. Thank you so much for the response. That will give you 17 random weights constrained to be within +/- 20% range. Hi Sam, the output shown above is incorrect for the particular stocks I have used, but as long as you enter your initial stock list in alphabetical order, your results will be correct. I have had a play around with the code and I have located the error…The list of stocks has to be in alphabetical order as this line of code: #convert daily stock prices into daily returns returns = data.pct_change(), #calculate mean daily return and covariance of daily returns mean_daily_returns = returns.mean(). If I multiply the weights of the maximum Sharpe ratio portfolio as stated on your webpage with the mean returns the code calculates and sum them up, I do not get the portfolio return you state. I have attached full code below. This simple calculation can obviously be carried out for any stock you have in mind, but not many investor portfolios are made up of just one stock – they are made up of 10s of stocks, 100s of stocks sometimes. This is because standard deviation does not scale linearly with time, variance does, and standard deviation if the square root of variance. some stocks are at +100% long, while others are -80% short), I want to figure out exactly how I can allocate this hypothetical $100,000 based on the above percentage allocations in real time? Is there any simple command or line of code I should add that will show all of my results in the console, intstead of the current where it cuts some out? It’s the 1.0 in the “weights” vector which represents how much cash you are actually holding in % terms. # I chose 1 as an arbitrary figure â you can choose anything that remains constant to represent the fact that cash is risk free (zero volatility) but also generates zero returns â hence the # âpriceâ of cash does not change. This is the most critical step towards being able to fully automate your portfolio construction and management processes. # And now, all thatâs left to do is pull out the weights of the stocks needed to create the two portfolios highlighted above, and that can be done as follows: # print portfolio to maximize sharpe ratio print(‘**********Portfolio to Maximize Sharpe Ratio**********’) print(max_sharpe_port), print(‘_____________________________________________________________________________________________________________’), # print portfolio to minimize portfolio variance print(‘**********Portfolio to Minimize Volatility**********’) print(min_vol_port), plt.show(plt.scatter) plt.show(plt.colorbar()). I would simply add a column to the DataFrame that held a constant – say 1 – and then assign a particular percentage of cash to that stream – it will result in calculating the relevant percentage for a cash amount that doesn’t change. Specifically, it is saying, ‘Redeclared i above without any usage’ in the statement ‘for i in range (16), and Name ‘x’ can not be defined in the statement ‘weights.append(x). If you do…let me know and I can have a rethink. Thanks~. For a more indepth explanation of this last point, please visit: http://www.macroption.com/why-is-volatility-proportional-to-square-root-of-time/. That the portfolio cannot be net long or net short more than lets say +20% or -20% in any individual stock? Thanks as always for your help. Also, I have 16 stocks here not 17, so that should be for i in range(16) instead of for i in range(17) I believe? We can calculate the portfolio expected return and volatility as follows: Great so we’re getting there, we now know the expected return and volatility of our current portfolio. **********Portfolio to Maximize Sharpe Ratio********** ret 1.191248 stdev 0.305746 sharpe 3.896200 AAL -0.055412 AAPL 0.047818 ADBE -0.062343 ADI -0.158002 ADP 0.155110 ADSK 0.094782 AKAM 0.026778 ALXN -0.061917 AMAT 0.074762 AMGN -0.195493 AMZN -0.180999 ATVI 0.027458 AVGO 0.191906 BIDU 0.019338 BIIB -0.024391 BMRN -0.152147 CA 0.010816 CELG -0.007887 CERN -0.149978 CHKP 0.017568 CHTR 0.119874 CMCSA -0.051849 COST 0.029636 CSCO 0.031001 CSX 0.180601 CTAS 0.142230 CTRP -0.149408, ……………………………. In the previous videos, we've covered how to find alpha factors, how to combine them, and how to analyze combined alpha factors. EDHEC Business School - Advanced Portfolio Construction and Analysis with Python. Data Analysis with Pandas and Customised Visuals with... Trading Strategy Performance Report in Python â Part... https://github.com/czielinski/portfolioopt, https://marketxls.com/calculate-sharpe-ratio-of-portfolio-in-excel/, http://www.macroption.com/why-is-volatility-proportional-to-square-root-of-time/, https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.random.choice.html, https://matplotlib.org/api/markers_api.html, https://pythonforfinance.net/2019/07/02/investment-portfolio-optimisation-with-python-revisited/. So let’s now assume that we hold a portfolio of 4 tech stocks, Apple, Microsoft, Amazon and Yahoo…how do we start to calculate the expected return and volatility of that portfolio? Or would I need to adjust the long/short code to adhere to my objectives stated? Second….the web.datareader appears to be unavailable now. The most important feature of the book includes the proposed methodological framework that integrates two individual subsystems, the portfolio selection subsystem and the portfolio optimization subsystem. Is the python optimization telling me that despite having a net short position of 50% apple due to my own discretion and preference to construct this portfolio, if I wanted to in fact optimize the portfolio fully based on both Sharpe Ratio, or Minimum Volatility, then I should rebalance this portfolio to actually be NET LONG apple (at 45.5% for Sharpe Ratio maximization) and NET LONG apple (at 30.26% to Maximize Volatility) instead of my desired -50% NET SHORT apple I initially specified in my portfolio? Ok I figured that may be the case and will dig into it on my end as well and keep you posted. I’m just asking as I’m still learning. Also please check out the comments section – VERY IMPORTANT POINT – is that there is a part of the code which rearranges our list of stocks into alphabetical order without being explicit about it – so please make sure that you enter your list of stocks to the code in alphabetical order so that the correct weight is applied to the correct stock during the iterative process of fulling the numpy array. Thanks! Any idea what could be going on with the 9 instead of 8 error? Please let me know. It makes feasible sense kind of too since many funds are net leveraged – or + on their book……….And not necessarily having the book sum = 100% as a restriction……. Offered by EDHEC Business School. The portfolio in the python code is built up in a bottom up fashion. if it’s the latter I suggest using the “to_csv” fucntionality of DataFrames to create a csv file output with the data. Portfolio construction through handcrafting: implementation This post is all about handcrafting; a method for doing portfolio construction which human beings can do without computing power, or at least with a spreadsheet. ###CODE### import pandas_datareader.data as web import numpy as np import pandas as pd, data = web.DataReader(stock, data_source=”yahoo”, start=’01/01/2010′)[‘Adj Close’], mean_return = returns.mean() return_std = returns.std(), annualized_return = round(mean_return * 252, 2) annualized_std = round(return_std * np.sqrt(252), 2), print(‘The annualised mean return of stock {} is {}, and the annualised volatility is {}’.format(stock[0], annualized_return, annualized_std)), print(returns.head(10)) print(data.head(10)), ###OUTPUT### The annualised mean return of stock AAPL is AAPL -0.2 dtype: float64, and the annualised volatility is AAPL 0.25 dtype: float64 AAPL Date 2017-12-29 NaN 2017-12-28 0.010932 2017-12-27 -0.002806 2017-12-26 -0.000176 2017-12-22 0.026030 2017-12-21 0.000000 2017-12-20 -0.003771 2017-12-19 0.001090 2017-12-18 0.010771 2017-12-15 -0.013887 AAPL Date 2017-12-29 169.229996 2017-12-28 171.080002 2017-12-27 170.600006 2017-12-26 170.570007 2017-12-22 175.009995 2017-12-21 175.009995 2017-12-20 174.350006 2017-12-19 174.539993 2017-12-18 176.419998 2017-12-15 173.970001. Thus, making it seem like that line of code is just being ignored. This method assigns equal weights to all components. We can locate these 2 portfolios by making a few changes to our code to store all the random weight arrays used for each run of the Monte Carlo simulation along side the expected return, standard deviation and Sharpe Ratio as we go along, then locate the point in the resulting DataFrame where the Sharpe Ratio is highest for portfolio “1” and where the standard deviation is lowest for portfolio “2”. The volatility of the portfolio depends very heavily on the variances of, and covariances between the stocks in question…the line: portfolio_std_dev = np.sqrt(np.dot(weights.T,np.dot(cov_matrix, weights))) * np.sqrt(252). Then – because we stored them as we went along, we can extract the array of weights that corresponds to each of those two portoflios and bang! If you agree that there is an error, please let me know where I can find the error in the code. Scroll about halfway down the page and you will see the explanation for “(numsides, style, angle)”. Read reviews and buy Multicriteria Portfolio Construction with Python - (Springer Optimization and Its Applications) by Elissaios Sarmas & Panos Xidonas Haris Doukas at Target. Are you referencing this to point out the difference in the way i have calculated the Sharpe Ratio vs how this article does? data[‘CASH’] = 1, # convert daily stock prices into daily returns returns = data.pct_change(), # calculate mean daily return and covariance of daily returns mean_daily_returns = returns.mean() cov_matrix = returns.cov(), #*********************************************************************************************************************************************** ## NOW , ASSUME WE WANT TO BE SHORT 50% APPLE, INSTEAD OF LONG 50% # WHEN YOU SHORT 50% APPLE, YOU CAN REINVEST THOSE FUNDS THAT YOU OBTAIN FROM BROKER FOR TAKING ON THE SHORT ACROSS OTHER STOCKS IN THE PORTFOLIO # HOWEVER, IN THIS EXAMPLE CODE BELOW WE WANT TO REMAIN NET SHORT, YET KEEP PROCEEDS FROM SHORT SALE IN CASH AND NOT REINVEST IT # NOTICE SUMS STILL ADD TO 1 FOR THE DATA FRAME #***********************************************************************************************************************************************, # set array holding portfolio weights of each stock # The 1.0 at the end is calculated as being the percentage of your portfolio that you hold in cash â in this instance it is actually 100% as you have financed the 0.2, 0.2 and 0.1 # holdings by selling 0.5 of Apple â leaving you flat and holding 100% of your portfolio value in cash. Which part of the code are you specifically referring to when you say it “rearranges our list of stocks into alphabetical order without being explicit about it â so please make sure that you enter your list of stocks to the code in alphabetical order so that the correct weight is applied to the correct stock during the iterative process of fulling the numpy array.” I will be sure to enter the list of stocks in alphabetical order going forward to comply to this, however just curious on which line of code does it? By investing in more than one stock, an investor can reap the benefits of diversification, particularly a reduction in the riskiness of the portfolio. Sorry the “.T” is the numpy “transpose” method and it doesn’t work on lists, it only works on numpy arrays – so we just need to recast the weights vector as a numpy array as follows: portfolio_std_dev = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights))) * np.sqrt(252) ValueError: shapes (17,17) and (1,) not aligned: 17 (dim 1) != 1 (dim 0). To run an optimisation of a portfolio which allows a cash holding will require some more modifications to the code. It would be great if you could explain me the logic behind np.zeros((3,num_portfolios)) preferably with a simple example. The Mean Variance Portfolio Construction Model is an implementation of the classical model. When I run the code with that line at the end, the code seems to run fine and spits out output in the console. Thank you so much for your time and concern in helping me. ð. EqualWeightingPortfolioConstructionModel.py, MeanVarianceOptimizationPortfolioConstructionModel.py, BlackLittermanPortfolioConstructionModel.py, EqualWeightingPortfolioConstructionModel.cs, MeanVarianceOptimizationPortfolioConstructionModel.cs, BlackLittermanPortfolioConstructionModel.cs. Thanks for providing some of your own code and take on this long/short construction. I found this formula Annualized Return=(1+ Return)1/N-1. Two portfolios that we may like to highlight as being “special” are 1) the portfolio with the highest Sharpe Ratio (i.e. Thank you very much for the prompt response. Thanks a lot for sharing your knowledge. @s666 going off the message I just sent you. e.g. These multiple Alpha Model sources can be seen as the "investor views" required of the classical model. When you say to add a column to the data frame, how would the mechanics of this actually look like. I just chose 1 as an arbitrary figure – you could have chosen anything that remained constant to represent the fact that cash is risk free (zero volatility) but also generates zero returns – hence the “price” of cash doesn’t change. There is a convex optimisation package available for Python (www.cvxopt.org) which may be of use here, but I’ve never been able to install it properly. Thanks for the code help. If we assume that you are trading cash equities, if you short sell you will actually receive a flow of funds into your portfolio which you can then use to purchase other shares. At the “portfolio_return = np.sum(mean_daily_returns * weights) * 252” sentence, are you annualyzing the portfolio return? If that is indeed the formula you wrote, it would caclulate the geometric annualised return if we assume that the “Return” in the formula represents the total returns experienced over the entire period of “N” years. Perhaps to solve your problem you could set the full file path in the name of the csv file, so something like: max_sharpe_port.to_csv(‘C:/XXX/XXX/XXX/Max Sharpe Portfolio.csv’) – obviously with the “Xs” representing an actual file path. Just wondering in the dataFrame columns, is there way to put some for loop so that when you add a stock in portfolio you dont need to manually change the code at dataFrame Columns as stocks[x]…. You can see the full description here – https://matplotlib.org/api/markers_api.html. Hi Donald – thanks for your post. Instructors: Lionel Martellini, PhD and Vijay Vaidyanathan, PhD. Itâs the 1.0 in the ‘weights’ vector which represents how much cash you are actually holding in % terms. Love your work and hope to hear back soon. Full code pasted below: *********************** CODE ***********************, import numpy as np import pandas as pd import pandas_datareader.data as web import matplotlib.pyplot as plt import random, # list of ETFs in portfolio # XLRE – REITs # XLF – Financial Select Sector SPDR ETF # XLV – Health Care Select Sector SPDR RTF # XLK – Technology sector SPDR ETF # XLE – Energy Select SPDR Fund # XLY- Consumer Discretionary Select Sector SPDR Fund # XLI – Industrial Select Sector SPDR Fund # XLP – Consumer Staples Select Sector SPDR Fund # XLU – Utilities Select Sector SPDR ETF # IBB – iShares Nasdaq Biotechnology ETF (GOES BACK TO 2001) # GDX – VanEck Vectors Gold Miners ETF (GOES BACK TO 2006) # EEM – Emerging Markets ETF ( GOES BACK t0 2003) # SHY – iShares 1-3 Year Treasury Bond ETF ( GOES BACK TO 2003) # IEI – iShares 3-7 Year Treasury Bond ETF ( GOES BACK TO FEB 2007) # IEF – iShares 7-10 Year Treasury Bond ETF (GOES BACK TO 2002) # TLT – iShares 20+ Year Treasury Bond ETF (GOES BACK TO 2002), for i in range(num_portfolios): # select random weights for portfolio holdings weights = [] for i in range(16): x = random.uniform(-200, 200) / 1000 weights.append(x). Your fomula above has unfortunately lost any formatting that was applied – but I think its safe to assume the original formula you are referring to is [(1 + Return)^(1 / N)] – 1. Thanks in advance for the help! If you wish to sit in cash, then you can just assume whatever % you have in cash has zero mean return and zero volatility. Perhaps generate random integers within a range (the length of your list) and pull out the corresponding stock at that list index. Hi – sorry bit confused by this. It is very helpful to learn Python …. Like all Algorithm Framework models, the Portfolio Construction Model also receives the OnSecuritiesChanged() event, which can optionally be used to perform actions when there are security additions or removals. Portfolio Construction Know what a balanced investment portfolio is and how to achieve it. Thanks for the amazing reply. Advanced Portfolio Construction and Analysis with Python. A tip: you can avoid the alphabetical order requirement by doing this: stocks = sorted([‘AAPL’,’AMZN’,’MSFT’,’YHOO’]), results[j+3,i] = weights[j] IndexError: index 3 is out of bounds for axis 0 with size 3. So using your example of being short 50% of Apple stock you would have a weight vector of: (weights = np.asarray([ -0.5, 0.2, 0.2, 0.1, 1.0]). This will capture the benefits of diversification of less than perfect correlation between the stocks in the portfolio. Welcome to part 12 of the algorithmic trading with Python and Quantopian tutorials. Hi Jan – fantastic spot!!! # now assume that we hold a portfolio of 4 tech stocks, Apple, Microsoft, Amazon and Yahooâ¦how do we start to calculate the expected return and volatility of that portfolio? I checked my directory through my folder as well and the CSV simply is never created! # first input needed will be the weights of the stocks in the portfolio # Assume portfolio is made up of: # 50% AAPL, 20% MSFT, 20% AMZN, and 10% YHOO. portfolio). “`(PLEASE NOTE THESE RESULTS ARE INCORRECT AS THEY WERE RUN PREVIOUS TO CORRECTLY SETTING MY INITIAL STOCK LIST IN ALPHABETICAL ORDER â I SHALL TRY TO FIX WHEN I GET A MOMENT)“`. Awesome article. However, for this specific code, it seems to not be doing anything for some odd reason. Always, any comments or questions, please visit: http: //www.macroption.com/why-is-volatility-proportional-to-square-root-of-time/ my folder as well and you... A chance please way it is very helpful little confused on what you want objects... 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