So the most simple way to achieve this is to create a lambda function that returns the sum of the portfolio weights, minus 1. In this post Iâ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. Change it from “bound = (0.0,1.0)” to “bound = (0.0,0.08)”. I hope that has been somewhat interesting to some of you at least..until next time! Programming: Create The Fictional Portfolio. is it possible to share a sample of the code for sector constraints and how to incorporate into existing MC code? If we could choose between multiple portfolio options with similar characteristics, we should select the portfolio with the highest Sharpe Ratio. In this post we will only show the code with minor explanations. These are highlighted with a red star for the maximum Sharp ratio portfolio, and a green star for the minimum variance portfolio. For your reference, see below the whole code used in this post. This course was a good connector/provided additional insight on using Python to process portfolio performance and data analysis. A portfolio is a vector w with the balances of each stock. Weâll see the returns of an equal-weighted portfolio comprising of the sectoral indices below. Next we begin the second approach to the optimisation – that uses the Scipy “optimize” functions. 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 plot colours the data points according to the value of VaR for that portfolio. optimization portfolio-optimization python. I am trying to do the exact same thing as you do in the first approach but with 24 different stocks. the max you can allocate for each stock is 20%.. You look like a remarkable dad! 2- If I wanted to add a portfolio tracking error constraint to the minimum variance function, how can I incorporate that in the code? In this post we will demonstrate how to use python to calculate the optimal portfolio and visualize the efficient frontier. Great work, appreciate your time to create. I have two questions about the second method of optimization using the minimize function. As noted by Alexey, it is much better to use CVaR than VaR. To start off, suppose you have \$10,000. I remember it now, deriving the formula for modern portfolio theory. We can find the answer to that questions by transforming our data into a Pandas DataFrame and performing some basic queries. This includes quadratic programming as a special case for the risk-return optimization. In my previous post, we learned how to calculate portfolio returns and portfolio risk using Python. 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. The pandas data reader is currently still working so you should be able to use it. Hi Chris, thanks for your comment also…I will make that the subject of my next post. That is exactly what we cover in my next post, portfolio optimization with Python. Hi Cristovam apologies for the late reply, actually I havnt yet but it was something I’ve been thinking about doing. Algorithmic Portfolio Optimization in Python. For the annualized returns, how come you are not raise the returns to 252? Anyway, it’s a great and inspiring article. I’ll get on to this as soon as I have a free moment. Compared to the traditional way of asset allocation such as 40/60 portfolio or mean-reversion portfolio, risk-basedâ¦ Similar variables are defined as before this time with the addition of “days” and “alpha”. Yellow coloured portfolios are preferable since they offer better risk adjusted returns. This method assigns equal weights to all components. This would be most useful when the returns across all interested assets are purely random and we have no views. The annualized return is 13.3% and the annualized risk is 21.7% Browse other questions tagged python pandas optimization scipy portfolio or ask your own question. So that is to say we will be calculating the one-year 95% VaR, and attempting to minimise that value. The hierarchical_portfolio module seeks to implement one of the recent advances in portfolio optimisation â the application of hierarchical clustering models in allocation. The constraints remain the same, so we just adapt the “max_sharpe_ratio” function above, rename it to “min_variance” and change the “args” variable to hold the correct arguments that we need to pass to our new “calc_portfolio_std” that we are minimising. The Overflow Blog Podcast 284: pros and cons of the SPA Portfolio Optimization using SAS and Python. Hi there, it depends whether you are working with the monte carol style random portfolio method, or the method using the scipy “optimize” approach. The data points are still coloured according to their corresponding VaR value. The calculation will happen in a for loop. The first function (calc_portfolio_perf) is created to help us calculate the annualised return, annualised standard deviation and annualised Sharpe ratio of a portfolio, given that we pass it certain arguments of course. let’s say that one instrument starts only in 2010 while another starts in 2005. Now we move onto the second approach to identify the minimum VaR portfolio. Is it something you would be particularly interested in seeing? It is built on top of cvxpy and closely integrated with pandas data structures. Portfolio Optimization with Python and SciPy. You notice the use of “.iloc” – the i stands for “integer” and the loc stands for “location” – using “iloc” requires that you pass it an integer, which seemingly you are not. That is the optimal weight based on the past 5-years price returns, statistics, modern portfolio theories, mathematics, and python. Portfolio Optimization using SAS and Python. Portfolio Optimization in Python. Apr 2, 2019 Author :: Kevin Vecmanis. This can look somewhat strange at first if you haven’t used the Scipy “optimize” capabilities before. Convex optimization can be done in Python with libraries like cvxpy and CVXOPT, but Quantopian just recently announced their Optimize API for notebooks and the Optimize API for algorithms. Hey Stuart, Hats off for this superb article. Thank you very much for taking the time to help out. If you continue to use the website we assume that you are happy with it. It is time to take another step forward and learn portfolio optimization with Python. 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. We see that portfolios with the higher Sharpe Ratio are shown as yellow. 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. We only need the fields “type”, “fun” and “args” so lets run through them. 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%. It’s almost the same code as above although this time we need to define a function to calculate and return the volatility of a portfolio, and use it as the function we wish the minimise (“calc_portfolio_std”). Hopefully that makes sense – let me know if you cant resolve it ð, Hi Stuart, thank you for your comments. The cost of being wrong due to underestimating VaR and that due to overestimating VaR is almost never symmetric – there is almost always a higher cost to an underestimation. (You can report issue about the content on this page here) Want to share your content on python-bloggers? Hi, Is it possible to include dividends on returns? Beginnerâs Guide to Portfolio Optimization with Python from Scratch. We will show how you can build a diversified portfolio that satisfies specific constraints. 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). Based on what we learned, we should be able to get the Rp and Op of any portfolio. These are shown below firstly for the maximum Sharpe portfolio, and then for the minimum variance portfolio. In this article, I would use python to plot out everything about these two assets. 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 = â¦ First of all this code is awesome and works exactly the way I would want a portfolio optimization setup to work. If you have liked the article feel free to share it in your social media channels. That is a tremendous accomplishment!! Optimizing Portfolios with Modern Portfolio Theory Using Python MPT and some basic Python implementations for tracking risk, performance, and optimizing your portfolio. Portfolio Optimization in Python. A blog about Python for Finance, programming and web development. If you would like to post your code here I am happy to take a look. 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 Failing over with falling over. 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! 1- When calling the ‘calc_portfolio_std’ function in sco.minimize, where are the “weights” variables being passed on from? Then find a portfolio that maximizes returns based on the selected risk level. 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). How will the return calculations and the correlation matrix take this into account? 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. The values are then indeed recorded and once all portfolios have been simulated, the results are stored in and returned as a Pandas DataFrame. You can provide your own risk-aversion level and compute the appropriate portfolio. Below we visualise the results of all the simulated portfolios, plotting each portfolio by it’s corresponding values of annualised return (y-axis) and annualised volatility (x-axis), and also identify the 2 portfolios we are interested in. portfolio_performance() calculates the expected return, volatility and Sharpe ratio for the optimised portfolio. So there you have it, two approaches(Monte Carlo “brute force” and use of Scipy’s “minimize” function) to optimise a portfolio of stocks based on minimising different cost functions ( i.e. Convex optimization can be done in Python with libraries like cvxpy and CVXOPT, but Quantopian just recently announced their Optimize API for notebooks and the Optimize API for algorithms. data.head () data.info () By looking at the info () of data, it seems like the âdateâ column is already in datetime format. Some of key functionality that Riskfolio-Lib offers: 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. This is the famous Markovitz Portfolio. The main benefit of a CVaR optimization is that it can be implemented as a linear programming problem. This part of the code is exactly the same that I used in my previous article. The second function is pretty much analogous to the one used for the Sharpe optimisation with some slight changes to variable names, parameters and arguments passed of course. Hi, I have many difficulties to introduce the “Short” possibility. 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. Beginnerâs Guide to Portfolio Optimization with Python from Scratch. The weights of the resulting minimum VaR portfolio is as shown below. The python packages I've seen have had very scant documentation and only really implement the basic efficient frontier (which on it's own is not that useful IMO). 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. 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? Thank you so much for sharing it. We already saw in my previous article how to calculate portfolio returns and portfolio risk. Hi people, I write this post to share a portfolio optimization library that I developed for Python called Riskfolio-Lib. â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.â As algorithmic traders, our portfolio is made up of strategies or rules and each of these manages one or more instruments. I second Scott, it would be interesting to see a backtest of the various optimizations ð and may I aks you what matplotlib theme do you use? Great stuff so far! Our goal is to construct a portfolio from those 10 stocks with the following constraints: A portfolio is a vector w with the balances of each stock. I know currently there is no dollars involved in terms of portfolio amount, but this is the piece I am looking to add on. We then call the required function and store the results in a variable so we can then extract and visualise them. the Markowitz portfolio, which minimises risk for a given target return â this was the main focus of Markowitz 1952; Efficient risk: the Sharpe-maximising portfolio for a given target risk. Portfolio optimization is a mathematically intensive process that can be accomplished with a variety of optimization functions that are freely available in Python. @2019 - All Rights Reserved PythonForFinance.net, Investment Portfolio Optimisation with Python – Revisited, https://docs.scipy.org/doc/scipy/reference/optimize.html), investment portfolio optimisation with python, Time Series Decomposition & Prediction in Python. 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). Feel free to have a look at it! Portfolio optimization python github Posted on 09.06.2020 09.06.2020 GitHub is home to over 40 million developers working together to host and review code, manage projects, and â¦ 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. portfolio risk) of the portfolio. Featured on Meta When is a closeable question also a âvery low qualityâ question? 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…. Thanks. Now I want to show the daily simple returns which is... Optimize The Portfolioâ¦ Close’ values were missing (probably because I didn’t choose the correct ticker), which I then replaced using a simple Forward Fill. By looking into the DataFrame, we see that each row represents a different portfolio. If you like the content of the blog and want to support it, enroll in my latest Udemy course: Financial Analysis with Python – Analysing Balance Sheet. I know this question has been asked under a different article of yours, but I couldn’t find the answer yet. The goal according to this theory is to select a level of risk that an investor is comfortable with. The “fun” refers to the function defining the constraint, in our case the constraint that the sum of the stock weights must be 1. The risk free rate is required for the calculation of the Sharpe ratio and should be provided as an annualised rate. 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”). The higher of a return you want, the higher of a risk (variance) you will need to take on. 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. Impressive work! Some of key functionality that Riskfolio-Lib offers: the negative Sharpe ratio, the variance and the Value at Risk). 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. It would also be nice if you can update the code adding a constraint for minimum % holding position and a max % holding position. Now we quickly calculate the mean returns and co-variance matrix of our list of stocks, set the number of portfolios we wish to simulate and finally we set the desired value of the risk free rate. Below is the Sharpe ratio formula where Rp is the return of the portfolio. We start again by creating our two functions – but this time instead of one that returns portfolio return, volatility and Sharpe ratio, it returns the parametric portfolio VaR to a confidence level determined by the value of the “alpha” argument (confidence level will be 1 – alpha), and to a time scale determined by the “days” argument. Second, I wanted to know how difficult it would be to implement a \$ value of the capital and constrain it such that it has to chose funds with a minimum fund amount (i.e. Hi Scott, thanks for your comment. Letâs transform the data a little bit to make it easier to work with. Given a weight w of the portfolio, you can calculate the variance of the stocks by using the covariance matrix. 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. Utilize powerful Python optimization libraries to build scientifically and systematically diversified portfolios . (I understand the “panda-restrictions” about the “i.loc”.) In this post we will only show the code with minor explanations. The “type” can be either “eq” or “ineq” referring to “equality” or “inequality” respectively. save_weights_to_file() saves the weights to csv, json, or txt. This is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. Finally, we convert our list into Numpy arrays: Now that we have created 2000 random portfolios, we can visualize them using a Scatter plot in Matplotlib: In the graph, each point represents a portfolio. 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. I am not able to post a picture here so it might be difficult to illustrate, but basically my graph looks more like a circle with the different portfolio points. Everything runs fine except for the fact that my graph looks off and it doesn’t have the typical minimum variance frontier. 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). This includes quadratic programming as a special case for the risk-return optimization. So, the “min-VaR_port” calculation run without complains. ð. Follow. Sounds like a nice idea to run some historical comparisons of the differing portfolio suggestions, see if the reality bares out the same as the theory. In my experience, a VaR or CVaR portfolio optimization problem is usually best specified as minimizing the VaR or CVaR and then using a constraint for the expected return. In the calculation of the portfolio standard deviation, where do you factor the multiplication of the constant ‘2’ in the calculus? While convex optimization can be used for many purposes, I think we're best suited to use it in the algorithm for portfolio management. Once again we see the results are very close to those we were presented with when using the Monte Carlo approach, with the weights being within a couple of percent of each other. I think you are right, it seems there is a small mistake regarding the annualization of the returns. 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. 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. Anyway, I started from scratch, and got (not null) values for VaR (results_frame). random weights) and calculate the returns, risk and Sharpe Ratio for each of them. This helped me a lot. For example, row 1 contains a portfolio with 18% weight in NVS, 45% in AAPL, etc. For example, young investors may prefer to find portfolios maximizing expected return. Indra A. We will then show how you can create a simple backtest that rebalances its portfolio in a Markowitz-optimal way. This library allows to optimize portfolios using several criterions like variance, CVaR, CDaR, Omega ratio, risk parity, among others. I'm looking for advice as to what additional analyses or functions / features I should add. Again we see the results are very close to those we were presented with when using the Monte Carlo approach. This final VaR value has then been converted to an absolute value, as VaR is more often than not reported as a positive value (it also allows us to run the required “minimization” function when it is cast as a positive value). Thanks for the impressive work. When quoting the official docs or referring to the actual function itself I shall use a “z” to fall in line. The arguments we will provide are, the weights of the portfolio constituents, the mean daily return of each of those constituents (as calculated over the historic data that we downloaded earlier), the co-variance matrix of the constituents and finally the risk free interest rate. One of the most relevant theories on portfolio optimization was developed by Harry Markowitz. Lets begin with loading the modules. vanguard funds require minimum of \$3000). 5/31/2018 Written by DD. The construction of long-only, long/short and market neutral portfolios is supported. We need a new function that calculates and returns just the VaR of a portfolio, this is defined first. 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. If so, ping me a message here and I will send you my contact details to forward the data file on to. Iâm done creating the fictional portfolio. Thanks for the intellectually stimulating content. The method I have chosen to use for the VaR calculation is to scale the portfolio standard deviation by the square root of the “days” value, then subtract the scaled standard deviation, multiplied by the relevant “Z value” according to the chosen value of “alpha” from the portfolio daily mean returns which have been scaled linearly according to the “days” value. set_weights() creates self.weights (np.ndarray) from a weights dict; clean_weights() rounds the weights and clips near-zeros. Now let’s run the simulation function and plot the results again. In this post I am going to be looking at portfolio optimisation methods, touching on both the use of Monte Carlo, “brute force” style optimisation and then the use of Scipy’s “optimize” function for “minimizing (or maximizing) objective functions, possibly subject to constraints”, as it states in the official docs (https://docs.scipy.org/doc/scipy/reference/optimize.html). 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