Portfolio Optimization in Python. So the most simple way to achieve this is to create a lambda function that returns the sum of the portfolio weights, minus 1. Given that I have certain benchmark returns and weights for the same stocks in my portfolio. One of the most relevant theories on portfolio optimization was developed by Harry Markowitz. Sure thing – it should be possible with the code below: and then change the code in the "simulate_random_portfolios" function so that instead of the lines: you have (for example - with 5 stocks that you want to sum to a weight of 1, with any individual stock being allowed to range from -1 to 1: You can ofcourse change the n,m,low, high arguments to fit your requirements. How does the bitcoin and gold chart comparison look like? Below is the Sharpe ratio formula where Rp is the return of the portfolio. Would love to see a comparison of historical returns & metrics using the various optimization approaches to historically holding different portfolios of assets classes (say ETFs) over time, rebalanced monthly. Congrats!! The risk free rate is required for the calculation of the Sharpe ratio and should be provided as an annualised rate. I have to apologise at this point for my jumping back and forth between the UK English spelling of the word “optimise” and the US English spelling (optimize)…my fingers just won’t allow me to type it with a “z” unless I absolutely have to, for some reason!!! These are highlighted with a red star for the maximum Sharp ratio portfolio, and a green star for the minimum variance portfolio. This module provides a set of functions for financial portfolio optimization, such as construction of Markowitz portfolios, minimum variance portfolios and tangency portfolios (i.e. For example, given w = [0.2, 0.3, 0.4, 0.1], will say that we have 20% in the first stock, 30% in the second, 40% in the third, and 10% in the final stock. For your reference, see below the whole code used in this post. If so, ping me a message here and I will send you my contact details to forward the data file on to. Our goal is to construct a portfolio from those 10 stocks with the following constraints: To start off, suppose you have $10,000. It all sums up to 100%. vanguard funds require minimum of $3000). A simple python project where we use price data from the NASDAQ website to help optimize our portfolio of stocks using modern portfolio theory. It is time to take another step forward and learn portfolio optimization with Python. For example, young investors may prefer to find portfolios maximizing expected return. cme = pdr.get_data_stooq(‘CME’, start, end). We then download price data for the stocks we wish to include in our portfolio. I hope that has been somewhat interesting to some of you at least..until next time! If you have questions feel free to have a look at it. Next we begin the second approach to the optimisation – that uses the Scipy “optimize” functions. It fails there with the following error code: “/home/ni/.local/lib/python3.6/site-packages/pandas/core/indexing.py”, line 1493, in _getitem_axis raise TypeError(“Cannot index by location index with a non-integer key”) Have you, or any of the people on this forum, had this issue? I’m done creating the fictional portfolio. The “minimum variance portfolio” is just what it sounds like, the portfolio with the lowest recorded variance (which also, by definition displays the lowest recorded standard deviation or “volatility”). Apologies for the late reply… What was the error you are receiving? This method assigns equal weights to all components. A blog about Python for Finance, programming and web development. The “bounds” just specify that each individual stock weight must be between 0 and 1, with the “args” being the arguments that we want to pass to the function we are trying to minimise (calc_neg_sharpe) – that is all the arguments EXCEPT the weights vector which of course is the variable we are changing to optimise the output. Some of key functionality that Riskfolio-Lib offers: If you would like to post your code here I am happy to take a look. Another approach to find the best possible portfolio is to use the Sharpe Ratio. How will the return calculations and the correlation matrix take this into account? Portfolio optimization in finance is the technique of creating a portfolio of assets, for which your investment has the maximum return and minimum risk. The way this needs to be entered is sort of a bit “back to front”. Building Python Financial Tools made easy step by step. 2- If I wanted to add a portfolio tracking error constraint to the minimum variance function, how can I incorporate that in the code? By altering the variables a bit, you should be able to reuse the code to find the best portfolio using your favourite stocks. My guess is that it was due to the fact that too many ‘Adj. This includes quadratic programming as a special case for the risk-return optimization. Similar variables are defined as before this time with the addition of “days” and “alpha”. So the first thing to do is to get the stock prices programmatically using Python. Thinking about managing your own stock portfolio? When we run the optimisation, we get the following results: When we compare this output with that from our Monte Carlo approach we can see that they are similar, but of course as explained above they will not be identical. Featured on Meta When is a closeable question also a “very low quality” question? Feel free to have a look at it! Portfolio optimization is the process of selecting the best portfolio (asset distribution), out of the set of all portfolios being considered, according to some objective. Introduction In this post you will learn about the basic idea behind Markowitz portfolio optimization as well as how to do it in Python. In this post we will demonstrate how to use python to calculate the optimal portfolio and visualize the efficient frontier. We need a new function that calculates and returns just the VaR of a portfolio, this is defined first. Hi Gus – I assume you are referring to the line that reads: #locate positon of portfolio with minimum VaR min_VaR_port = results_frame.iloc[results_frame[‘VaR’].idxmin()]. save_weights_to_file() saves the weights to csv, json, or txt. Compared to the traditional way of asset allocation such as 40/60 portfolio or mean-reversion portfolio, risk-based… In this installment I demonstrate the code and concepts required to build a Markowitz Optimal Portfolio in Python, including the calculation of the capital market line. We will always experience some discrepancies however as we can never run enough simulated portfolios to replicate the exact weights we are searching for…we can get close, but never exact. optimization portfolio-optimization python. For example, given w = [0.2, 0.3, 0.4, 0.1], will say that we have 20% in the first stock, 30% in the second, 40% in the third, and 10% in the final stock. Thank you very much for taking the time to help out. It’s admittedly a bit strange looking for some people at first, but there you go…. In this article, I would use python to plot out everything about these two assets. The higher of a return you want, the higher of a risk (variance) you will need to take on. How can I provide my own historical data from a csv or spreadsheet file instead of reading from on online source? If possible try to get it correctly formatted as python code by wrapping it with: at the start and end – NOTE: DONT include the underscores at the start and end of each line -I have just added them to allow the actual wrappers to be visible and not changed into HTML themselves…. This helped me a lot. But how can we identify which portfolio (i.e. This part of the code is exactly the same that I used in my previous article. For other posts on Python for Finance feel free to check some of my other entries. I’ll get on to this as soon as I have a free moment. Browse other questions tagged python pandas optimization scipy portfolio or ask your own question. I’m sorry, Im not understanding…. Maximum quadratic utility. Congratulations for your work.Very inspiring. I am going to use the five... Financial Calculations. I remember it now, deriving the formula for modern portfolio theory. Markowitz Portfolio Optimization in Python/v3 Tutorial on the basic idea behind Markowitz portfolio optimization and how to do it with Python and plotly. set_weights() creates self.weights (np.ndarray) from a weights dict; clean_weights() rounds the weights and clips near-zeros. The higher the Sharpe Ratio, the better a portfolio returns have been relative to the taken risk. Hi Chris, thanks for your comment also…I will make that the subject of my next post. Hi jojo, apologies for the late reply… To assign sector constraints etc should be possible of course, it would depend on you having the data of which stock related to which sector. We only need the fields “type”, “fun” and “args” so lets run through them. If we could choose between multiple portfolio options with similar characteristics, we should select the portfolio with the highest Sharpe Ratio. The “eq” means we are looking for our function to equate to zero (this is what the equality is in reference to – equality to zero in effect). no_of_stocks = Strategy_B.shape[1] no_of_stocks weights = cp.Variable(no_of_stocks) weights.shape (np.array(Strategy_B)*weights) # Save the portfolio returns in a variable portfolio_returns = (np.array(Strategy_B)*weights) portfolio_returns final_portfolio_value = cp.sum(cp.log(1+portfolio_returns)) final_portfolio_value objective = cp.Maximize(final_portfolio… Let’s transform the data a little bit to make it easier to work with. Thinking about managing your own stock portfolio? The “type” can be either “eq” or “ineq” referring to “equality” or “inequality” respectively. Anyway, I started from scratch, and got (not null) values for VaR (results_frame). In this post I’ll be looking at investment portfolio optimisation with python, the fundamental concept of diversification and the creation of an efficient frontier that can be used by investors to choose specific mixes of assets based on investment goals; that is, the trade off between their desired level of portfolio return vs their desired level of portfolio risk. Portfolio Optimization in Python. wow i did not get any notification for you reply.. haha.. i just saw it. the negative Sharpe ratio, the variance and the Value at Risk). Portfolio Optimization: Optimization Algorithm We define the function as get_ret_vol_sr and pass in weights We make sure that weights are a Numpy array We calculate return, volatility, and the Sharpe Ratio Return an array of return, volatility, and the Sharpe Ratio That is the optimal weight based on the past 5-years price returns, statistics, modern portfolio theories, mathematics, and python. If you have liked the article feel free to share it in your social media channels. We may have investors pursuing different objectives when optimizing their portfolio. Algorithmic Portfolio Optimization in Python. Now let us move on to the problem of identifying the portfolio weights that minimise the Value at Risk (VaR). The Overflow Blog Failing over with falling over. 32% bitcoin and 68% gold . PyPortfolioOpt is a library that implements portfolio optimisation methods, including classical mean-variance optimisation techniques and Black-Litterman allocation, as well as more recent developments in the field like shrinkage and Hierarchical Risk Parity, along with some novel experimental features like exponentially-weighted covariance matrices. The data points are coloured according to their respective Sharpe ratios, with blue signifying a higher value, and red a lower value. After running the code, I printed out what those weights were, and they were different form the weights resulting from the minimum variance function. This is going to illustrate how to implement the Mean-Variance portfolio theory (aka the markowitz model) in python to minimize the variance of your portfolio given a set target average return. The weights are a solution to the optimization problem for different levels of expected returns, Thanks. For this we'll simply plot our returns against the time and the following code will do that We'll get the following graph as our output Regards, Gus. Going foward, did you even tried implementing the Black-Litterman model using Python? I decided to restrict the weight of any individual stock to 10%. You obviously have a deep understanding of finance and programming. Investor’s Portfolio Optimization using Python with Practical Examples. When quoting the official docs or referring to the actual function itself I shall use a “z” to fall in line. The hierarchical_portfolio module seeks to implement one of the recent advances in portfolio optimisation – the application of hierarchical clustering models in allocation. df = data.set_index ('date') table = df.pivot (columns='ticker') # By specifying col … See below a summary of the Python portfolio optimization process that we will follow: We will start by retrieving stock prices using a financial free API and creating a Pandas Dataframe with the daily stock returns. Utilize powerful Python optimization libraries to build scientifically and systematically diversified portfolios . Note: this page is part of the documentation for version 3 of Plotly.py, which is not the most recent version . the Markowitz portfolio, which minimises risk for a given target return – this was the main focus of Markowitz 1952; Efficient risk: the Sharpe-maximising portfolio for a given target risk. I just have a few issues when running the code. This would be most useful when the returns across all interested assets are purely random and we have no views. What is the correlation between bitcoin and gold? In my previous post, we learned how to calculate portfolio returns and portfolio risk using Python. The main benefit of a CVaR optimization is that it can be implemented as a linear programming problem. The code is fairly brief but there are a couple of things worth mentioning. Michael Michael. So firstly we define a function (very similar to our earlier function) that calculates and returns the negative Sharpe ratio of a portfolio. Firstly, Scipy offers a “minimize” function, but no “maximize” function. Sanket Karve in Towards Data Science. Note that we use Numpy to generate random arrays containing each of the portfolio weights. Having our portfolio weights, we can move on to calculate the annualised portfolio returns, risk and Sharpe Ratio. They will allow us to find out which portfolio has the highest returns and Sharpe Ratio and minimum risk: Within seconds, our Python code returns the portfolio with the highest Sharpe Ratio as well as the portfolio with the minimum risk. After which, I would draw out an efficient frontier graph and pinpoint the Sharpe ratio for portfolio optimization. Portfolio Optimization with Python using Efficient Frontier with Practical Examples by Shruti Dash | Portfolio optimization in finance is the technique of creating a portfolio of assets, for which your investment has the maximum return and minimum risk. The weightings of each stock are not more than a couple of percent away between the two approaches…hopefully that indicates we did something right at least! Similarly, an increase in portfolio standard deviation increases VaR but decreases the Sharpe ratio – so what maximises VaR in terms of portfolio standard deviation actually minimises the Sharpe ratio. Again the code is rather similar to the optimisation code used to calculate the maximum Sharpe and minimum variance portfolios, again with some minor tweaking. Great work, appreciate your time to create. Given a weight w of the portfolio, you can calculate the variance of the stocks by using the covariance matrix. The higher of a return you want, the higher of a risk (variance) you will need to take on. Next, we are going to generate 2000 random portfolios (i.e. def calc_neg_sharpe(weights, mean_returns, cov, rf): portfolio_return = np.sum(mean_returns * weights) * 252 portfolio_std = np.sqrt(np.dot(weights.T, np.dot(cov, weights))) * np.sqrt(252) sharpe_ratio = (portfolio_return - rf) / portfolio_std return -sharpe_ratio constraints = ({'type': 'eq', 'fun': lambda x: np.sum(x) - 1}) def max_sharpe_ratio(mean_returns, cov, rf): num_assets = … We can do that by optimising our portfolio. We hope you enjoy it … Portfolio Optimization using SAS and Python. Along with the rise of the popularity of the risk factor investing among institutional investors since the 2008-2009 financial crisis, risk-based asset allocation also enterned the mainstream as risk management starting to become the core of most investment processes. Hello Stuart, I’m trying to follow this amazing investment tutorial/Python-code, and in my PC (Linux/Python 3.6.9), it runs well till it reaches the “localization of the portfolio with minimum VaR” (after the random portfolios simulation). Introduction In this post you will learn about the basic idea behind Markowitz portfolio optimization as well as how to do it in Python. Programming: Create The Fictional Portfolio. For the annualized returns, how come you are not raise the returns to 252? share | improve this question | follow | asked Aug 7 '17 at 16:38. Finally, the above approach where returns are entered as zero (effectively removing them from the calculation) is sometimes favoured as it is a more “pessimistic” view of a portfolio’s VaR and when dealing with the quantification of risk, or in fact any “downside” forecast, it is wise to err on the side of caution and make decisions based on a worst case scenario. Given a weight w of the portfolio, you can calculate the variance of the stocks by using the covariance matrix. That is 2000 portfolios containing our 4 stocks with different weights. Indra A. Then we define a variable I have labelled “constraints”. Financial Portfolio Optimization. Nothing changes here from our original function that calculated VaR, only that we return a single VaR value rather than the three original values (that previously included portfolio return and standard deviation). Medium is an open platform where 170 million readers come to … As a note, VaR is sometimes calculated in such a way that the mean returns of the portfolio are considered to be small enough that they can be entered into the equation with a zero value – this tends to make more sense when we are looking at VaR over short time periods like a daily or a weekly VaR figure, however when we start to look at annualised VaR figures it begins to make more sense to incorporate a “non-zero” return element. Hi Chris, perhaps you could specify a starting portfolio value and then create a constraint such that the percentage held in any asset must equate to a certain absolute value in terms of dollars… So if you had a portfolio starting value of 100,000 and the minimum you wanted was 3,000 as mentioned, you could just set the constraint at 3%. Awesome work very well explained, thank you! Either you have made a typo and used an integer key with “.loc” (notice the lack of i) which only accepts label based keys, or vice versa you are using a label with iloc. I.e. the max you can allocate for each stock is 20%.. You look like a remarkable dad! The goal according to this theory is to select a level of risk that an investor is comfortable with. And lowest risk? Is it something you would be particularly interested in seeing? So that is to say we will be calculating the one-year 95% VaR, and attempting to minimise that value. The annualized return is 13.3% and the annualized risk is 21.7% Hi, Is it possible to include dividends on returns? I am a current PhD Computer Science candidate, a CFA Charterholder (CFAI) and Certified Financial Risk Manager (GARP) with over 16 years experience as a financial derivatives trader in London. I really like your professional, storytelling-like approach for optimisation and previous topic. With this approach we try to discover the optimal weights by simply creating a large number of random portfolios, all with varying combinations of constituent stock weightings, calculating and recording the Sharpe ratio of each of these randomly weighted portfolio and then finally extracting the details corresponding to the result with the highest value. The data points are still coloured according to their corresponding VaR value. The more random portfolios that we create and calculate the Sharpe ratio for, theoretically the closer we get to the weightings of the “real” optimal portfolio. In the mean time, if you have any questions about the package, or portfolio optimisation in general, please let me know. In this example I have chosen to set the rate to zero, but the functionality is there to easily amend this for your own purposes. Portfolio optimization is a mathematically intensive process that can be accomplished with a variety of optimization functions that are freely available in Python. It is built on top of cvxpy and closely integrated with pandas data structures. The frontier is visible. This time there is no need to negate the output of our function as it is already a minimisation problem this time (as opposed to the Sharpe ratio when we wanted to find the maximum). Portfolio Optimization using SAS and Python. Hi Cristovam apologies for the late reply, actually I havnt yet but it was something I’ve been thinking about doing. Hi people, I write this post to share a portfolio optimization library that I developed for Python called Riskfolio-Lib. Portfolio Optimization in Python. Portfolio optimization implementation in Python We start optimizing our portfolio by doing some visualization so we have a general idea that how our data looks like. You can use this piece of code a modify accordingly: #set dates start = datetime.datetime(2018, 3, 1) end = datetime.datetime(2018, 12, 31), #fetch data cme = pdr.get_data_yahoo(‘CME’, start, end), you can also easily use data feed from stooq.com or stooq.pl – you will find more macro data there i guess. I have chosen 252 days (to represent a year’s worth of trading days) and an alpha of 0.05, corresponding to a 95% confidence level. The Overflow Blog Podcast 284: pros and cons of the SPA Hopefully that makes sense – let me know if you cant resolve it 😉, Hi Stuart, thank you for your comments. Any guess what the problem could be? 😉. Now I want to show the daily simple returns which is... Optimize The Portfolio… And the calculation of the Sharpe ratio was: From this we can see that VaR falls when portfolio returns increase and vice versa, whereas the Sharpe ratio increases as portfolio returns increase – so what minimises VaR in terms of returns actually maximises the Sharpe ratio. PyPortfolioOpt is a library that implements portfolio optimisation methods, including classical efficient frontier techniques and Black-Litterman allocation, as well as more recent developments in the field like shrinkage and Hierarchical Risk Parity, along with some novel experimental features like exponentially-weighted covariance matrices. Using the Python SciPy library (and the Broyden–Fletcher–Goldfarb–Shanno algorithm), we optimise our functions in … 428 4 4 silver badges 13 13 bronze badges $\endgroup$ add a comment | 2 Answers Active Oldest Votes. We will generate 2000 random portfolios. Some of key functionality that Riskfolio-Lib offers: 5/31/2018 Written by DD. Now you might notice at this point that the results of the minimum VaR portfolio simulations look pretty similar to those of the maximum Sharpe ratio portfolio but that is to be expected considering the calculation method chosen for VaR. We see that portfolios with the higher Sharpe Ratio are shown as yellow. (You can report issue about the content on this page here) Want to share your content on python-bloggers? Hi, I have many difficulties to introduce the “Short” possibility. portfolio_performance() calculates the expected return, volatility and Sharpe ratio for the optimised portfolio. “An efficient portfolio is defined as a portfolio with minimal risk for a given return, or, equivalently, as the portfolio with the highest return for a given level of risk.” As algorithmic traders, our portfolio is made up of strategies or rules and each of these manages one or more instruments. We have covered quite a lot on portfolio and portfolio optimization with Python in the last two posts. It is a pleasure to read for someone who isn’t as proficient in Python yet, because the explanations for the different lines of code are extremely helpful. Riskfolio-Lib is a library for making quantitative strategic asset allocation or portfolio optimization in Python. Multiplying by 252 is only right if we’re dealing with log returns but it’s not the case here. Hi Stuart, Thanks a lot, it worked! To set up the first part of the problem at hand – say we are building, or have a portfolio of stocks, and we wish to balance/rebalance our holdings in such as way that they match the weights that would match the “optimal” weights if “optimal” meant the portfolio with the highest Sharpe ratio, also known as the “mean-variance optimal” portfolio. Portfolio optimization could be done in python using the cvxopt package which covers convex optimization. In this article, we will show a very simplified version of the portfolio optimization problem, which can be cast into an LP framework and solved efficiently using simple Python scripting. Such an allocation would give an average return of about 20%. Hi, great article, was wondering how you would modify your code if you wanted to include short positions. Lets begin with loading the modules. If just considering one single stock I guess the risk and return would just be the historic CAGR and the annualised standard deviation of the stock returns no? I started by declaring my parameters and sets, including my risk threshold, my stock portfolio, the expected return of my stock portfolio, and covariance matrix estimated using the shrinkage estimator of Ledoit and Wolf(2003). The “min_VaR” function acts much as the “max_sharpe_ratio” and “min_variance” functions did, just with some tweaks to alter the arguments as needed. Portfolio Optimization in Python. While convex optimization can be used for many purposes, I think we're best suited to use it in the algorithm for portfolio management. Given a weight w of the documentation for version 3 of Plotly.py, which is the. And I want to share a portfolio using Python ( VaR ), actually I havnt for. Higher value, and then for the same, as are the “ max_sharpe_ratio ” function Carlo approach reuse code... 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